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

Percentage Accurate: 75.1% → 89.4%

Time: 19.5s

Alternatives: 15

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_2 := y \cdot \frac{b}{t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{\frac{z}{t}}{a + \left(1 + t\_2\right)}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + t\_2\right)} + \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0))))
        (t_2 (* y (/ b t))))
   (if (<= t_1 (- INFINITY))
     (* y (/ (/ z t) (+ a (+ 1.0 t_2))))
     (if (<= t_1 5e+298)
       t_1
       (if (<= t_1 INFINITY)
         (+ (* (/ y t) (/ z (+ 1.0 (+ a t_2)))) (/ x a))
         (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = y * (b / t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * ((z / t) / (a + (1.0 + t_2)));
	} else if (t_1 <= 5e+298) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((y / t) * (z / (1.0 + (a + t_2)))) + (x / a);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = y * (b / t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((z / t) / (a + (1.0 + t_2)));
	} else if (t_1 <= 5e+298) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = ((y / t) * (z / (1.0 + (a + t_2)))) + (x / a);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	t_2 = y * (b / t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * ((z / t) / (a + (1.0 + t_2)))
	elif t_1 <= 5e+298:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = ((y / t) * (z / (1.0 + (a + t_2)))) + (x / a)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	t_2 = Float64(y * Float64(b / t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(z / t) / Float64(a + Float64(1.0 + t_2))));
	elseif (t_1 <= 5e+298)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(y / t) * Float64(z / Float64(1.0 + Float64(a + t_2)))) + Float64(x / a));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	t_2 = y * (b / t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * ((z / t) / (a + (1.0 + t_2)));
	elseif (t_1 <= 5e+298)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = ((y / t) * (z / (1.0 + (a + t_2)))) + (x / a);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(N[(z / t), $MachinePrecision] / N[(a + N[(1.0 + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+298], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(a + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / a), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 39.6%

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

      1. remove-double-neg 39.6%

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

      2. associate-/l* 65.6%

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

      3. remove-double-neg 65.6%

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

      4. associate-/l* 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in x around 0 73.1%

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

      1. associate-/l* 90.8%

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

      2. associate-/r* 82.4%

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

      3. +-commutative 82.4%

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

      4. associate-*r/ 37.7%

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

      5. associate-+l+ 37.7%

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

      6. +-commutative 37.7%

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

      7. associate-*r/ 82.4%

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

      8. associate-*l/ 82.5%

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

      9. *-commutative 82.5%

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

   7. Simplified 82.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.0000000000000003e298

   1. Initial program 89.1%

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

   if 5.0000000000000003e298 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 6.2%

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

      1. remove-double-neg 6.2%

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

      2. associate-/l* 35.4%

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

      3. remove-double-neg 35.4%

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

      4. associate-/l* 35.4%

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

   3. Simplified 35.4%

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

   5. Taylor expanded in x around 0 41.5%

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

      1. +-commutative 41.5%

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

      2. associate-/l* 99.1%

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

      3. associate-+r+ 99.1%

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

      4. associate-*r/ 83.9%

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

      5. associate-+r+ 83.9%

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

      6. associate-*r/ 83.9%

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

   7. Simplified 83.9%

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

   8. Taylor expanded in z around 0 41.5%

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

      1. times-frac 85.9%

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

      2. *-commutative 85.9%

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

      3. associate-*r/ 85.9%

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

   10. Simplified 85.9%

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

   11. Taylor expanded in a around inf 85.9%

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

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

   1. Initial program 0.0%

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

      1. remove-double-neg 0.0%

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

      2. associate-/l* 0.4%

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

      3. remove-double-neg 0.4%

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

      4. associate-/l* 12.1%

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

   3. Simplified 12.1%

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

   5. Taylor expanded in y around inf 86.4%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;y \cdot \frac{\frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)} + \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{\frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;y \cdot \frac{z}{t \cdot \left(\left(a + 1\right) + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_1 (- INFINITY))
     (* y (/ (/ z t) (+ a (+ 1.0 (* y (/ b t))))))
     (if (<= t_1 5e+298)
       t_1
       (if (<= t_1 INFINITY)
         (* y (/ z (* t (+ (+ a 1.0) (* b (/ y t))))))
         (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * ((z / t) / (a + (1.0 + (y * (b / t)))));
	} else if (t_1 <= 5e+298) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = y * (z / (t * ((a + 1.0) + (b * (y / t)))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((z / t) / (a + (1.0 + (y * (b / t)))));
	} else if (t_1 <= 5e+298) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = y * (z / (t * ((a + 1.0) + (b * (y / t)))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * ((z / t) / (a + (1.0 + (y * (b / t)))))
	elif t_1 <= 5e+298:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = y * (z / (t * ((a + 1.0) + (b * (y / t)))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(z / t) / Float64(a + Float64(1.0 + Float64(y * Float64(b / t))))));
	elseif (t_1 <= 5e+298)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(y * Float64(z / Float64(t * Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * ((z / t) / (a + (1.0 + (y * (b / t)))));
	elseif (t_1 <= 5e+298)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = y * (z / (t * ((a + 1.0) + (b * (y / t)))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(N[(z / t), $MachinePrecision] / N[(a + N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+298], t$95$1, If[LessEqual[t$95$1, Infinity], N[(y * N[(z / N[(t * N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 39.6%

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

      1. remove-double-neg 39.6%

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

      2. associate-/l* 65.6%

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

      3. remove-double-neg 65.6%

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

      4. associate-/l* 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in x around 0 73.1%

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

      1. associate-/l* 90.8%

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

      2. associate-/r* 82.4%

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

      3. +-commutative 82.4%

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

      4. associate-*r/ 37.7%

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

      5. associate-+l+ 37.7%

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

      6. +-commutative 37.7%

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

      7. associate-*r/ 82.4%

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

      8. associate-*l/ 82.5%

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

      9. *-commutative 82.5%

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

   7. Simplified 82.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.0000000000000003e298

   1. Initial program 89.1%

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

   if 5.0000000000000003e298 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 6.2%

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

      1. remove-double-neg 6.2%

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

      2. associate-/l* 35.4%

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

      3. remove-double-neg 35.4%

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

      4. associate-/l* 35.4%

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

   3. Simplified 35.4%

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

   5. Taylor expanded in x around 0 41.5%

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

      1. associate-/l* 92.1%

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

      2. associate-+r+ 92.1%

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

      3. associate-*r/ 77.0%

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

   7. Simplified 77.0%

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

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

   1. Initial program 0.0%

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

      1. remove-double-neg 0.0%

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

      2. associate-/l* 0.4%

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

      3. remove-double-neg 0.4%

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

      4. associate-/l* 12.1%

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

   3. Simplified 12.1%

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

   5. Taylor expanded in y around inf 86.4%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;y \cdot \frac{\frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;y \cdot \frac{z}{t \cdot \left(\left(a + 1\right) + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-256}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-291}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-244}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-124}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ (* y (/ b t)) (+ a 1.0)))))
   (if (<= t -2.9e-90)
     t_1
     (if (<= t -8e-256)
       (/ z b)
       (if (<= t -1.6e-291)
         (/ (+ x (* z (/ y t))) (+ (/ (* y b) t) (+ a 1.0)))
         (if (<= t 9.5e-244)
           (/ z b)
           (if (<= t 5.8e-124)
             (/ (* 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))) / ((y * (b / t)) + (a + 1.0));
	double tmp;
	if (t <= -2.9e-90) {
		tmp = t_1;
	} else if (t <= -8e-256) {
		tmp = z / b;
	} else if (t <= -1.6e-291) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else if (t <= 9.5e-244) {
		tmp = z / b;
	} else if (t <= 5.8e-124) {
		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))) / ((y * (b / t)) + (a + 1.0d0))
    if (t <= (-2.9d-90)) then
        tmp = t_1
    else if (t <= (-8d-256)) then
        tmp = z / b
    else if (t <= (-1.6d-291)) then
        tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0d0))
    else if (t <= 9.5d-244) then
        tmp = z / b
    else if (t <= 5.8d-124) 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))) / ((y * (b / t)) + (a + 1.0));
	double tmp;
	if (t <= -2.9e-90) {
		tmp = t_1;
	} else if (t <= -8e-256) {
		tmp = z / b;
	} else if (t <= -1.6e-291) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else if (t <= 9.5e-244) {
		tmp = z / b;
	} else if (t <= 5.8e-124) {
		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))) / ((y * (b / t)) + (a + 1.0))
	tmp = 0
	if t <= -2.9e-90:
		tmp = t_1
	elif t <= -8e-256:
		tmp = z / b
	elif t <= -1.6e-291:
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0))
	elif t <= 9.5e-244:
		tmp = z / b
	elif t <= 5.8e-124:
		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(y * Float64(b / t)) + Float64(a + 1.0)))
	tmp = 0.0
	if (t <= -2.9e-90)
		tmp = t_1;
	elseif (t <= -8e-256)
		tmp = Float64(z / b);
	elseif (t <= -1.6e-291)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	elseif (t <= 9.5e-244)
		tmp = Float64(z / b);
	elseif (t <= 5.8e-124)
		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))) / ((y * (b / t)) + (a + 1.0));
	tmp = 0.0;
	if (t <= -2.9e-90)
		tmp = t_1;
	elseif (t <= -8e-256)
		tmp = z / b;
	elseif (t <= -1.6e-291)
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	elseif (t <= 9.5e-244)
		tmp = z / b;
	elseif (t <= 5.8e-124)
		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[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e-90], t$95$1, If[LessEqual[t, -8e-256], N[(z / b), $MachinePrecision], If[LessEqual[t, -1.6e-291], 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, 9.5e-244], N[(z / b), $MachinePrecision], If[LessEqual[t, 5.8e-124], 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 4 regimes

2. if t < -2.89999999999999983e-90 or 5.8000000000000004e-124 < t

   1. Initial program 80.2%

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

      1. remove-double-neg 80.2%

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

      2. associate-/l* 83.0%

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

      3. remove-double-neg 83.0%

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

      4. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   if -2.89999999999999983e-90 < t < -7.99999999999999982e-256 or -1.6000000000000001e-291 < t < 9.4999999999999995e-244

   1. Initial program 46.9%

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

      1. remove-double-neg 46.9%

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

      2. associate-/l* 37.8%

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

      3. remove-double-neg 37.8%

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

      4. associate-/l* 32.4%

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

   3. Simplified 32.4%

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

   5. Taylor expanded in y around inf 70.3%

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

   if -7.99999999999999982e-256 < t < -1.6000000000000001e-291

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 87.5%

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

   4. Applied egg-rr 87.5%

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

   if 9.4999999999999995e-244 < t < 5.8000000000000004e-124

   1. Initial program 60.1%

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

      1. remove-double-neg 60.1%

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

      2. associate-/l* 50.5%

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

      3. remove-double-neg 50.5%

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

      4. associate-/l* 47.6%

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

   3. Simplified 47.6%

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

   5. Taylor expanded in x around 0 65.7%

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

   6. Taylor expanded in t around 0 74.5%

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

      1. +-commutative 74.5%

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

      2. *-commutative 74.5%

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

   8. Simplified 74.5%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-90}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-256}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-291}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-244}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-124}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{b}{t} + \left(a + 1\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-91}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{t\_1}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-256}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-291}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-243}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-123}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* y (/ b t)) (+ a 1.0))))
   (if (<= t -9.5e-91)
     (/ (+ x (/ y (/ t z))) t_1)
     (if (<= t -8e-256)
       (/ z b)
       (if (<= t -3e-291)
         (/ (+ x (* z (/ y t))) (+ (/ (* y b) t) (+ a 1.0)))
         (if (<= t 2.9e-243)
           (/ z b)
           (if (<= t 5.6e-123)
             (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
             (/ (+ x (* y (/ z t))) t_1))))))))

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 tmp;
	if (t <= -9.5e-91) {
		tmp = (x + (y / (t / z))) / t_1;
	} else if (t <= -8e-256) {
		tmp = z / b;
	} else if (t <= -3e-291) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else if (t <= 2.9e-243) {
		tmp = z / b;
	} else if (t <= 5.6e-123) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = (x + (y * (z / t))) / 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 = (y * (b / t)) + (a + 1.0d0)
    if (t <= (-9.5d-91)) then
        tmp = (x + (y / (t / z))) / t_1
    else if (t <= (-8d-256)) then
        tmp = z / b
    else if (t <= (-3d-291)) then
        tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0d0))
    else if (t <= 2.9d-243) then
        tmp = z / b
    else if (t <= 5.6d-123) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else
        tmp = (x + (y * (z / t))) / 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 = (y * (b / t)) + (a + 1.0);
	double tmp;
	if (t <= -9.5e-91) {
		tmp = (x + (y / (t / z))) / t_1;
	} else if (t <= -8e-256) {
		tmp = z / b;
	} else if (t <= -3e-291) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else if (t <= 2.9e-243) {
		tmp = z / b;
	} else if (t <= 5.6e-123) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = (x + (y * (z / t))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * (b / t)) + (a + 1.0)
	tmp = 0
	if t <= -9.5e-91:
		tmp = (x + (y / (t / z))) / t_1
	elif t <= -8e-256:
		tmp = z / b
	elif t <= -3e-291:
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0))
	elif t <= 2.9e-243:
		tmp = z / b
	elif t <= 5.6e-123:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	else:
		tmp = (x + (y * (z / t))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0))
	tmp = 0.0
	if (t <= -9.5e-91)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / t_1);
	elseif (t <= -8e-256)
		tmp = Float64(z / b);
	elseif (t <= -3e-291)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	elseif (t <= 2.9e-243)
		tmp = Float64(z / b);
	elseif (t <= 5.6e-123)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * (b / t)) + (a + 1.0);
	tmp = 0.0;
	if (t <= -9.5e-91)
		tmp = (x + (y / (t / z))) / t_1;
	elseif (t <= -8e-256)
		tmp = z / b;
	elseif (t <= -3e-291)
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	elseif (t <= 2.9e-243)
		tmp = z / b;
	elseif (t <= 5.6e-123)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	else
		tmp = (x + (y * (z / t))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e-91], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, -8e-256], N[(z / b), $MachinePrecision], If[LessEqual[t, -3e-291], 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, 2.9e-243], N[(z / b), $MachinePrecision], If[LessEqual[t, 5.6e-123], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -9.5e-91

   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. remove-double-neg 83.8%

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

      2. associate-/l* 84.5%

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

      3. remove-double-neg 84.5%

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

      4. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

      1. clear-num 75.2%

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

      2. un-div-inv 75.3%

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

   6. Applied egg-rr 92.7%

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

   if -9.5e-91 < t < -7.99999999999999982e-256 or -3.0000000000000001e-291 < t < 2.89999999999999977e-243

   1. Initial program 46.9%

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

      1. remove-double-neg 46.9%

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

      2. associate-/l* 37.8%

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

      3. remove-double-neg 37.8%

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

      4. associate-/l* 32.4%

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

   3. Simplified 32.4%

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

   5. Taylor expanded in y around inf 70.3%

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

   if -7.99999999999999982e-256 < t < -3.0000000000000001e-291

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 87.5%

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

   4. Applied egg-rr 87.5%

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

   if 2.89999999999999977e-243 < t < 5.5999999999999998e-123

   1. Initial program 60.1%

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

      1. remove-double-neg 60.1%

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

      2. associate-/l* 50.5%

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

      3. remove-double-neg 50.5%

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

      4. associate-/l* 47.6%

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

   3. Simplified 47.6%

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

   5. Taylor expanded in x around 0 65.7%

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

   6. Taylor expanded in t around 0 74.5%

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

      1. +-commutative 74.5%

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

      2. *-commutative 74.5%

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

   8. Simplified 74.5%

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

   if 5.5999999999999998e-123 < t

   1. Initial program 76.1%

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

      1. remove-double-neg 76.1%

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

      2. associate-/l* 81.4%

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

      3. remove-double-neg 81.4%

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

      4. associate-/l* 85.0%

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

   3. Simplified 85.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing
3. Recombined 5 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-91}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-256}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-291}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-243}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-123}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-244}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-123}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ (* y (/ b t)) (+ a 1.0)))))
   (if (<= t -9.5e-91)
     t_1
     (if (<= t 7.2e-244)
       (/ z b)
       (if (<= t 8.5e-123) (/ (* 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))) / ((y * (b / t)) + (a + 1.0));
	double tmp;
	if (t <= -9.5e-91) {
		tmp = t_1;
	} else if (t <= 7.2e-244) {
		tmp = z / b;
	} else if (t <= 8.5e-123) {
		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))) / ((y * (b / t)) + (a + 1.0d0))
    if (t <= (-9.5d-91)) then
        tmp = t_1
    else if (t <= 7.2d-244) then
        tmp = z / b
    else if (t <= 8.5d-123) 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))) / ((y * (b / t)) + (a + 1.0));
	double tmp;
	if (t <= -9.5e-91) {
		tmp = t_1;
	} else if (t <= 7.2e-244) {
		tmp = z / b;
	} else if (t <= 8.5e-123) {
		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))) / ((y * (b / t)) + (a + 1.0))
	tmp = 0
	if t <= -9.5e-91:
		tmp = t_1
	elif t <= 7.2e-244:
		tmp = z / b
	elif t <= 8.5e-123:
		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(y * Float64(b / t)) + Float64(a + 1.0)))
	tmp = 0.0
	if (t <= -9.5e-91)
		tmp = t_1;
	elseif (t <= 7.2e-244)
		tmp = Float64(z / b);
	elseif (t <= 8.5e-123)
		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))) / ((y * (b / t)) + (a + 1.0));
	tmp = 0.0;
	if (t <= -9.5e-91)
		tmp = t_1;
	elseif (t <= 7.2e-244)
		tmp = z / b;
	elseif (t <= 8.5e-123)
		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[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e-91], t$95$1, If[LessEqual[t, 7.2e-244], N[(z / b), $MachinePrecision], If[LessEqual[t, 8.5e-123], 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 < -9.5e-91 or 8.4999999999999995e-123 < t

   1. Initial program 80.2%

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

      1. remove-double-neg 80.2%

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

      2. associate-/l* 83.0%

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

      3. remove-double-neg 83.0%

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

      4. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   if -9.5e-91 < t < 7.1999999999999995e-244

   1. Initial program 53.9%

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

      1. remove-double-neg 53.9%

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

      2. associate-/l* 44.4%

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

      3. remove-double-neg 44.4%

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

      4. associate-/l* 38.0%

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

   3. Simplified 38.0%

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

   5. Taylor expanded in y around inf 64.8%

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

   if 7.1999999999999995e-244 < t < 8.4999999999999995e-123

   1. Initial program 60.1%

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

      1. remove-double-neg 60.1%

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

      2. associate-/l* 50.5%

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

      3. remove-double-neg 50.5%

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

      4. associate-/l* 47.6%

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

   3. Simplified 47.6%

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

   5. Taylor expanded in x around 0 65.7%

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

   6. Taylor expanded in t around 0 74.5%

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

      1. +-commutative 74.5%

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

      2. *-commutative 74.5%

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

   8. Simplified 74.5%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-91}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-244}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-123}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-60}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-243}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.06 \cdot 10^{-119}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.9e-60)
   (/ (+ x (/ y (/ t z))) (+ a 1.0))
   (if (<= t 1.9e-243)
     (/ z b)
     (if (<= t 2.06e-119)
       (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
       (/ (+ 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 (t <= -3.9e-60) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else if (t <= 1.9e-243) {
		tmp = z / b;
	} else if (t <= 2.06e-119) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} 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 (t <= (-3.9d-60)) then
        tmp = (x + (y / (t / z))) / (a + 1.0d0)
    else if (t <= 1.9d-243) then
        tmp = z / b
    else if (t <= 2.06d-119) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    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 (t <= -3.9e-60) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else if (t <= 1.9e-243) {
		tmp = z / b;
	} else if (t <= 2.06e-119) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.9e-60:
		tmp = (x + (y / (t / z))) / (a + 1.0)
	elif t <= 1.9e-243:
		tmp = z / b
	elif t <= 2.06e-119:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	else:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.9e-60)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0));
	elseif (t <= 1.9e-243)
		tmp = Float64(z / b);
	elseif (t <= 2.06e-119)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.9e-60)
		tmp = (x + (y / (t / z))) / (a + 1.0);
	elseif (t <= 1.9e-243)
		tmp = z / b;
	elseif (t <= 2.06e-119)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	else
		tmp = (x + (y * (z / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.9e-60], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-243], N[(z / b), $MachinePrecision], If[LessEqual[t, 2.06e-119], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.9000000000000002e-60

   1. Initial program 83.7%

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

      1. remove-double-neg 83.7%

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

      2. associate-/l* 85.7%

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

      3. remove-double-neg 85.7%

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

      4. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in b around 0 73.3%

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

      1. associate-*r/ 78.1%

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

   7. Simplified 78.1%

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

      1. clear-num 78.1%

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

      2. un-div-inv 78.1%

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

   9. Applied egg-rr 78.1%

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

   if -3.9000000000000002e-60 < t < 1.8999999999999999e-243

   1. Initial program 57.1%

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

      1. remove-double-neg 57.1%

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

      2. associate-/l* 47.1%

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

      3. remove-double-neg 47.1%

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

      4. associate-/l* 41.4%

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

   3. Simplified 41.4%

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

   5. Taylor expanded in y around inf 64.2%

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

   if 1.8999999999999999e-243 < t < 2.06000000000000001e-119

   1. Initial program 61.3%

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

      1. remove-double-neg 61.3%

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

      2. associate-/l* 52.0%

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

      3. remove-double-neg 52.0%

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

      4. associate-/l* 49.1%

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

   3. Simplified 49.1%

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

   5. Taylor expanded in x around 0 66.7%

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

   6. Taylor expanded in t around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. *-commutative 75.2%

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

   8. Simplified 75.2%

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

   if 2.06000000000000001e-119 < t

   1. Initial program 75.8%

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

      1. remove-double-neg 75.8%

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

      2. associate-/l* 81.2%

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

      3. remove-double-neg 81.2%

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

      4. associate-/l* 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in b around 0 73.1%

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

      1. associate-*r/ 77.4%

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

   7. Simplified 77.4%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-60}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-243}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.06 \cdot 10^{-119}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-61} \lor \neg \left(t \leq 1.7 \cdot 10^{-91}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -5.5e+41)
     t_1
     (if (<= t -2.4e+19)
       (* t (/ (/ x b) y))
       (if (or (<= t -9e-61) (not (<= t 1.7e-91))) 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 (t <= -5.5e+41) {
		tmp = t_1;
	} else if (t <= -2.4e+19) {
		tmp = t * ((x / b) / y);
	} else if ((t <= -9e-61) || !(t <= 1.7e-91)) {
		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 (t <= (-5.5d+41)) then
        tmp = t_1
    else if (t <= (-2.4d+19)) then
        tmp = t * ((x / b) / y)
    else if ((t <= (-9d-61)) .or. (.not. (t <= 1.7d-91))) 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 (t <= -5.5e+41) {
		tmp = t_1;
	} else if (t <= -2.4e+19) {
		tmp = t * ((x / b) / y);
	} else if ((t <= -9e-61) || !(t <= 1.7e-91)) {
		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 t <= -5.5e+41:
		tmp = t_1
	elif t <= -2.4e+19:
		tmp = t * ((x / b) / y)
	elif (t <= -9e-61) or not (t <= 1.7e-91):
		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 (t <= -5.5e+41)
		tmp = t_1;
	elseif (t <= -2.4e+19)
		tmp = Float64(t * Float64(Float64(x / b) / y));
	elseif ((t <= -9e-61) || !(t <= 1.7e-91))
		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 (t <= -5.5e+41)
		tmp = t_1;
	elseif (t <= -2.4e+19)
		tmp = t * ((x / b) / y);
	elseif ((t <= -9e-61) || ~((t <= 1.7e-91)))
		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[t, -5.5e+41], t$95$1, If[LessEqual[t, -2.4e+19], N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -9e-61], N[Not[LessEqual[t, 1.7e-91]], $MachinePrecision]], t$95$1, N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5000000000000003e41 or -2.4e19 < t < -9e-61 or 1.70000000000000013e-91 < t

   1. Initial program 81.2%

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

      1. remove-double-neg 81.2%

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

      2. associate-/l* 85.2%

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

      3. remove-double-neg 85.2%

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

      4. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in y around 0 63.6%

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

   if -5.5000000000000003e41 < t < -2.4e19

   1. Initial program 72.2%

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

      1. remove-double-neg 72.2%

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

      2. associate-/l* 72.4%

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

      3. remove-double-neg 72.4%

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

      4. associate-/l* 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in x around inf 59.1%

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

      1. associate-+r+ 59.1%

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

      2. associate-*r/ 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in b around inf 57.5%

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

      1. associate-/l* 58.5%

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

      2. associate-/r* 85.2%

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

   10. Simplified 85.2%

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

   if -9e-61 < t < 1.70000000000000013e-91

   1. Initial program 58.8%

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

      1. remove-double-neg 58.8%

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

      2. associate-/l* 49.8%

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

      3. remove-double-neg 49.8%

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

      4. associate-/l* 44.5%

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

   3. Simplified 44.5%

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

   5. Taylor expanded in y around inf 60.3%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-61} \lor \neg \left(t \leq 1.7 \cdot 10^{-91}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{b} \cdot \frac{t}{y}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-60} \lor \neg \left(t \leq 1.5 \cdot 10^{-90}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -6.5e+41)
     t_1
     (if (<= t -3.2e+20)
       (* (/ x b) (/ t y))
       (if (or (<= t -2.15e-60) (not (<= t 1.5e-90))) 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 (t <= -6.5e+41) {
		tmp = t_1;
	} else if (t <= -3.2e+20) {
		tmp = (x / b) * (t / y);
	} else if ((t <= -2.15e-60) || !(t <= 1.5e-90)) {
		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 (t <= (-6.5d+41)) then
        tmp = t_1
    else if (t <= (-3.2d+20)) then
        tmp = (x / b) * (t / y)
    else if ((t <= (-2.15d-60)) .or. (.not. (t <= 1.5d-90))) 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 (t <= -6.5e+41) {
		tmp = t_1;
	} else if (t <= -3.2e+20) {
		tmp = (x / b) * (t / y);
	} else if ((t <= -2.15e-60) || !(t <= 1.5e-90)) {
		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 t <= -6.5e+41:
		tmp = t_1
	elif t <= -3.2e+20:
		tmp = (x / b) * (t / y)
	elif (t <= -2.15e-60) or not (t <= 1.5e-90):
		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 (t <= -6.5e+41)
		tmp = t_1;
	elseif (t <= -3.2e+20)
		tmp = Float64(Float64(x / b) * Float64(t / y));
	elseif ((t <= -2.15e-60) || !(t <= 1.5e-90))
		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 (t <= -6.5e+41)
		tmp = t_1;
	elseif (t <= -3.2e+20)
		tmp = (x / b) * (t / y);
	elseif ((t <= -2.15e-60) || ~((t <= 1.5e-90)))
		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[t, -6.5e+41], t$95$1, If[LessEqual[t, -3.2e+20], N[(N[(x / b), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.15e-60], N[Not[LessEqual[t, 1.5e-90]], $MachinePrecision]], t$95$1, N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.49999999999999975e41 or -3.2e20 < t < -2.15e-60 or 1.5000000000000001e-90 < t

   1. Initial program 81.2%

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

      1. remove-double-neg 81.2%

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

      2. associate-/l* 85.2%

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

      3. remove-double-neg 85.2%

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

      4. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in y around 0 63.6%

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

   if -6.49999999999999975e41 < t < -3.2e20

   1. Initial program 72.2%

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

      1. remove-double-neg 72.2%

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

      2. associate-/l* 72.4%

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

      3. remove-double-neg 72.4%

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

      4. associate-/l* 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in x around inf 59.1%

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

      1. associate-+r+ 59.1%

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

      2. associate-*r/ 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in b around inf 57.5%

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

      1. *-commutative 57.5%

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

      2. times-frac 85.7%

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

   10. Applied egg-rr 85.7%

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

   if -2.15e-60 < t < 1.5000000000000001e-90

   1. Initial program 58.8%

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

      1. remove-double-neg 58.8%

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

      2. associate-/l* 49.8%

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

      3. remove-double-neg 49.8%

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

      4. associate-/l* 44.5%

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

   3. Simplified 44.5%

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

   5. Taylor expanded in y around inf 60.3%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{b} \cdot \frac{t}{y}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-60} \lor \neg \left(t \leq 1.5 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-60} \lor \neg \left(t \leq 2.7 \cdot 10^{-91}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.7e-60) (not (<= t 2.7e-91)))
   (/ x (+ 1.0 (+ a (/ (* y b) t))))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.7e-60) || !(t <= 2.7e-91)) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} 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 <= (-2.7d-60)) .or. (.not. (t <= 2.7d-91))) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    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 <= -2.7e-60) || !(t <= 2.7e-91)) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.7e-60) or not (t <= 2.7e-91):
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.7e-60) || !(t <= 2.7e-91))
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	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 <= -2.7e-60) || ~((t <= 2.7e-91)))
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.7e-60], N[Not[LessEqual[t, 2.7e-91]], $MachinePrecision]], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7e-60 or 2.6999999999999997e-91 < t

   1. Initial program 80.7%

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

      1. remove-double-neg 80.7%

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

      2. associate-/l* 84.6%

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

      3. remove-double-neg 84.6%

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

      4. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in x around inf 65.7%

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

   if -2.7e-60 < t < 2.6999999999999997e-91

   1. Initial program 58.8%

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

      1. remove-double-neg 58.8%

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

      2. associate-/l* 49.8%

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

      3. remove-double-neg 49.8%

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

      4. associate-/l* 44.5%

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

   3. Simplified 44.5%

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

   5. Taylor expanded in y around inf 60.3%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-60} \lor \neg \left(t \leq 2.7 \cdot 10^{-91}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-61} \lor \neg \left(t \leq 4.7 \cdot 10^{-92}\right):\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -9.5e-61) (not (<= t 4.7e-92)))
   (/ x (+ (+ a 1.0) (* b (/ y t))))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9.5e-61) || !(t <= 4.7e-92)) {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	} 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 <= (-9.5d-61)) .or. (.not. (t <= 4.7d-92))) then
        tmp = x / ((a + 1.0d0) + (b * (y / t)))
    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 <= -9.5e-61) || !(t <= 4.7e-92)) {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -9.5e-61) or not (t <= 4.7e-92):
		tmp = x / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -9.5e-61) || !(t <= 4.7e-92))
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	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 <= -9.5e-61) || ~((t <= 4.7e-92)))
		tmp = x / ((a + 1.0) + (b * (y / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -9.5e-61], N[Not[LessEqual[t, 4.7e-92]], $MachinePrecision]], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.49999999999999986e-61 or 4.69999999999999993e-92 < t

   1. Initial program 80.7%

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

      1. remove-double-neg 80.7%

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

      2. associate-/l* 84.6%

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

      3. remove-double-neg 84.6%

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

      4. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in x around inf 65.7%

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

      1. associate-+r+ 65.7%

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

      2. associate-*r/ 68.9%

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

   7. Simplified 68.9%

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

   if -9.49999999999999986e-61 < t < 4.69999999999999993e-92

   1. Initial program 58.8%

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

      1. remove-double-neg 58.8%

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

      2. associate-/l* 49.8%

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

      3. remove-double-neg 49.8%

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

      4. associate-/l* 44.5%

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

   3. Simplified 44.5%

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

   5. Taylor expanded in y around inf 60.3%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-61} \lor \neg \left(t \leq 4.7 \cdot 10^{-92}\right):\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-60} \lor \neg \left(t \leq 9 \cdot 10^{-103}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.4e-60) (not (<= t 9e-103)))
   (/ (+ x (* y (/ z t))) (+ a 1.0))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.4e-60) || !(t <= 9e-103)) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.4d-60)) .or. (.not. (t <= 9d-103))) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.4e-60) || !(t <= 9e-103)) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.4e-60) or not (t <= 9e-103):
		tmp = (x + (y * (z / t))) / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.4e-60) || !(t <= 9e-103))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.4e-60) || ~((t <= 9e-103)))
		tmp = (x + (y * (z / t))) / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.4e-60], N[Not[LessEqual[t, 9e-103]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4000000000000001e-60 or 9e-103 < t

   1. Initial program 81.1%

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

      1. remove-double-neg 81.1%

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

      2. associate-/l* 84.9%

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

      3. remove-double-neg 84.9%

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

      4. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in b around 0 74.3%

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

      1. associate-*r/ 79.0%

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

   7. Simplified 79.0%

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

   if -1.4000000000000001e-60 < t < 9e-103

   1. Initial program 57.7%

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

      1. remove-double-neg 57.7%

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

      2. associate-/l* 48.4%

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

      3. remove-double-neg 48.4%

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

      4. associate-/l* 43.9%

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

   3. Simplified 43.9%

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

   5. Taylor expanded in y around inf 61.0%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-60} \lor \neg \left(t \leq 9 \cdot 10^{-103}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-60}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-101}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.2e-60)
   (/ (+ x (/ y (/ t z))) (+ a 1.0))
   (if (<= t 8.5e-101) (/ z 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 (t <= -2.2e-60) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else if (t <= 8.5e-101) {
		tmp = z / 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 (t <= (-2.2d-60)) then
        tmp = (x + (y / (t / z))) / (a + 1.0d0)
    else if (t <= 8.5d-101) then
        tmp = z / 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 (t <= -2.2e-60) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else if (t <= 8.5e-101) {
		tmp = z / b;
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.2e-60:
		tmp = (x + (y / (t / z))) / (a + 1.0)
	elif t <= 8.5e-101:
		tmp = z / 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 (t <= -2.2e-60)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0));
	elseif (t <= 8.5e-101)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.2e-60)
		tmp = (x + (y / (t / z))) / (a + 1.0);
	elseif (t <= 8.5e-101)
		tmp = z / b;
	else
		tmp = (x + (y * (z / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.2e-60], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-101], N[(z / b), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1999999999999999e-60

   1. Initial program 83.7%

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

      1. remove-double-neg 83.7%

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

      2. associate-/l* 85.7%

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

      3. remove-double-neg 85.7%

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

      4. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in b around 0 73.3%

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

      1. associate-*r/ 78.1%

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

   7. Simplified 78.1%

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

      1. clear-num 78.1%

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

      2. un-div-inv 78.1%

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

   9. Applied egg-rr 78.1%

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

   if -2.1999999999999999e-60 < t < 8.49999999999999941e-101

   1. Initial program 57.7%

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

      1. remove-double-neg 57.7%

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

      2. associate-/l* 48.4%

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

      3. remove-double-neg 48.4%

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

      4. associate-/l* 43.9%

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

   3. Simplified 43.9%

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

   5. Taylor expanded in y around inf 61.0%

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

   if 8.49999999999999941e-101 < t

   1. Initial program 78.2%

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

      1. remove-double-neg 78.2%

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

      2. associate-/l* 84.0%

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

      3. remove-double-neg 84.0%

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

      4. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in b around 0 75.4%

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

      1. associate-*r/ 79.9%

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

   7. Simplified 79.9%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-60}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-101}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-61} \lor \neg \left(t \leq 1.22 \cdot 10^{-91}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -8.2e-61) (not (<= t 1.22e-91))) (/ 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 <= -8.2e-61) || !(t <= 1.22e-91)) {
		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 <= (-8.2d-61)) .or. (.not. (t <= 1.22d-91))) 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 <= -8.2e-61) || !(t <= 1.22e-91)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -8.2e-61) or not (t <= 1.22e-91):
		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 <= -8.2e-61) || !(t <= 1.22e-91))
		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 <= -8.2e-61) || ~((t <= 1.22e-91)))
		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, -8.2e-61], N[Not[LessEqual[t, 1.22e-91]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.19999999999999998e-61 or 1.21999999999999998e-91 < t

   1. Initial program 80.7%

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

      1. remove-double-neg 80.7%

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

      2. associate-/l* 84.6%

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

      3. remove-double-neg 84.6%

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

      4. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in y around 0 61.3%

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

   if -8.19999999999999998e-61 < t < 1.21999999999999998e-91

   1. Initial program 58.8%

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

      1. remove-double-neg 58.8%

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

      2. associate-/l* 49.8%

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

      3. remove-double-neg 49.8%

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

      4. associate-/l* 44.5%

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

   3. Simplified 44.5%

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

   5. Taylor expanded in y around inf 60.3%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-61} \lor \neg \left(t \leq 1.22 \cdot 10^{-91}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 42.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6900000000 \lor \neg \left(y \leq 3.4 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6900000000.0) (not (<= y 3.4e+38))) (/ z b) (/ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6900000000.0) || !(y <= 3.4e+38)) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-6900000000.0d0)) .or. (.not. (y <= 3.4d+38))) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6900000000.0) || !(y <= 3.4e+38)) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6900000000.0) or not (y <= 3.4e+38):
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6900000000.0) || !(y <= 3.4e+38))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6900000000.0) || ~((y <= 3.4e+38)))
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6900000000.0], N[Not[LessEqual[y, 3.4e+38]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.9e9 or 3.39999999999999996e38 < y

   1. Initial program 48.9%

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

      1. remove-double-neg 48.9%

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

      2. associate-/l* 53.3%

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

      3. remove-double-neg 53.3%

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

      4. associate-/l* 61.5%

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

   3. Simplified 61.5%

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

   5. Taylor expanded in y around inf 52.9%

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

   if -6.9e9 < y < 3.39999999999999996e38

   1. Initial program 93.4%

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

      1. remove-double-neg 93.4%

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

      2. associate-/l* 85.7%

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

      3. remove-double-neg 85.7%

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

      4. associate-/l* 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in x around inf 70.4%

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

      1. associate-+r+ 70.4%

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

      2. associate-*r/ 70.4%

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

   7. Simplified 70.4%

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

   8. Taylor expanded in a around inf 43.0%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6900000000 \lor \neg \left(y \leq 3.4 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 25.4% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.3%

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

   1. remove-double-neg 71.3%

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

   2. associate-/l* 69.6%

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

   3. remove-double-neg 69.6%

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

   4. associate-/l* 71.4%

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

3. Simplified 71.4%

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

5. Taylor expanded in x around inf 50.1%

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

   1. associate-+r+ 50.1%

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

   2. associate-*r/ 51.9%

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

7. Simplified 51.9%

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

8. Taylor expanded in a around inf 30.5%

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

9. Final simplification 30.5%

   \[\leadsto \frac{x}{a} \]
10. Add Preprocessing

Developer target: 78.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024048 
(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))))