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

Percentage Accurate: 75.0% → 91.5%

Time: 21.6s

Alternatives: 21

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.0% 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: 91.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t\_2}{t\_1 + \left(a + 1\right)}\\ t_4 := 1 + \left(a + t\_1\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_4} + \frac{y}{t \cdot t\_4}\right)\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{t\_2}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;y \cdot \frac{z}{t \cdot \mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (/ t_2 (+ t_1 (+ a 1.0))))
        (t_4 (+ 1.0 (+ a t_1))))
   (if (<= t_3 (- INFINITY))
     (* z (+ (/ x (* z t_4)) (/ y (* t t_4))))
     (if (<= t_3 2e+306)
       (/ t_2 (+ (* b (/ y t)) (+ a 1.0)))
       (if (<= t_3 INFINITY)
         (* y (/ z (* t (fma y (/ b t) (+ a 1.0)))))
         (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / (t_1 + (a + 1.0));
	double t_4 = 1.0 + (a + t_1);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = z * ((x / (z * t_4)) + (y / (t * t_4)));
	} else if (t_3 <= 2e+306) {
		tmp = t_2 / ((b * (y / t)) + (a + 1.0));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = y * (z / (t * fma(y, (b / t), (a + 1.0))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	t_3 = Float64(t_2 / Float64(t_1 + Float64(a + 1.0)))
	t_4 = Float64(1.0 + Float64(a + t_1))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_4)) + Float64(y / Float64(t * t_4))));
	elseif (t_3 <= 2e+306)
		tmp = Float64(t_2 / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	elseif (t_3 <= Inf)
		tmp = Float64(y * Float64(z / Float64(t * fma(y, Float64(b / t), Float64(a + 1.0)))));
	else
		tmp = Float64(z / b);
	end
	return 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[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(z * N[(N[(x / N[(z * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+306], N[(t$95$2 / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(y * N[(z / N[(t * N[(y * N[(b / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 50.5%

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

      1. associate-/l* 70.2%

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

      2. associate-/l* 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in z around inf 99.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000003e306

   1. Initial program 91.0%

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

      1. *-commutative 91.0%

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

      2. associate-/l* 91.8%

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

   4. Applied egg-rr 91.8%

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

   if 2.00000000000000003e306 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 18.1%

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

      1. associate-/l* 40.7%

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

      2. associate-/l* 40.7%

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

   3. Simplified 40.7%

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

   5. Taylor expanded in x around 0 53.5%

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

      1. associate-/l* 99.4%

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

      2. associate-+r+ 99.4%

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

      3. associate-*r/ 62.9%

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

      4. *-commutative 62.9%

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

      5. associate-/r/ 99.4%

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

      6. +-commutative 99.4%

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

      7. associate-/r/ 62.9%

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

      8. *-commutative 62.9%

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

      9. associate-*r/ 99.4%

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

      10. associate-*l/ 99.4%

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

      11. *-commutative 99.4%

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

      12. fma-define 99.4%

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

   7. Simplified 99.4%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.0%

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

      2. associate-/l* 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in y around inf 100.0%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;y \cdot \frac{z}{t \cdot \mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := 1 + \left(a + t\_1\right)\\ t_3 := x + \frac{y \cdot z}{t}\\ t_4 := \frac{t\_3}{t\_1 + \left(a + 1\right)}\\ t_5 := z \cdot \left(\frac{x}{z \cdot t\_2} + \frac{y}{t \cdot t\_2}\right)\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{+197}:\\ \;\;\;\;\frac{t\_3}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ 1.0 (+ a t_1)))
        (t_3 (+ x (/ (* y z) t)))
        (t_4 (/ t_3 (+ t_1 (+ a 1.0))))
        (t_5 (* z (+ (/ x (* z t_2)) (/ y (* t t_2))))))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 5e+197)
       (/ t_3 (+ (* b (/ y t)) (+ a 1.0)))
       (if (<= t_4 INFINITY) t_5 (/ 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 = 1.0 + (a + t_1);
	double t_3 = x + ((y * z) / t);
	double t_4 = t_3 / (t_1 + (a + 1.0));
	double t_5 = z * ((x / (z * t_2)) + (y / (t * t_2)));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= 5e+197) {
		tmp = t_3 / ((b * (y / t)) + (a + 1.0));
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} 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 = 1.0 + (a + t_1);
	double t_3 = x + ((y * z) / t);
	double t_4 = t_3 / (t_1 + (a + 1.0));
	double t_5 = z * ((x / (z * t_2)) + (y / (t * t_2)));
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else if (t_4 <= 5e+197) {
		tmp = t_3 / ((b * (y / t)) + (a + 1.0));
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = 1.0 + (a + t_1)
	t_3 = x + ((y * z) / t)
	t_4 = t_3 / (t_1 + (a + 1.0))
	t_5 = z * ((x / (z * t_2)) + (y / (t * t_2)))
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_5
	elif t_4 <= 5e+197:
		tmp = t_3 / ((b * (y / t)) + (a + 1.0))
	elif t_4 <= math.inf:
		tmp = t_5
	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(1.0 + Float64(a + t_1))
	t_3 = Float64(x + Float64(Float64(y * z) / t))
	t_4 = Float64(t_3 / Float64(t_1 + Float64(a + 1.0)))
	t_5 = Float64(z * Float64(Float64(x / Float64(z * t_2)) + Float64(y / Float64(t * t_2))))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= 5e+197)
		tmp = Float64(t_3 / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	elseif (t_4 <= Inf)
		tmp = t_5;
	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 = 1.0 + (a + t_1);
	t_3 = x + ((y * z) / t);
	t_4 = t_3 / (t_1 + (a + 1.0));
	t_5 = z * ((x / (z * t_2)) + (y / (t * t_2)));
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_5;
	elseif (t_4 <= 5e+197)
		tmp = t_3 / ((b * (y / t)) + (a + 1.0));
	elseif (t_4 <= Inf)
		tmp = t_5;
	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[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(z * N[(N[(x / N[(z * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, 5e+197], N[(t$95$3 / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$5, N[(z / b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0 or 5.00000000000000009e197 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 55.6%

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

      1. associate-/l* 63.6%

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

      2. associate-/l* 63.6%

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

   3. Simplified 63.6%

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

   5. Taylor expanded in z around inf 99.6%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.00000000000000009e197

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-/l* 91.4%

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

   4. Applied egg-rr 91.4%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.0%

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

      2. associate-/l* 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in y around inf 100.0%

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

4. Final simplification 93.1%

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

Alternative 3: 88.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-186}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-180}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0))) (t_2 (/ (+ x (/ (* y z) t)) t_1)))
   (if (<= t_2 -4e-186)
     (/ (+ x (* z (/ y t))) t_1)
     (if (<= t_2 2e-180)
       (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
       (if (<= t_2 2e+306) t_2 (/ (+ z (/ (* x t) y)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -4e-186) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_2 <= 2e-180) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((y * b) / t) + (a + 1.0d0)
    t_2 = (x + ((y * z) / t)) / t_1
    if (t_2 <= (-4d-186)) then
        tmp = (x + (z * (y / t))) / t_1
    else if (t_2 <= 2d-180) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else if (t_2 <= 2d+306) then
        tmp = t_2
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -4e-186) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_2 <= 2e-180) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * b) / t) + (a + 1.0)
	t_2 = (x + ((y * z) / t)) / t_1
	tmp = 0
	if t_2 <= -4e-186:
		tmp = (x + (z * (y / t))) / t_1
	elif t_2 <= 2e-180:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	elif t_2 <= 2e+306:
		tmp = t_2
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_2 <= -4e-186)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	elseif (t_2 <= 2e-180)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * b) / t) + (a + 1.0);
	t_2 = (x + ((y * z) / t)) / t_1;
	tmp = 0.0;
	if (t_2 <= -4e-186)
		tmp = (x + (z * (y / t))) / t_1;
	elseif (t_2 <= 2e-180)
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-186], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 2e-180], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+306], t$95$2, N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -3.9999999999999996e-186

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-/l* 92.2%

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

   4. Applied egg-rr 92.2%

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

   if -3.9999999999999996e-186 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2e-180

   1. Initial program 68.4%

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

      1. associate-/l* 71.5%

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

      2. associate-/l* 81.0%

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

   3. Simplified 81.0%

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

   if 2e-180 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000003e306

   1. Initial program 99.6%

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

   if 2.00000000000000003e306 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 6.0%

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

      1. associate-/l* 13.6%

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

      2. associate-/l* 13.6%

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

   3. Simplified 13.6%

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

   5. Taylor expanded in y around inf 58.8%

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

      1. associate-/l* 58.8%

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

      2. associate-/r* 58.8%

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

      3. associate-/l* 58.8%

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

      4. associate-/l* 70.9%

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

      5. *-commutative 70.9%

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

   7. Simplified 70.9%

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

   8. Taylor expanded in b around inf 75.7%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -4 \cdot 10^{-186}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{-180}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a}\\ t_2 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -3.25 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8.3 \cdot 10^{-156}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-158}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-64}:\\ \;\;\;\;\frac{x \cdot t}{t + y \cdot b}\\ \mathbf{elif}\;a \leq 1.9:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) a)) (t_2 (+ x (/ (* y z) t))))
   (if (<= a -3.25e+44)
     t_1
     (if (<= a -8.3e-156)
       (/ z b)
       (if (<= a 3.1e-158)
         t_2
         (if (<= a 1.85e-64)
           (/ (* x t) (+ t (* y b)))
           (if (<= a 1.9) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / a;
	double t_2 = x + ((y * z) / t);
	double tmp;
	if (a <= -3.25e+44) {
		tmp = t_1;
	} else if (a <= -8.3e-156) {
		tmp = z / b;
	} else if (a <= 3.1e-158) {
		tmp = t_2;
	} else if (a <= 1.85e-64) {
		tmp = (x * t) / (t + (y * b));
	} else if (a <= 1.9) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / a
    t_2 = x + ((y * z) / t)
    if (a <= (-3.25d+44)) then
        tmp = t_1
    else if (a <= (-8.3d-156)) then
        tmp = z / b
    else if (a <= 3.1d-158) then
        tmp = t_2
    else if (a <= 1.85d-64) then
        tmp = (x * t) / (t + (y * b))
    else if (a <= 1.9d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / a;
	double t_2 = x + ((y * z) / t);
	double tmp;
	if (a <= -3.25e+44) {
		tmp = t_1;
	} else if (a <= -8.3e-156) {
		tmp = z / b;
	} else if (a <= 3.1e-158) {
		tmp = t_2;
	} else if (a <= 1.85e-64) {
		tmp = (x * t) / (t + (y * b));
	} else if (a <= 1.9) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / a
	t_2 = x + ((y * z) / t)
	tmp = 0
	if a <= -3.25e+44:
		tmp = t_1
	elif a <= -8.3e-156:
		tmp = z / b
	elif a <= 3.1e-158:
		tmp = t_2
	elif a <= 1.85e-64:
		tmp = (x * t) / (t + (y * b))
	elif a <= 1.9:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / a)
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (a <= -3.25e+44)
		tmp = t_1;
	elseif (a <= -8.3e-156)
		tmp = Float64(z / b);
	elseif (a <= 3.1e-158)
		tmp = t_2;
	elseif (a <= 1.85e-64)
		tmp = Float64(Float64(x * t) / Float64(t + Float64(y * b)));
	elseif (a <= 1.9)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / a;
	t_2 = x + ((y * z) / t);
	tmp = 0.0;
	if (a <= -3.25e+44)
		tmp = t_1;
	elseif (a <= -8.3e-156)
		tmp = z / b;
	elseif (a <= 3.1e-158)
		tmp = t_2;
	elseif (a <= 1.85e-64)
		tmp = (x * t) / (t + (y * b));
	elseif (a <= 1.9)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.25e+44], t$95$1, If[LessEqual[a, -8.3e-156], N[(z / b), $MachinePrecision], If[LessEqual[a, 3.1e-158], t$95$2, If[LessEqual[a, 1.85e-64], N[(N[(x * t), $MachinePrecision] / N[(t + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.25000000000000009e44 or 1.8999999999999999 < a

   1. Initial program 82.9%

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

      1. associate-/l* 78.1%

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

      2. associate-/l* 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in a around inf 68.2%

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

   if -3.25000000000000009e44 < a < -8.29999999999999993e-156

   1. Initial program 72.5%

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

      1. associate-/l* 67.4%

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

      2. associate-/l* 62.4%

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

   3. Simplified 62.4%

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

   5. Taylor expanded in y around inf 45.4%

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

   if -8.29999999999999993e-156 < a < 3.10000000000000018e-158 or 1.84999999999999999e-64 < a < 1.8999999999999999

   1. Initial program 77.6%

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

      1. associate-/l* 76.5%

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

      2. associate-/l* 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in b around 0 59.9%

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

   6. Taylor expanded in a around 0 59.3%

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

   if 3.10000000000000018e-158 < a < 1.84999999999999999e-64

   1. Initial program 91.5%

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

      1. associate-/l* 91.5%

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

      2. associate-/l* 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in t around 0 91.6%

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

   6. Taylor expanded in x around inf 75.6%

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

   7. Taylor expanded in a around 0 75.6%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.25 \cdot 10^{+44}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a \leq -8.3 \cdot 10^{-156}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-158}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-64}:\\ \;\;\;\;\frac{x \cdot t}{t + y \cdot b}\\ \mathbf{elif}\;a \leq 1.9:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{a}\\ \mathbf{if}\;a \leq -6.4 \cdot 10^{+44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-156}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-58}:\\ \;\;\;\;\frac{x \cdot t}{t + y \cdot b}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))) (t_2 (/ t_1 a)))
   (if (<= a -6.4e+44)
     t_2
     (if (<= a -4.3e-156)
       (/ z b)
       (if (<= a 9.8e-158)
         t_1
         (if (<= a 2.95e-58)
           (/ (* x t) (+ t (* y b)))
           (if (<= a 1.0) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / a;
	double tmp;
	if (a <= -6.4e+44) {
		tmp = t_2;
	} else if (a <= -4.3e-156) {
		tmp = z / b;
	} else if (a <= 9.8e-158) {
		tmp = t_1;
	} else if (a <= 2.95e-58) {
		tmp = (x * t) / (t + (y * b));
	} else if (a <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    t_2 = t_1 / a
    if (a <= (-6.4d+44)) then
        tmp = t_2
    else if (a <= (-4.3d-156)) then
        tmp = z / b
    else if (a <= 9.8d-158) then
        tmp = t_1
    else if (a <= 2.95d-58) then
        tmp = (x * t) / (t + (y * b))
    else if (a <= 1.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / a;
	double tmp;
	if (a <= -6.4e+44) {
		tmp = t_2;
	} else if (a <= -4.3e-156) {
		tmp = z / b;
	} else if (a <= 9.8e-158) {
		tmp = t_1;
	} else if (a <= 2.95e-58) {
		tmp = (x * t) / (t + (y * b));
	} else if (a <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / a
	tmp = 0
	if a <= -6.4e+44:
		tmp = t_2
	elif a <= -4.3e-156:
		tmp = z / b
	elif a <= 9.8e-158:
		tmp = t_1
	elif a <= 2.95e-58:
		tmp = (x * t) / (t + (y * b))
	elif a <= 1.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / a)
	tmp = 0.0
	if (a <= -6.4e+44)
		tmp = t_2;
	elseif (a <= -4.3e-156)
		tmp = Float64(z / b);
	elseif (a <= 9.8e-158)
		tmp = t_1;
	elseif (a <= 2.95e-58)
		tmp = Float64(Float64(x * t) / Float64(t + Float64(y * b)));
	elseif (a <= 1.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = t_1 / a;
	tmp = 0.0;
	if (a <= -6.4e+44)
		tmp = t_2;
	elseif (a <= -4.3e-156)
		tmp = z / b;
	elseif (a <= 9.8e-158)
		tmp = t_1;
	elseif (a <= 2.95e-58)
		tmp = (x * t) / (t + (y * b));
	elseif (a <= 1.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / a), $MachinePrecision]}, If[LessEqual[a, -6.4e+44], t$95$2, If[LessEqual[a, -4.3e-156], N[(z / b), $MachinePrecision], If[LessEqual[a, 9.8e-158], t$95$1, If[LessEqual[a, 2.95e-58], N[(N[(x * t), $MachinePrecision] / N[(t + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.40000000000000009e44 or 1 < a

   1. Initial program 82.9%

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

      1. associate-/l* 78.1%

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

      2. associate-/l* 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in a around inf 71.3%

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

   if -6.40000000000000009e44 < a < -4.29999999999999977e-156

   1. Initial program 72.5%

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

      1. associate-/l* 67.4%

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

      2. associate-/l* 62.4%

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

   3. Simplified 62.4%

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

   5. Taylor expanded in y around inf 45.4%

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

   if -4.29999999999999977e-156 < a < 9.79999999999999986e-158 or 2.95e-58 < a < 1

   1. Initial program 77.6%

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

      1. associate-/l* 76.5%

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

      2. associate-/l* 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in b around 0 59.9%

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

   6. Taylor expanded in a around 0 59.3%

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

   if 9.79999999999999986e-158 < a < 2.95e-58

   1. Initial program 91.5%

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

      1. associate-/l* 91.5%

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

      2. associate-/l* 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in t around 0 91.6%

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

   6. Taylor expanded in x around inf 75.6%

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

   7. Taylor expanded in a around 0 75.6%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{+44}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-156}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-158}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-58}:\\ \;\;\;\;\frac{x \cdot t}{t + y \cdot b}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{-136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-273}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))))
   (if (<= t -3.3e-136)
     t_1
     (if (<= t -2.6e-273)
       (/ (+ x (* z (/ y t))) (+ (/ (* y b) t) (+ a 1.0)))
       (if (<= t 6e-211) (/ (* y z) (+ (* y b) (* t (+ a 1.0)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -3.3e-136) {
		tmp = t_1;
	} else if (t <= -2.6e-273) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else if (t <= 6e-211) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    if (t <= (-3.3d-136)) then
        tmp = t_1
    else if (t <= (-2.6d-273)) then
        tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0d0))
    else if (t <= 6d-211) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -3.3e-136) {
		tmp = t_1;
	} else if (t <= -2.6e-273) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else if (t <= 6e-211) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	tmp = 0
	if t <= -3.3e-136:
		tmp = t_1
	elif t <= -2.6e-273:
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0))
	elif t <= 6e-211:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))))
	tmp = 0.0
	if (t <= -3.3e-136)
		tmp = t_1;
	elseif (t <= -2.6e-273)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	elseif (t <= 6e-211)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	tmp = 0.0;
	if (t <= -3.3e-136)
		tmp = t_1;
	elseif (t <= -2.6e-273)
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	elseif (t <= 6e-211)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e-136], t$95$1, If[LessEqual[t, -2.6e-273], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-211], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.30000000000000018e-136 or 6.00000000000000009e-211 < t

   1. Initial program 83.2%

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

      1. associate-/l* 85.6%

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

      2. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   if -3.30000000000000018e-136 < t < -2.59999999999999983e-273

   1. Initial program 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-/l* 78.0%

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

   4. Applied egg-rr 78.0%

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

   if -2.59999999999999983e-273 < t < 6.00000000000000009e-211

   1. Initial program 65.5%

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

      1. associate-/l* 47.0%

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

      2. associate-/l* 43.4%

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

   3. Simplified 43.4%

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

   5. Taylor expanded in t around 0 47.0%

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

   6. Taylor expanded in x around 0 92.5%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-136}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-273}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-273}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-213}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y (/ t z))) (+ (+ a 1.0) (* y (/ b t))))))
   (if (<= t -7.5e-139)
     t_1
     (if (<= t -2.4e-273)
       (/ (+ x (* z (/ y t))) (+ (/ (* y b) t) (+ a 1.0)))
       (if (<= t 2.4e-213) (/ (* y z) (+ (* y b) (* t (+ a 1.0)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -7.5e-139) {
		tmp = t_1;
	} else if (t <= -2.4e-273) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else if (t <= 2.4e-213) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / (t / z))) / ((a + 1.0d0) + (y * (b / t)))
    if (t <= (-7.5d-139)) then
        tmp = t_1
    else if (t <= (-2.4d-273)) then
        tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0d0))
    else if (t <= 2.4d-213) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -7.5e-139) {
		tmp = t_1;
	} else if (t <= -2.4e-273) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else if (t <= 2.4e-213) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)))
	tmp = 0
	if t <= -7.5e-139:
		tmp = t_1
	elif t <= -2.4e-273:
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0))
	elif t <= 2.4e-213:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))))
	tmp = 0.0
	if (t <= -7.5e-139)
		tmp = t_1;
	elseif (t <= -2.4e-273)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	elseif (t <= 2.4e-213)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	tmp = 0.0;
	if (t <= -7.5e-139)
		tmp = t_1;
	elseif (t <= -2.4e-273)
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	elseif (t <= 2.4e-213)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e-139], t$95$1, If[LessEqual[t, -2.4e-273], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-213], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.5000000000000001e-139 or 2.39999999999999996e-213 < t

   1. Initial program 83.2%

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

      1. associate-/l* 85.6%

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

      2. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

      1. clear-num 87.6%

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

      2. un-div-inv 87.7%

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

   6. Applied egg-rr 87.7%

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

   if -7.5000000000000001e-139 < t < -2.39999999999999982e-273

   1. Initial program 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-/l* 78.0%

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

   4. Applied egg-rr 78.0%

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

   if -2.39999999999999982e-273 < t < 2.39999999999999996e-213

   1. Initial program 65.5%

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

      1. associate-/l* 47.0%

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

      2. associate-/l* 43.4%

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

   3. Simplified 43.4%

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

   5. Taylor expanded in t around 0 47.0%

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

   6. Taylor expanded in x around 0 92.5%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-139}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-273}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-213}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-142}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -1.82 \cdot 10^{-273}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.7e-142)
   (/ (+ x (/ y (/ t z))) (+ (+ a 1.0) (* y (/ b t))))
   (if (<= t -1.82e-273)
     (/ (+ x (* z (/ y t))) (+ (/ (* y b) t) (+ a 1.0)))
     (if (<= t 5.2e-211)
       (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
       (/ (+ x (/ (* y z) t)) (+ (* b (/ y t)) (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.7e-142) {
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	} else if (t <= -1.82e-273) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else if (t <= 5.2e-211) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = (x + ((y * z) / t)) / ((b * (y / t)) + (a + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.7d-142)) then
        tmp = (x + (y / (t / z))) / ((a + 1.0d0) + (y * (b / t)))
    else if (t <= (-1.82d-273)) then
        tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0d0))
    else if (t <= 5.2d-211) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else
        tmp = (x + ((y * z) / t)) / ((b * (y / t)) + (a + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.7e-142) {
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	} else if (t <= -1.82e-273) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else if (t <= 5.2e-211) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = (x + ((y * z) / t)) / ((b * (y / t)) + (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.7e-142:
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)))
	elif t <= -1.82e-273:
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0))
	elif t <= 5.2e-211:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	else:
		tmp = (x + ((y * z) / t)) / ((b * (y / t)) + (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.7e-142)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t <= -1.82e-273)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	elseif (t <= 5.2e-211)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.7e-142)
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	elseif (t <= -1.82e-273)
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	elseif (t <= 5.2e-211)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	else
		tmp = (x + ((y * z) / t)) / ((b * (y / t)) + (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.7e-142], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.82e-273], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-211], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.6999999999999999e-142

   1. Initial program 75.5%

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

      1. associate-/l* 77.4%

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

      2. associate-/l* 81.5%

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

   3. Simplified 81.5%

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

      1. clear-num 81.5%

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

      2. un-div-inv 81.8%

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

   6. Applied egg-rr 81.8%

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

   if -4.6999999999999999e-142 < t < -1.81999999999999997e-273

   1. Initial program 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-/l* 78.0%

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

   4. Applied egg-rr 78.0%

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

   if -1.81999999999999997e-273 < t < 5.2e-211

   1. Initial program 65.5%

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

      1. associate-/l* 47.0%

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

      2. associate-/l* 43.4%

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

   3. Simplified 43.4%

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

   5. Taylor expanded in t around 0 47.0%

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

   6. Taylor expanded in x around 0 92.5%

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

   if 5.2e-211 < t

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

      2. associate-/l* 93.6%

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

   4. Applied egg-rr 93.6%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-142}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -1.82 \cdot 10^{-273}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+75}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \frac{x}{t + y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -6.2e+24)
     t_1
     (if (<= t 1.1e-16)
       (/ (+ z (/ (* x t) y)) b)
       (if (<= t 1.1e+75)
         (/ (+ x (* y (/ z t))) a)
         (if (<= t 5e+132) (* t (/ x (+ t (* y b)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -6.2e+24) {
		tmp = t_1;
	} else if (t <= 1.1e-16) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 1.1e+75) {
		tmp = (x + (y * (z / t))) / a;
	} else if (t <= 5e+132) {
		tmp = t * (x / (t + (y * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-6.2d+24)) then
        tmp = t_1
    else if (t <= 1.1d-16) then
        tmp = (z + ((x * t) / y)) / b
    else if (t <= 1.1d+75) then
        tmp = (x + (y * (z / t))) / a
    else if (t <= 5d+132) then
        tmp = t * (x / (t + (y * b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -6.2e+24) {
		tmp = t_1;
	} else if (t <= 1.1e-16) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 1.1e+75) {
		tmp = (x + (y * (z / t))) / a;
	} else if (t <= 5e+132) {
		tmp = t * (x / (t + (y * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -6.2e+24:
		tmp = t_1
	elif t <= 1.1e-16:
		tmp = (z + ((x * t) / y)) / b
	elif t <= 1.1e+75:
		tmp = (x + (y * (z / t))) / a
	elif t <= 5e+132:
		tmp = t * (x / (t + (y * b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -6.2e+24)
		tmp = t_1;
	elseif (t <= 1.1e-16)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (t <= 1.1e+75)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / a);
	elseif (t <= 5e+132)
		tmp = Float64(t * Float64(x / Float64(t + Float64(y * b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -6.2e+24)
		tmp = t_1;
	elseif (t <= 1.1e-16)
		tmp = (z + ((x * t) / y)) / b;
	elseif (t <= 1.1e+75)
		tmp = (x + (y * (z / t))) / a;
	elseif (t <= 5e+132)
		tmp = t * (x / (t + (y * b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e+24], t$95$1, If[LessEqual[t, 1.1e-16], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t, 1.1e+75], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 5e+132], N[(t * N[(x / N[(t + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.20000000000000022e24 or 5.0000000000000001e132 < t

   1. Initial program 88.3%

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

      1. associate-/l* 92.1%

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

      2. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in y around 0 68.6%

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

   if -6.20000000000000022e24 < t < 1.1e-16

   1. Initial program 71.9%

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

      1. associate-/l* 61.3%

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

      2. associate-/l* 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in y around inf 45.8%

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

      1. associate-/l* 45.1%

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

      2. associate-/r* 46.4%

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

      3. associate-/l* 45.8%

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

      4. associate-/l* 48.0%

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

      5. *-commutative 48.0%

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

   7. Simplified 48.0%

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

   8. Taylor expanded in b around inf 57.7%

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

   if 1.1e-16 < t < 1.10000000000000006e75

   1. Initial program 91.1%

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

      1. associate-/l* 99.7%

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

      2. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around inf 78.4%

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

   if 1.10000000000000006e75 < t < 5.0000000000000001e132

   1. Initial program 93.0%

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

      1. associate-/l* 99.8%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 93.2%

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

   6. Taylor expanded in x around inf 72.5%

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

   7. Taylor expanded in a around 0 65.1%

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

      1. associate-/l* 65.5%

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

      2. *-commutative 65.5%

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

   9. Simplified 65.5%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+75}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \frac{x}{t + y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 79.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-159} \lor \neg \left(t \leq 1.55 \cdot 10^{-211}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -9.5e-159) (not (<= t 1.55e-211)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (/ (* y z) (+ (* y b) (* t (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9.5e-159) || !(t <= 1.55e-211)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (y * z) / ((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) :: tmp
    if ((t <= (-9.5d-159)) .or. (.not. (t <= 1.55d-211))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = (y * z) / ((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 tmp;
	if ((t <= -9.5e-159) || !(t <= 1.55e-211)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -9.5e-159) or not (t <= 1.55e-211):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -9.5e-159) || !(t <= 1.55e-211))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -9.5e-159) || ~((t <= 1.55e-211)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	else
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -9.5e-159], N[Not[LessEqual[t, 1.55e-211]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.4999999999999997e-159 or 1.54999999999999998e-211 < t

   1. Initial program 83.8%

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

      1. associate-/l* 85.7%

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

      2. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   if -9.4999999999999997e-159 < t < 1.54999999999999998e-211

   1. Initial program 67.2%

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

      1. associate-/l* 46.2%

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

      2. associate-/l* 39.4%

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

   3. Simplified 39.4%

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

   5. Taylor expanded in t around 0 46.1%

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

   6. Taylor expanded in x around 0 76.5%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-159} \lor \neg \left(t \leq 1.55 \cdot 10^{-211}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 3.105 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \frac{\frac{z}{a + 1}}{t}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= y -2.7e+14)
     (/ z b)
     (if (<= y 3.105e-135)
       t_1
       (if (<= y 6.4e-16)
         (* y (/ (/ z (+ a 1.0)) t))
         (if (<= y 4.5e+121) t_1 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (y <= -2.7e+14) {
		tmp = z / b;
	} else if (y <= 3.105e-135) {
		tmp = t_1;
	} else if (y <= 6.4e-16) {
		tmp = y * ((z / (a + 1.0)) / t);
	} else if (y <= 4.5e+121) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (y <= (-2.7d+14)) then
        tmp = z / b
    else if (y <= 3.105d-135) then
        tmp = t_1
    else if (y <= 6.4d-16) then
        tmp = y * ((z / (a + 1.0d0)) / t)
    else if (y <= 4.5d+121) then
        tmp = t_1
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (y <= -2.7e+14) {
		tmp = z / b;
	} else if (y <= 3.105e-135) {
		tmp = t_1;
	} else if (y <= 6.4e-16) {
		tmp = y * ((z / (a + 1.0)) / t);
	} else if (y <= 4.5e+121) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if y <= -2.7e+14:
		tmp = z / b
	elif y <= 3.105e-135:
		tmp = t_1
	elif y <= 6.4e-16:
		tmp = y * ((z / (a + 1.0)) / t)
	elif y <= 4.5e+121:
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (y <= -2.7e+14)
		tmp = Float64(z / b);
	elseif (y <= 3.105e-135)
		tmp = t_1;
	elseif (y <= 6.4e-16)
		tmp = Float64(y * Float64(Float64(z / Float64(a + 1.0)) / t));
	elseif (y <= 4.5e+121)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (y <= -2.7e+14)
		tmp = z / b;
	elseif (y <= 3.105e-135)
		tmp = t_1;
	elseif (y <= 6.4e-16)
		tmp = y * ((z / (a + 1.0)) / t);
	elseif (y <= 4.5e+121)
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+14], N[(z / b), $MachinePrecision], If[LessEqual[y, 3.105e-135], t$95$1, If[LessEqual[y, 6.4e-16], N[(y * N[(N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+121], t$95$1, N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e14 or 4.5000000000000003e121 < y

   1. Initial program 55.9%

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

      1. associate-/l* 61.6%

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

      2. associate-/l* 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in y around inf 53.6%

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

   if -2.7e14 < y < 3.1049999999999998e-135 or 6.40000000000000046e-16 < y < 4.5000000000000003e121

   1. Initial program 95.0%

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

      1. associate-/l* 85.5%

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

      2. associate-/l* 80.6%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in y around 0 63.5%

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

   if 3.1049999999999998e-135 < y < 6.40000000000000046e-16

   1. Initial program 94.3%

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

      1. *-commutative 94.3%

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

      2. associate-/l* 94.2%

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

   4. Applied egg-rr 94.2%

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

   5. Taylor expanded in x around 0 56.4%

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

   6. Taylor expanded in y around 0 50.9%

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

      1. associate-/l* 50.8%

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

   8. Simplified 50.8%

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

      1. *-un-lft-identity 50.8%

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

      2. times-frac 56.0%

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

   10. Applied egg-rr 56.0%

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

       1. associate-*l/ 55.9%

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

       2. *-lft-identity 55.9%

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

   12. Simplified 55.9%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 3.105 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \frac{\frac{z}{a + 1}}{t}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+121}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+24} \lor \neg \left(t \leq 6 \cdot 10^{-211}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.05e+24) (not (<= t 6e-211)))
   (/ x (+ 1.0 (+ a (/ (* y b) t))))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.05e+24) || !(t <= 6e-211)) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.05d+24)) .or. (.not. (t <= 6d-211))) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.05e+24) || !(t <= 6e-211)) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.05e+24) or not (t <= 6e-211):
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.05e+24) || !(t <= 6e-211))
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.05e+24) || ~((t <= 6e-211)))
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.05e+24], N[Not[LessEqual[t, 6e-211]], $MachinePrecision]], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.05e24 or 6.00000000000000009e-211 < t

   1. Initial program 89.0%

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

      1. associate-/l* 92.7%

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

      2. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in x around inf 72.5%

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

   if -2.05e24 < t < 6.00000000000000009e-211

   1. Initial program 67.7%

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

      1. associate-/l* 54.5%

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

      2. associate-/l* 50.8%

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

   3. Simplified 50.8%

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

   5. Taylor expanded in y around inf 44.2%

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

      1. associate-/l* 43.3%

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

      2. associate-/r* 45.1%

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

      3. associate-/l* 44.2%

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

      4. associate-/l* 46.1%

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

      5. *-commutative 46.1%

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

   7. Simplified 46.1%

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

   8. Taylor expanded in b around inf 58.9%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+24} \lor \neg \left(t \leq 6 \cdot 10^{-211}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+112} \lor \neg \left(y \leq 6 \cdot 10^{+121}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.15e+112) (not (<= y 6e+121)))
   (/ (+ z (/ (* x t) y)) b)
   (/ (+ x (/ (* y z) t)) (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.15e+112) || !(y <= 6e+121)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.15d+112)) .or. (.not. (y <= 6d+121))) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.15e+112) || !(y <= 6e+121)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.15e+112) or not (y <= 6e+121):
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.15e+112) || !(y <= 6e+121))
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.15e+112) || ~((y <= 6e+121)))
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.15e+112], N[Not[LessEqual[y, 6e+121]], $MachinePrecision]], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.14999999999999991e112 or 6.0000000000000005e121 < y

   1. Initial program 53.1%

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

      1. associate-/l* 60.1%

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

      2. associate-/l* 67.4%

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

   3. Simplified 67.4%

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

   5. Taylor expanded in y around inf 43.3%

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

      1. associate-/l* 47.0%

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

      2. associate-/r* 51.7%

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

      3. associate-/l* 53.4%

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

      4. associate-/l* 57.1%

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

      5. *-commutative 57.1%

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

   7. Simplified 57.1%

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

   8. Taylor expanded in b around inf 61.4%

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

   if -2.14999999999999991e112 < y < 6.0000000000000005e121

   1. Initial program 92.2%

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

      1. associate-/l* 84.1%

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

      2. associate-/l* 80.6%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in b around 0 74.8%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+112} \lor \neg \left(y \leq 6 \cdot 10^{+121}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 69.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+111} \lor \neg \left(y \leq 5.2 \cdot 10^{+121}\right):\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.2e+111) (not (<= y 5.2e+121)))
   (/ (+ z (* x (/ t y))) b)
   (/ (+ x (/ (* y z) t)) (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.2e+111) || !(y <= 5.2e+121)) {
		tmp = (z + (x * (t / y))) / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-6.2d+111)) .or. (.not. (y <= 5.2d+121))) then
        tmp = (z + (x * (t / y))) / b
    else
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.2e+111) || !(y <= 5.2e+121)) {
		tmp = (z + (x * (t / y))) / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.2e+111) or not (y <= 5.2e+121):
		tmp = (z + (x * (t / y))) / b
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.2e+111) || !(y <= 5.2e+121))
		tmp = Float64(Float64(z + Float64(x * Float64(t / y))) / b);
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.2e+111) || ~((y <= 5.2e+121)))
		tmp = (z + (x * (t / y))) / b;
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.2e+111], N[Not[LessEqual[y, 5.2e+121]], $MachinePrecision]], N[(N[(z + N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2000000000000001e111 or 5.1999999999999998e121 < y

   1. Initial program 53.1%

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

      1. associate-/l* 60.1%

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

      2. associate-/l* 67.4%

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

   3. Simplified 67.4%

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

   5. Taylor expanded in y around inf 43.3%

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

      1. associate-/l* 47.0%

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

      2. associate-/r* 51.7%

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

      3. associate-/l* 53.4%

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

      4. associate-/l* 57.1%

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

      5. *-commutative 57.1%

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

   7. Simplified 57.1%

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

   8. Taylor expanded in b around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. *-un-lft-identity 61.4%

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

      3. times-frac 68.7%

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

   10. Applied egg-rr 68.7%

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

   if -6.2000000000000001e111 < y < 5.1999999999999998e121

   1. Initial program 92.2%

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

      1. associate-/l* 84.1%

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

      2. associate-/l* 80.6%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in b around 0 74.8%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+111} \lor \neg \left(y \leq 5.2 \cdot 10^{+121}\right):\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-211}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.05e+24)
   (/ x (+ (+ a 1.0) (* y (/ b t))))
   (if (<= t 6e-211)
     (/ (+ z (/ (* x t) y)) b)
     (/ x (+ 1.0 (+ a (/ (* y b) t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.05e+24) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else if (t <= 6e-211) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.05d+24)) then
        tmp = x / ((a + 1.0d0) + (y * (b / t)))
    else if (t <= 6d-211) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.05e+24) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else if (t <= 6e-211) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.05e+24:
		tmp = x / ((a + 1.0) + (y * (b / t)))
	elif t <= 6e-211:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.05e+24)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t <= 6e-211)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.05e+24)
		tmp = x / ((a + 1.0) + (y * (b / t)));
	elseif (t <= 6e-211)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = x / (1.0 + (a + ((y * b) / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.05e+24], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-211], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.05e24

   1. Initial program 85.6%

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

      1. *-commutative 85.6%

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

      2. associate-/l* 92.8%

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

   4. Applied egg-rr 92.8%

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

   5. Taylor expanded in x around inf 71.7%

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

      1. associate-+r+ 71.7%

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

      2. *-commutative 71.7%

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

      3. associate-/l* 75.4%

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

   7. Simplified 75.4%

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

   if -2.05e24 < t < 6.00000000000000009e-211

   1. Initial program 67.7%

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

      1. associate-/l* 54.5%

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

      2. associate-/l* 50.8%

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

   3. Simplified 50.8%

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

   5. Taylor expanded in y around inf 44.2%

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

      1. associate-/l* 43.3%

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

      2. associate-/r* 45.1%

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

      3. associate-/l* 44.2%

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

      4. associate-/l* 46.1%

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

      5. *-commutative 46.1%

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

   7. Simplified 46.1%

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

   8. Taylor expanded in b around inf 58.9%

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

   if 6.00000000000000009e-211 < t

   1. Initial program 90.9%

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

      1. associate-/l* 93.8%

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

      2. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in x around inf 72.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-211}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 63.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-211}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.05e+24)
   (/ x (+ (+ a 1.0) (* y (/ b t))))
   (if (<= t 6e-211)
     (/ (+ z (/ (* x t) y)) b)
     (/ x (+ (* b (/ y t)) (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.05e+24) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else if (t <= 6e-211) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / ((b * (y / t)) + (a + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.05d+24)) then
        tmp = x / ((a + 1.0d0) + (y * (b / t)))
    else if (t <= 6d-211) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = x / ((b * (y / t)) + (a + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.05e+24) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else if (t <= 6e-211) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / ((b * (y / t)) + (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.05e+24:
		tmp = x / ((a + 1.0) + (y * (b / t)))
	elif t <= 6e-211:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = x / ((b * (y / t)) + (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.05e+24)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t <= 6e-211)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(x / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.05e+24)
		tmp = x / ((a + 1.0) + (y * (b / t)));
	elseif (t <= 6e-211)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = x / ((b * (y / t)) + (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.05e+24], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-211], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.05e24

   1. Initial program 85.6%

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

      1. *-commutative 85.6%

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

      2. associate-/l* 92.8%

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

   4. Applied egg-rr 92.8%

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

   5. Taylor expanded in x around inf 71.7%

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

      1. associate-+r+ 71.7%

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

      2. *-commutative 71.7%

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

      3. associate-/l* 75.4%

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

   7. Simplified 75.4%

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

   if -2.05e24 < t < 6.00000000000000009e-211

   1. Initial program 67.7%

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

      1. associate-/l* 54.5%

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

      2. associate-/l* 50.8%

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

   3. Simplified 50.8%

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

   5. Taylor expanded in y around inf 44.2%

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

      1. associate-/l* 43.3%

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

      2. associate-/r* 45.1%

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

      3. associate-/l* 44.2%

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

      4. associate-/l* 46.1%

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

      5. *-commutative 46.1%

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

   7. Simplified 46.1%

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

   8. Taylor expanded in b around inf 58.9%

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

   if 6.00000000000000009e-211 < t

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

      2. associate-/l* 93.6%

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

   4. Applied egg-rr 93.6%

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

   5. Taylor expanded in x around inf 75.7%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-211}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 65.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-211}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.05e+24)
   (/ (+ x (* y (/ z t))) (+ a 1.0))
   (if (<= t 6e-211)
     (/ (+ z (/ (* x t) y)) b)
     (/ x (+ (* b (/ y t)) (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.05e+24) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (t <= 6e-211) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / ((b * (y / t)) + (a + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.05d+24)) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else if (t <= 6d-211) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = x / ((b * (y / t)) + (a + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.05e+24) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (t <= 6e-211) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / ((b * (y / t)) + (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.05e+24:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	elif t <= 6e-211:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = x / ((b * (y / t)) + (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.05e+24)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	elseif (t <= 6e-211)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(x / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.05e+24)
		tmp = (x + (y * (z / t))) / (a + 1.0);
	elseif (t <= 6e-211)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = x / ((b * (y / t)) + (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.05e+24], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-211], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.05e24

   1. Initial program 85.6%

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

      1. associate-/l* 90.8%

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

      2. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in y around 0 87.5%

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

   if -2.05e24 < t < 6.00000000000000009e-211

   1. Initial program 67.7%

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

      1. associate-/l* 54.5%

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

      2. associate-/l* 50.8%

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

   3. Simplified 50.8%

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

   5. Taylor expanded in y around inf 44.2%

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

      1. associate-/l* 43.3%

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

      2. associate-/r* 45.1%

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

      3. associate-/l* 44.2%

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

      4. associate-/l* 46.1%

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

      5. *-commutative 46.1%

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

   7. Simplified 46.1%

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

   8. Taylor expanded in b around inf 58.9%

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

   if 6.00000000000000009e-211 < t

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

      2. associate-/l* 93.6%

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

   4. Applied egg-rr 93.6%

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

   5. Taylor expanded in x around inf 75.7%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-211}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 41.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-246}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.9e+44)
   (/ x a)
   (if (<= a 1.5e-246) (/ z b) (if (<= a 1.0) x (/ x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.9e+44) {
		tmp = x / a;
	} else if (a <= 1.5e-246) {
		tmp = z / b;
	} else if (a <= 1.0) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.9d+44)) then
        tmp = x / a
    else if (a <= 1.5d-246) then
        tmp = z / b
    else if (a <= 1.0d0) then
        tmp = x
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.9e+44) {
		tmp = x / a;
	} else if (a <= 1.5e-246) {
		tmp = z / b;
	} else if (a <= 1.0) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.9e+44:
		tmp = x / a
	elif a <= 1.5e-246:
		tmp = z / b
	elif a <= 1.0:
		tmp = x
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.9e+44)
		tmp = Float64(x / a);
	elseif (a <= 1.5e-246)
		tmp = Float64(z / b);
	elseif (a <= 1.0)
		tmp = x;
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.9e+44)
		tmp = x / a;
	elseif (a <= 1.5e-246)
		tmp = z / b;
	elseif (a <= 1.0)
		tmp = x;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.9e+44], N[(x / a), $MachinePrecision], If[LessEqual[a, 1.5e-246], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.0], x, N[(x / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.9000000000000002e44 or 1 < a

   1. Initial program 82.9%

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

      1. associate-/l* 78.1%

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

      2. associate-/l* 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in y around 0 49.4%

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

   6. Taylor expanded in a around inf 49.2%

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

   if -2.9000000000000002e44 < a < 1.5e-246

   1. Initial program 71.4%

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

      1. associate-/l* 66.9%

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

      2. associate-/l* 66.9%

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

   3. Simplified 66.9%

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

   5. Taylor expanded in y around inf 42.5%

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

   if 1.5e-246 < a < 1

   1. Initial program 89.1%

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

      1. associate-/l* 91.4%

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

      2. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in y around 0 52.8%

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

   6. Taylor expanded in a around 0 51.6%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-246}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 56.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+24} \lor \neg \left(t \leq 9.4 \cdot 10^{-64}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.6e+24) (not (<= t 9.4e-64))) (/ 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 <= -2.6e+24) || !(t <= 9.4e-64)) {
		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 <= (-2.6d+24)) .or. (.not. (t <= 9.4d-64))) 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 <= -2.6e+24) || !(t <= 9.4e-64)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.6e+24) or not (t <= 9.4e-64):
		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 <= -2.6e+24) || !(t <= 9.4e-64))
		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 <= -2.6e+24) || ~((t <= 9.4e-64)))
		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, -2.6e+24], N[Not[LessEqual[t, 9.4e-64]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5999999999999998e24 or 9.3999999999999996e-64 < t

   1. Initial program 89.8%

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

      1. associate-/l* 94.1%

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

      2. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in y around 0 64.0%

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

   if -2.5999999999999998e24 < t < 9.3999999999999996e-64

   1. Initial program 69.9%

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

      1. associate-/l* 58.5%

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

      2. associate-/l* 53.9%

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

   3. Simplified 53.9%

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

   5. Taylor expanded in y around inf 50.7%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+24} \lor \neg \left(t \leq 9.4 \cdot 10^{-64}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 41.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-5} \lor \neg \left(a \leq 1\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -4.4e-5) (not (<= a 1.0))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4.4e-5) || !(a <= 1.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-4.4d-5)) .or. (.not. (a <= 1.0d0))) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4.4e-5) || !(a <= 1.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -4.4e-5) or not (a <= 1.0):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -4.4e-5) || !(a <= 1.0))
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -4.4e-5) || ~((a <= 1.0)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -4.4e-5], N[Not[LessEqual[a, 1.0]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -4.3999999999999999e-5 or 1 < a

   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. associate-/l* 77.9%

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

      2. associate-/l* 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in y around 0 46.6%

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

   6. Taylor expanded in a around inf 46.4%

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

   if -4.3999999999999999e-5 < a < 1

   1. Initial program 77.5%

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

      1. associate-/l* 75.2%

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

      2. associate-/l* 73.6%

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

   3. Simplified 73.6%

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

   5. Taylor expanded in y around 0 39.0%

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

   6. Taylor expanded in a around 0 38.0%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-5} \lor \neg \left(a \leq 1\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 20.0% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.0%

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

   1. associate-/l* 76.6%

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

   2. associate-/l* 76.5%

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

3. Simplified 76.5%

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

5. Taylor expanded in y around 0 42.9%

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

6. Taylor expanded in a around 0 20.4%

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

7. Final simplification 20.4%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 79.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{if}\;t < -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.036967103737246 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024079 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

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

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