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

Percentage Accurate: 75.3% → 89.5%

Time: 16.6s

Alternatives: 21

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_3 := \mathsf{fma}\left(y, \frac{b}{t}, a\right) + 1\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_3} + \frac{\frac{y}{t}}{t\_3}\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\frac{t\_1}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t)))
        (t_2 (/ t_1 (+ (/ (* y b) t) (+ a 1.0))))
        (t_3 (+ (fma y (/ b t) a) 1.0)))
   (if (<= t_2 (- INFINITY))
     (* z (+ (/ x (* z t_3)) (/ (/ y t) t_3)))
     (if (<= t_2 5e+305) (/ t_1 (+ (* b (/ y t)) (+ a 1.0))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double t_3 = fma(y, (b / t), a) + 1.0;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * ((x / (z * t_3)) + ((y / t) / t_3));
	} else if (t_2 <= 5e+305) {
		tmp = t_1 / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	t_3 = Float64(fma(y, Float64(b / t), a) + 1.0)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_3)) + Float64(Float64(y / t) / t_3)));
	elseif (t_2 <= 5e+305)
		tmp = Float64(t_1 / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * N[(b / t), $MachinePrecision] + a), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z * N[(N[(x / N[(z * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+305], N[(t$95$1 / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 27.3%

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

      1. associate-/l* 68.3%

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

      2. associate-/l* 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in z around inf 81.1%

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

      1. associate-*r/ 81.1%

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

      2. +-commutative 81.1%

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

      3. associate-*r/ 81.1%

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

      4. associate-*l/ 81.1%

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

      5. *-commutative 81.1%

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

      6. fma-define 81.1%

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

      7. associate-/r* 92.5%

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

      8. associate-*r/ 77.8%

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

      9. +-commutative 77.8%

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

      10. associate-*r/ 92.5%

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

      11. associate-*l/ 87.8%

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

      12. *-commutative 87.8%

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

      13. fma-define 87.8%

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

   7. Simplified 87.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.00000000000000009e305

   1. Initial program 91.6%

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

      1. *-commutative 91.6%

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

      2. associate-/l* 91.6%

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

   4. Applied egg-rr 91.6%

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

   if 5.00000000000000009e305 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.9%

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

      1. associate-/l* 19.8%

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

      2. 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 87.2%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(\mathsf{fma}\left(y, \frac{b}{t}, a\right) + 1\right)} + \frac{\frac{y}{t}}{\mathsf{fma}\left(y, \frac{b}{t}, a\right) + 1}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t\_2}{t\_1}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;y \cdot \frac{z}{t \cdot t\_1}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\frac{t\_2}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0)))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (/ t_2 t_1)))
   (if (<= t_3 (- INFINITY))
     (* y (/ z (* t t_1)))
     (if (<= t_3 5e+305) (/ t_2 (+ (* b (/ y t)) (+ a 1.0))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = y * (z / (t * t_1));
	} else if (t_3 <= 5e+305) {
		tmp = t_2 / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (z / (t * t_1));
	} else if (t_3 <= 5e+305) {
		tmp = t_2 / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * b) / t) + (a + 1.0)
	t_2 = x + ((y * z) / t)
	t_3 = t_2 / t_1
	tmp = 0
	if t_3 <= -math.inf:
		tmp = y * (z / (t * t_1))
	elif t_3 <= 5e+305:
		tmp = t_2 / ((b * (y / t)) + (a + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	t_3 = Float64(t_2 / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(y * Float64(z / Float64(t * t_1)));
	elseif (t_3 <= 5e+305)
		tmp = Float64(t_2 / Float64(Float64(b * Float64(y / 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)
	t_1 = ((y * b) / t) + (a + 1.0);
	t_2 = x + ((y * z) / t);
	t_3 = t_2 / t_1;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = y * (z / (t * t_1));
	elseif (t_3 <= 5e+305)
		tmp = t_2 / ((b * (y / t)) + (a + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(y * N[(z / N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+305], N[(t$95$2 / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 27.3%

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

      1. associate-/l* 68.3%

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

      2. associate-/l* 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in x around 0 39.8%

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

      1. associate-/l* 72.2%

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

      2. associate-+r+ 72.2%

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

      3. *-commutative 72.2%

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

   7. Simplified 72.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.00000000000000009e305

   1. Initial program 91.6%

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

      1. *-commutative 91.6%

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

      2. associate-/l* 91.6%

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

   4. Applied egg-rr 91.6%

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

   if 5.00000000000000009e305 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.9%

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

      1. associate-/l* 19.8%

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

      2. 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 87.2%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;y \cdot \frac{z}{t \cdot \left(\frac{y \cdot b}{t} + \left(a + 1\right)\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t\_2}{t\_1}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_1} + \frac{y}{t \cdot t\_1}\right)\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\frac{t\_2}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0)))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (/ t_2 t_1)))
   (if (<= t_3 (- INFINITY))
     (* z (+ (/ x (* z t_1)) (/ y (* t t_1))))
     (if (<= t_3 5e+305) (/ t_2 (+ (* b (/ y t)) (+ a 1.0))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = z * ((x / (z * t_1)) + (y / (t * t_1)));
	} else if (t_3 <= 5e+305) {
		tmp = t_2 / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = z * ((x / (z * t_1)) + (y / (t * t_1)));
	} else if (t_3 <= 5e+305) {
		tmp = t_2 / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * b) / t) + (a + 1.0)
	t_2 = x + ((y * z) / t)
	t_3 = t_2 / t_1
	tmp = 0
	if t_3 <= -math.inf:
		tmp = z * ((x / (z * t_1)) + (y / (t * t_1)))
	elif t_3 <= 5e+305:
		tmp = t_2 / ((b * (y / t)) + (a + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	t_3 = Float64(t_2 / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_1)) + Float64(y / Float64(t * t_1))));
	elseif (t_3 <= 5e+305)
		tmp = Float64(t_2 / Float64(Float64(b * Float64(y / 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)
	t_1 = ((y * b) / t) + (a + 1.0);
	t_2 = x + ((y * z) / t);
	t_3 = t_2 / t_1;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = z * ((x / (z * t_1)) + (y / (t * t_1)));
	elseif (t_3 <= 5e+305)
		tmp = t_2 / ((b * (y / t)) + (a + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(z * N[(N[(x / N[(z * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+305], N[(t$95$2 / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 27.3%

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

      1. associate-/l* 68.3%

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

      2. associate-/l* 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in z around inf 81.1%

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

      1. associate-+r+ 81.1%

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

      2. *-commutative 81.1%

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

      3. associate-+r+ 81.1%

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

      4. *-commutative 81.1%

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

   7. Simplified 81.1%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.00000000000000009e305

   1. Initial program 91.6%

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

      1. *-commutative 91.6%

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

      2. associate-/l* 91.6%

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

   4. Applied egg-rr 91.6%

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

   if 5.00000000000000009e305 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.9%

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

      1. associate-/l* 19.8%

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

      2. 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 87.2%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(\frac{y \cdot b}{t} + \left(a + 1\right)\right)} + \frac{y}{t \cdot \left(\frac{y \cdot b}{t} + \left(a + 1\right)\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ t_2 := y \cdot \frac{\frac{z}{a}}{t} + \frac{x}{a}\\ t_3 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -88000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-193}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-181}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 7000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (* t (/ x (* y b)))))
        (t_2 (+ (* y (/ (/ z a) t)) (/ x a)))
        (t_3 (+ x (/ (* y z) t))))
   (if (<= a -88000000.0)
     t_2
     (if (<= a -1e-52)
       t_1
       (if (<= a -2.2e-193)
         t_3
         (if (<= a -3.6e-294)
           t_1
           (if (<= a 4e-181) t_3 (if (<= a 7000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + (t * (x / (y * b)));
	double t_2 = (y * ((z / a) / t)) + (x / a);
	double t_3 = x + ((y * z) / t);
	double tmp;
	if (a <= -88000000.0) {
		tmp = t_2;
	} else if (a <= -1e-52) {
		tmp = t_1;
	} else if (a <= -2.2e-193) {
		tmp = t_3;
	} else if (a <= -3.6e-294) {
		tmp = t_1;
	} else if (a <= 4e-181) {
		tmp = t_3;
	} else if (a <= 7000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z / b) + (t * (x / (y * b)))
    t_2 = (y * ((z / a) / t)) + (x / a)
    t_3 = x + ((y * z) / t)
    if (a <= (-88000000.0d0)) then
        tmp = t_2
    else if (a <= (-1d-52)) then
        tmp = t_1
    else if (a <= (-2.2d-193)) then
        tmp = t_3
    else if (a <= (-3.6d-294)) then
        tmp = t_1
    else if (a <= 4d-181) then
        tmp = t_3
    else if (a <= 7000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + (t * (x / (y * b)));
	double t_2 = (y * ((z / a) / t)) + (x / a);
	double t_3 = x + ((y * z) / t);
	double tmp;
	if (a <= -88000000.0) {
		tmp = t_2;
	} else if (a <= -1e-52) {
		tmp = t_1;
	} else if (a <= -2.2e-193) {
		tmp = t_3;
	} else if (a <= -3.6e-294) {
		tmp = t_1;
	} else if (a <= 4e-181) {
		tmp = t_3;
	} else if (a <= 7000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + (t * (x / (y * b)))
	t_2 = (y * ((z / a) / t)) + (x / a)
	t_3 = x + ((y * z) / t)
	tmp = 0
	if a <= -88000000.0:
		tmp = t_2
	elif a <= -1e-52:
		tmp = t_1
	elif a <= -2.2e-193:
		tmp = t_3
	elif a <= -3.6e-294:
		tmp = t_1
	elif a <= 4e-181:
		tmp = t_3
	elif a <= 7000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(t * Float64(x / Float64(y * b))))
	t_2 = Float64(Float64(y * Float64(Float64(z / a) / t)) + Float64(x / a))
	t_3 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (a <= -88000000.0)
		tmp = t_2;
	elseif (a <= -1e-52)
		tmp = t_1;
	elseif (a <= -2.2e-193)
		tmp = t_3;
	elseif (a <= -3.6e-294)
		tmp = t_1;
	elseif (a <= 4e-181)
		tmp = t_3;
	elseif (a <= 7000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + (t * (x / (y * b)));
	t_2 = (y * ((z / a) / t)) + (x / a);
	t_3 = x + ((y * z) / t);
	tmp = 0.0;
	if (a <= -88000000.0)
		tmp = t_2;
	elseif (a <= -1e-52)
		tmp = t_1;
	elseif (a <= -2.2e-193)
		tmp = t_3;
	elseif (a <= -3.6e-294)
		tmp = t_1;
	elseif (a <= 4e-181)
		tmp = t_3;
	elseif (a <= 7000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(t * N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(z / a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + N[(x / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -88000000.0], t$95$2, If[LessEqual[a, -1e-52], t$95$1, If[LessEqual[a, -2.2e-193], t$95$3, If[LessEqual[a, -3.6e-294], t$95$1, If[LessEqual[a, 4e-181], t$95$3, If[LessEqual[a, 7000000.0], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.8e7 or 7e6 < a

   1. Initial program 74.9%

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

      1. associate-/l* 76.0%

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

      2. associate-/l* 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in a around inf 58.3%

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

   6. Taylor expanded in x around 0 56.5%

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

      1. +-commutative 56.5%

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

      2. associate-/l* 62.6%

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

      3. associate-/r* 67.3%

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

   8. Simplified 67.3%

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

   if -8.8e7 < a < -1e-52 or -2.19999999999999977e-193 < a < -3.6000000000000001e-294 or 4.00000000000000019e-181 < a < 7e6

   1. Initial program 68.7%

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

      1. associate-/l* 68.7%

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

      2. associate-/l* 71.5%

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

   3. Simplified 71.5%

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

   5. Taylor expanded in b around inf 41.7%

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

   6. Taylor expanded in t around 0 66.7%

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

      1. associate-/l* 65.9%

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

      2. *-commutative 65.9%

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

   8. Simplified 65.9%

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

   if -1e-52 < a < -2.19999999999999977e-193 or -3.6000000000000001e-294 < a < 4.00000000000000019e-181

   1. Initial program 79.1%

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

      1. associate-/l* 75.2%

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

      2. associate-/l* 75.2%

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

   3. Simplified 75.2%

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

   5. Taylor expanded in b around 0 64.0%

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

      1. associate-*r/ 60.1%

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

      2. *-commutative 60.1%

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

      3. div-inv 60.1%

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

      4. associate-*l* 64.1%

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

   7. Applied egg-rr 64.1%

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

   8. Taylor expanded in a around 0 64.0%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -88000000:\\ \;\;\;\;y \cdot \frac{\frac{z}{a}}{t} + \frac{x}{a}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-52}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-193}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-294}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-181}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 7000000:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{z}{a}}{t} + \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-264}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-308}:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(a + 1\right)} + \frac{y}{t \cdot \left(a + 1\right)}\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-128}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))))
   (if (<= t -2.2e-108)
     t_1
     (if (<= t -6.5e-264)
       (+ (/ z b) (/ (/ (* x t) b) y))
       (if (<= t 8e-308)
         (* z (+ (/ x (* z (+ a 1.0))) (/ y (* t (+ a 1.0)))))
         (if (<= t 6.2e-128) (+ (/ z b) (* t (/ x (* y b)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -2.2e-108) {
		tmp = t_1;
	} else if (t <= -6.5e-264) {
		tmp = (z / b) + (((x * t) / b) / y);
	} else if (t <= 8e-308) {
		tmp = z * ((x / (z * (a + 1.0))) + (y / (t * (a + 1.0))));
	} else if (t <= 6.2e-128) {
		tmp = (z / b) + (t * (x / (y * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    if (t <= (-2.2d-108)) then
        tmp = t_1
    else if (t <= (-6.5d-264)) then
        tmp = (z / b) + (((x * t) / b) / y)
    else if (t <= 8d-308) then
        tmp = z * ((x / (z * (a + 1.0d0))) + (y / (t * (a + 1.0d0))))
    else if (t <= 6.2d-128) then
        tmp = (z / b) + (t * (x / (y * b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -2.2e-108) {
		tmp = t_1;
	} else if (t <= -6.5e-264) {
		tmp = (z / b) + (((x * t) / b) / y);
	} else if (t <= 8e-308) {
		tmp = z * ((x / (z * (a + 1.0))) + (y / (t * (a + 1.0))));
	} else if (t <= 6.2e-128) {
		tmp = (z / b) + (t * (x / (y * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	tmp = 0
	if t <= -2.2e-108:
		tmp = t_1
	elif t <= -6.5e-264:
		tmp = (z / b) + (((x * t) / b) / y)
	elif t <= 8e-308:
		tmp = z * ((x / (z * (a + 1.0))) + (y / (t * (a + 1.0))))
	elif t <= 6.2e-128:
		tmp = (z / b) + (t * (x / (y * b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))))
	tmp = 0.0
	if (t <= -2.2e-108)
		tmp = t_1;
	elseif (t <= -6.5e-264)
		tmp = Float64(Float64(z / b) + Float64(Float64(Float64(x * t) / b) / y));
	elseif (t <= 8e-308)
		tmp = Float64(z * Float64(Float64(x / Float64(z * Float64(a + 1.0))) + Float64(y / Float64(t * Float64(a + 1.0)))));
	elseif (t <= 6.2e-128)
		tmp = Float64(Float64(z / b) + Float64(t * Float64(x / Float64(y * b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	tmp = 0.0;
	if (t <= -2.2e-108)
		tmp = t_1;
	elseif (t <= -6.5e-264)
		tmp = (z / b) + (((x * t) / b) / y);
	elseif (t <= 8e-308)
		tmp = z * ((x / (z * (a + 1.0))) + (y / (t * (a + 1.0))));
	elseif (t <= 6.2e-128)
		tmp = (z / b) + (t * (x / (y * b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e-108], t$95$1, If[LessEqual[t, -6.5e-264], N[(N[(z / b), $MachinePrecision] + N[(N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-308], N[(z * N[(N[(x / N[(z * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e-128], N[(N[(z / b), $MachinePrecision] + N[(t * N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.2000000000000001e-108 or 6.20000000000000005e-128 < t

   1. Initial program 79.4%

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

      1. associate-/l* 85.0%

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

      2. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   if -2.2000000000000001e-108 < t < -6.5000000000000001e-264

   1. Initial program 65.4%

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

      1. associate-/l* 46.0%

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

      2. associate-/l* 40.9%

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

   3. Simplified 40.9%

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

   5. Taylor expanded in y around -inf 50.1%

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

   6. Taylor expanded in x around inf 75.4%

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

      1. mul-1-neg 75.4%

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

      2. *-commutative 75.4%

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

      3. distribute-frac-neg 75.4%

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

      4. distribute-lft-neg-in 75.4%

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

   8. Simplified 75.4%

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

   if -6.5000000000000001e-264 < t < 8.00000000000000026e-308

   1. Initial program 65.0%

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

      1. associate-/l* 39.4%

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

      2. associate-/l* 39.1%

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

   3. Simplified 39.1%

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

   5. Taylor expanded in b around 0 56.6%

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

   6. Taylor expanded in z around inf 82.1%

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

   if 8.00000000000000026e-308 < t < 6.20000000000000005e-128

   1. Initial program 60.9%

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

      1. associate-/l* 50.2%

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

      2. 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 b around inf 50.0%

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

   6. Taylor expanded in t around 0 79.1%

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

      1. associate-/l* 80.2%

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

      2. *-commutative 80.2%

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

   8. Simplified 80.2%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-108}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-264}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-308}:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(a + 1\right)} + \frac{y}{t \cdot \left(a + 1\right)}\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-128}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+74}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-14} \lor \neg \left(b \leq 3800\right) \land b \leq 3.4 \cdot 10^{+57}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.05e+74)
   (+ (/ z b) (* t (/ x (* y b))))
   (if (or (<= b 1.4e-14) (and (not (<= b 3800.0)) (<= b 3.4e+57)))
     (/ (+ x (* z (/ y t))) (+ a 1.0))
     (+ (/ z b) (/ (* t (/ x b)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.05e+74) {
		tmp = (z / b) + (t * (x / (y * b)));
	} else if ((b <= 1.4e-14) || (!(b <= 3800.0) && (b <= 3.4e+57))) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = (z / b) + ((t * (x / b)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.05d+74)) then
        tmp = (z / b) + (t * (x / (y * b)))
    else if ((b <= 1.4d-14) .or. (.not. (b <= 3800.0d0)) .and. (b <= 3.4d+57)) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else
        tmp = (z / b) + ((t * (x / b)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.05e+74) {
		tmp = (z / b) + (t * (x / (y * b)));
	} else if ((b <= 1.4e-14) || (!(b <= 3800.0) && (b <= 3.4e+57))) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = (z / b) + ((t * (x / b)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.05e+74:
		tmp = (z / b) + (t * (x / (y * b)))
	elif (b <= 1.4e-14) or (not (b <= 3800.0) and (b <= 3.4e+57)):
		tmp = (x + (z * (y / t))) / (a + 1.0)
	else:
		tmp = (z / b) + ((t * (x / b)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.05e+74)
		tmp = Float64(Float64(z / b) + Float64(t * Float64(x / Float64(y * b))));
	elseif ((b <= 1.4e-14) || (!(b <= 3800.0) && (b <= 3.4e+57)))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.05e+74)
		tmp = (z / b) + (t * (x / (y * b)));
	elseif ((b <= 1.4e-14) || (~((b <= 3800.0)) && (b <= 3.4e+57)))
		tmp = (x + (z * (y / t))) / (a + 1.0);
	else
		tmp = (z / b) + ((t * (x / b)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.05e+74], N[(N[(z / b), $MachinePrecision] + N[(t * N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 1.4e-14], And[N[Not[LessEqual[b, 3800.0]], $MachinePrecision], LessEqual[b, 3.4e+57]]], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.0499999999999999e74

   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. associate-/l* 53.2%

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

      2. associate-/l* 53.0%

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

   3. Simplified 53.0%

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

   5. Taylor expanded in b around inf 48.7%

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

   6. Taylor expanded in t around 0 72.3%

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

      1. associate-/l* 73.6%

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

      2. *-commutative 73.6%

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

   8. Simplified 73.6%

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

   if -1.0499999999999999e74 < b < 1.4e-14 or 3800 < b < 3.39999999999999992e57

   1. Initial program 83.3%

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

      1. associate-/l* 84.2%

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

      2. associate-/l* 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in b around 0 72.7%

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

      1. *-commutative 83.3%

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

      2. associate-/l* 85.7%

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

   7. Applied egg-rr 77.5%

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

   if 1.4e-14 < b < 3800 or 3.39999999999999992e57 < b

   1. Initial program 63.1%

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

      1. associate-/l* 61.5%

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

      2. associate-/l* 66.5%

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

   3. Simplified 66.5%

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

   5. Taylor expanded in y around -inf 60.6%

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

   6. Taylor expanded in x around inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. associate-*r/ 79.5%

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

      3. distribute-rgt-neg-in 79.5%

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

      4. distribute-neg-frac2 79.5%

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

   8. Simplified 79.5%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+74}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-14} \lor \neg \left(b \leq 3800\right) \land b \leq 3.4 \cdot 10^{+57}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{if}\;b \leq -8 \cdot 10^{+73}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5000:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* z (/ y t))) (+ a 1.0))))
   (if (<= b -8e+73)
     (+ (/ z b) (* t (/ x (* y b))))
     (if (<= b 1.45e-14)
       t_1
       (if (<= b 5000.0)
         (+ (/ z b) (/ (/ (* x t) b) y))
         (if (<= b 1.35e+57) t_1 (+ (/ z b) (/ (* t (/ x b)) y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / (a + 1.0);
	double tmp;
	if (b <= -8e+73) {
		tmp = (z / b) + (t * (x / (y * b)));
	} else if (b <= 1.45e-14) {
		tmp = t_1;
	} else if (b <= 5000.0) {
		tmp = (z / b) + (((x * t) / b) / y);
	} else if (b <= 1.35e+57) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((t * (x / b)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z * (y / t))) / (a + 1.0d0)
    if (b <= (-8d+73)) then
        tmp = (z / b) + (t * (x / (y * b)))
    else if (b <= 1.45d-14) then
        tmp = t_1
    else if (b <= 5000.0d0) then
        tmp = (z / b) + (((x * t) / b) / y)
    else if (b <= 1.35d+57) then
        tmp = t_1
    else
        tmp = (z / b) + ((t * (x / b)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / (a + 1.0);
	double tmp;
	if (b <= -8e+73) {
		tmp = (z / b) + (t * (x / (y * b)));
	} else if (b <= 1.45e-14) {
		tmp = t_1;
	} else if (b <= 5000.0) {
		tmp = (z / b) + (((x * t) / b) / y);
	} else if (b <= 1.35e+57) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((t * (x / b)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (z * (y / t))) / (a + 1.0)
	tmp = 0
	if b <= -8e+73:
		tmp = (z / b) + (t * (x / (y * b)))
	elif b <= 1.45e-14:
		tmp = t_1
	elif b <= 5000.0:
		tmp = (z / b) + (((x * t) / b) / y)
	elif b <= 1.35e+57:
		tmp = t_1
	else:
		tmp = (z / b) + ((t * (x / b)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0))
	tmp = 0.0
	if (b <= -8e+73)
		tmp = Float64(Float64(z / b) + Float64(t * Float64(x / Float64(y * b))));
	elseif (b <= 1.45e-14)
		tmp = t_1;
	elseif (b <= 5000.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(Float64(x * t) / b) / y));
	elseif (b <= 1.35e+57)
		tmp = t_1;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (z * (y / t))) / (a + 1.0);
	tmp = 0.0;
	if (b <= -8e+73)
		tmp = (z / b) + (t * (x / (y * b)));
	elseif (b <= 1.45e-14)
		tmp = t_1;
	elseif (b <= 5000.0)
		tmp = (z / b) + (((x * t) / b) / y);
	elseif (b <= 1.35e+57)
		tmp = t_1;
	else
		tmp = (z / b) + ((t * (x / b)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8e+73], N[(N[(z / b), $MachinePrecision] + N[(t * N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e-14], t$95$1, If[LessEqual[b, 5000.0], N[(N[(z / b), $MachinePrecision] + N[(N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e+57], t$95$1, N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.99999999999999986e73

   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. associate-/l* 53.2%

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

      2. associate-/l* 53.0%

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

   3. Simplified 53.0%

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

   5. Taylor expanded in b around inf 48.7%

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

   6. Taylor expanded in t around 0 72.3%

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

      1. associate-/l* 73.6%

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

      2. *-commutative 73.6%

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

   8. Simplified 73.6%

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

   if -7.99999999999999986e73 < b < 1.4500000000000001e-14 or 5e3 < b < 1.3499999999999999e57

   1. Initial program 83.3%

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

      1. associate-/l* 84.2%

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

      2. associate-/l* 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in b around 0 72.7%

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

      1. *-commutative 83.3%

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

      2. associate-/l* 85.7%

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

   7. Applied egg-rr 77.5%

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

   if 1.4500000000000001e-14 < b < 5e3

   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. associate-/l* 57.8%

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

      2. associate-/l* 58.0%

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

   3. Simplified 58.0%

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

   5. Taylor expanded in y around -inf 66.6%

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

   6. Taylor expanded in x around inf 79.8%

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

      1. mul-1-neg 79.8%

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

      2. *-commutative 79.8%

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

      3. distribute-frac-neg 79.8%

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

      4. distribute-lft-neg-in 79.8%

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

   8. Simplified 79.8%

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

   if 1.3499999999999999e57 < b

   1. Initial program 63.7%

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

      1. associate-/l* 62.0%

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

      2. associate-/l* 67.8%

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

   3. Simplified 67.8%

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

   5. Taylor expanded in y around -inf 59.8%

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

   6. Taylor expanded in x around inf 73.5%

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

      1. mul-1-neg 73.5%

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

      2. associate-*r/ 79.4%

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

      3. distribute-rgt-neg-in 79.4%

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

      4. distribute-neg-frac2 79.4%

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

   8. Simplified 79.4%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+73}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-14}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 5000:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+57}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+239}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+261}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.8e+239)
   (/ z b)
   (if (<= y 3.8e+261)
     (/ (+ x (* z (/ y t))) (+ (* b (/ y t)) (+ a 1.0)))
     (+ (/ z b) (* t (/ x (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.8e+239) {
		tmp = z / b;
	} else if (y <= 3.8e+261) {
		tmp = (x + (z * (y / t))) / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = (z / b) + (t * (x / (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.8d+239)) then
        tmp = z / b
    else if (y <= 3.8d+261) then
        tmp = (x + (z * (y / t))) / ((b * (y / t)) + (a + 1.0d0))
    else
        tmp = (z / b) + (t * (x / (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.8e+239) {
		tmp = z / b;
	} else if (y <= 3.8e+261) {
		tmp = (x + (z * (y / t))) / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = (z / b) + (t * (x / (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.8e+239:
		tmp = z / b
	elif y <= 3.8e+261:
		tmp = (x + (z * (y / t))) / ((b * (y / t)) + (a + 1.0))
	else:
		tmp = (z / b) + (t * (x / (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.8e+239)
		tmp = Float64(z / b);
	elseif (y <= 3.8e+261)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(Float64(z / b) + Float64(t * Float64(x / Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.8e+239)
		tmp = z / b;
	elseif (y <= 3.8e+261)
		tmp = (x + (z * (y / t))) / ((b * (y / t)) + (a + 1.0));
	else
		tmp = (z / b) + (t * (x / (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.8e+239], N[(z / b), $MachinePrecision], If[LessEqual[y, 3.8e+261], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(t * N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000001e239

   1. Initial program 39.9%

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

      1. associate-/l* 49.2%

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

      2. associate-/l* 53.8%

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

   3. Simplified 53.8%

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

   5. Taylor expanded in y around inf 72.5%

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

   if -3.8000000000000001e239 < y < 3.8000000000000002e261

   1. Initial program 79.1%

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

      1. *-commutative 79.1%

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

      2. associate-/l* 82.5%

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

   4. Applied egg-rr 82.5%

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

      1. *-commutative 79.1%

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

      2. associate-/l* 79.5%

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

   6. Applied egg-rr 84.6%

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

   if 3.8000000000000002e261 < y

   1. Initial program 45.3%

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

      1. associate-/l* 40.5%

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

      2. associate-/l* 49.3%

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

   3. Simplified 49.3%

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

   5. Taylor expanded in b around inf 28.2%

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

   6. Taylor expanded in t around 0 82.5%

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

      1. associate-/l* 82.4%

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

      2. *-commutative 82.4%

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

   8. Simplified 82.4%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+239}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+261}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{\frac{z}{a}}{t} + \frac{x}{a}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-178}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 32500:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* y (/ (/ z a) t)) (/ x a))))
   (if (<= a -2.3e-10)
     t_1
     (if (<= a 4.2e-178)
       (+ x (/ (* y z) t))
       (if (<= a 32500.0) (/ z b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * ((z / a) / t)) + (x / a);
	double tmp;
	if (a <= -2.3e-10) {
		tmp = t_1;
	} else if (a <= 4.2e-178) {
		tmp = x + ((y * z) / t);
	} else if (a <= 32500.0) {
		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 = (y * ((z / a) / t)) + (x / a)
    if (a <= (-2.3d-10)) then
        tmp = t_1
    else if (a <= 4.2d-178) then
        tmp = x + ((y * z) / t)
    else if (a <= 32500.0d0) 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 = (y * ((z / a) / t)) + (x / a);
	double tmp;
	if (a <= -2.3e-10) {
		tmp = t_1;
	} else if (a <= 4.2e-178) {
		tmp = x + ((y * z) / t);
	} else if (a <= 32500.0) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * ((z / a) / t)) + (x / a)
	tmp = 0
	if a <= -2.3e-10:
		tmp = t_1
	elif a <= 4.2e-178:
		tmp = x + ((y * z) / t)
	elif a <= 32500.0:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(Float64(z / a) / t)) + Float64(x / a))
	tmp = 0.0
	if (a <= -2.3e-10)
		tmp = t_1;
	elseif (a <= 4.2e-178)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (a <= 32500.0)
		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 = (y * ((z / a) / t)) + (x / a);
	tmp = 0.0;
	if (a <= -2.3e-10)
		tmp = t_1;
	elseif (a <= 4.2e-178)
		tmp = x + ((y * z) / t);
	elseif (a <= 32500.0)
		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[(N[(y * N[(N[(z / a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + N[(x / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e-10], t$95$1, If[LessEqual[a, 4.2e-178], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 32500.0], N[(z / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.30000000000000007e-10 or 32500 < a

   1. Initial program 74.1%

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

      1. associate-/l* 75.2%

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

      2. associate-/l* 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in a around inf 56.9%

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

   6. Taylor expanded in x around 0 55.2%

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

      1. +-commutative 55.2%

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

      2. associate-/l* 61.0%

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

      3. associate-/r* 65.6%

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

   8. Simplified 65.6%

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

   if -2.30000000000000007e-10 < a < 4.2e-178

   1. Initial program 78.1%

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

      1. associate-/l* 74.5%

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

      2. associate-/l* 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in b around 0 53.9%

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

      1. associate-*r/ 50.3%

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

      2. *-commutative 50.3%

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

      3. div-inv 50.3%

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

      4. associate-*l* 53.9%

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

   7. Applied egg-rr 53.9%

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

   8. Taylor expanded in a around 0 53.3%

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

   if 4.2e-178 < a < 32500

   1. Initial program 62.9%

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

      1. associate-/l* 66.2%

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

      2. associate-/l* 72.6%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in y around inf 52.7%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \frac{\frac{z}{a}}{t} + \frac{x}{a}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-178}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 32500:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{z}{a}}{t} + \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+69}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \frac{x}{y \cdot b}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-21} \lor \neg \left(y \leq 5.8 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.4e+69)
   (/ z b)
   (if (<= y -1.85e-15)
     (* t (/ x (* y b)))
     (if (or (<= y -3.6e-21) (not (<= y 5.8e+96))) (/ z b) (/ x (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.4e+69) {
		tmp = z / b;
	} else if (y <= -1.85e-15) {
		tmp = t * (x / (y * b));
	} else if ((y <= -3.6e-21) || !(y <= 5.8e+96)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.4d+69)) then
        tmp = z / b
    else if (y <= (-1.85d-15)) then
        tmp = t * (x / (y * b))
    else if ((y <= (-3.6d-21)) .or. (.not. (y <= 5.8d+96))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.4e+69) {
		tmp = z / b;
	} else if (y <= -1.85e-15) {
		tmp = t * (x / (y * b));
	} else if ((y <= -3.6e-21) || !(y <= 5.8e+96)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.4e+69:
		tmp = z / b
	elif y <= -1.85e-15:
		tmp = t * (x / (y * b))
	elif (y <= -3.6e-21) or not (y <= 5.8e+96):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.4e+69)
		tmp = Float64(z / b);
	elseif (y <= -1.85e-15)
		tmp = Float64(t * Float64(x / Float64(y * b)));
	elseif ((y <= -3.6e-21) || !(y <= 5.8e+96))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.4e+69)
		tmp = z / b;
	elseif (y <= -1.85e-15)
		tmp = t * (x / (y * b));
	elseif ((y <= -3.6e-21) || ~((y <= 5.8e+96)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.4e+69], N[(z / b), $MachinePrecision], If[LessEqual[y, -1.85e-15], N[(t * N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3.6e-21], N[Not[LessEqual[y, 5.8e+96]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.39999999999999991e69 or -1.85000000000000008e-15 < y < -3.59999999999999989e-21 or 5.79999999999999955e96 < y

   1. Initial program 51.1%

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

      1. associate-/l* 60.4%

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

      2. associate-/l* 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in y around inf 58.4%

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

   if -1.39999999999999991e69 < y < -1.85000000000000008e-15

   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. associate-/l* 76.1%

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

      2. associate-/l* 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in x around inf 58.8%

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

   6. Taylor expanded in y around inf 51.3%

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

      1. associate-/l* 51.5%

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

      2. *-commutative 51.5%

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

   8. Simplified 51.5%

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

   if -3.59999999999999989e-21 < y < 5.79999999999999955e96

   1. Initial program 90.8%

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

      1. associate-/l* 83.2%

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

      2. associate-/l* 79.5%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in y around 0 53.6%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+69}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \frac{x}{y \cdot b}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-21} \lor \neg \left(y \leq 5.8 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+68}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{b \cdot \frac{y}{t} + 1}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-21} \lor \neg \left(y \leq 5.5 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.5e+68)
   (/ z b)
   (if (<= y -5e-16)
     (/ x (+ (* b (/ y t)) 1.0))
     (if (or (<= y -3.5e-21) (not (<= y 5.5e+96))) (/ z b) (/ x (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.5e+68) {
		tmp = z / b;
	} else if (y <= -5e-16) {
		tmp = x / ((b * (y / t)) + 1.0);
	} else if ((y <= -3.5e-21) || !(y <= 5.5e+96)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4.5d+68)) then
        tmp = z / b
    else if (y <= (-5d-16)) then
        tmp = x / ((b * (y / t)) + 1.0d0)
    else if ((y <= (-3.5d-21)) .or. (.not. (y <= 5.5d+96))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.5e+68) {
		tmp = z / b;
	} else if (y <= -5e-16) {
		tmp = x / ((b * (y / t)) + 1.0);
	} else if ((y <= -3.5e-21) || !(y <= 5.5e+96)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.5e+68:
		tmp = z / b
	elif y <= -5e-16:
		tmp = x / ((b * (y / t)) + 1.0)
	elif (y <= -3.5e-21) or not (y <= 5.5e+96):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.5e+68)
		tmp = Float64(z / b);
	elseif (y <= -5e-16)
		tmp = Float64(x / Float64(Float64(b * Float64(y / t)) + 1.0));
	elseif ((y <= -3.5e-21) || !(y <= 5.5e+96))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.5e+68)
		tmp = z / b;
	elseif (y <= -5e-16)
		tmp = x / ((b * (y / t)) + 1.0);
	elseif ((y <= -3.5e-21) || ~((y <= 5.5e+96)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.5e+68], N[(z / b), $MachinePrecision], If[LessEqual[y, -5e-16], N[(x / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3.5e-21], N[Not[LessEqual[y, 5.5e+96]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5000000000000003e68 or -5.0000000000000004e-16 < y < -3.5000000000000003e-21 or 5.5000000000000002e96 < y

   1. Initial program 51.1%

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

      1. associate-/l* 60.4%

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

      2. associate-/l* 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in y around inf 58.4%

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

   if -4.5000000000000003e68 < y < -5.0000000000000004e-16

   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. associate-/l* 76.1%

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

      2. associate-/l* 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in x around inf 58.8%

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

   6. Taylor expanded in a around 0 56.8%

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

      1. associate-/l* 56.7%

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

   8. Simplified 56.7%

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

   if -3.5000000000000003e-21 < y < 5.5000000000000002e96

   1. Initial program 90.8%

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

      1. associate-/l* 83.2%

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

      2. associate-/l* 79.5%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in y around 0 53.6%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+68}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{b \cdot \frac{y}{t} + 1}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-21} \lor \neg \left(y \leq 5.5 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -4.25 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + 1}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-21} \lor \neg \left(y \leq 5.5 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.5e+69)
   (/ z b)
   (if (<= y -4.25e-16)
     (/ x (+ (/ (* y b) t) 1.0))
     (if (or (<= y -3.6e-21) (not (<= y 5.5e+96))) (/ z b) (/ x (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.5e+69) {
		tmp = z / b;
	} else if (y <= -4.25e-16) {
		tmp = x / (((y * b) / t) + 1.0);
	} else if ((y <= -3.6e-21) || !(y <= 5.5e+96)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.5d+69)) then
        tmp = z / b
    else if (y <= (-4.25d-16)) then
        tmp = x / (((y * b) / t) + 1.0d0)
    else if ((y <= (-3.6d-21)) .or. (.not. (y <= 5.5d+96))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.5e+69) {
		tmp = z / b;
	} else if (y <= -4.25e-16) {
		tmp = x / (((y * b) / t) + 1.0);
	} else if ((y <= -3.6e-21) || !(y <= 5.5e+96)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.5e+69:
		tmp = z / b
	elif y <= -4.25e-16:
		tmp = x / (((y * b) / t) + 1.0)
	elif (y <= -3.6e-21) or not (y <= 5.5e+96):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.5e+69)
		tmp = Float64(z / b);
	elseif (y <= -4.25e-16)
		tmp = Float64(x / Float64(Float64(Float64(y * b) / t) + 1.0));
	elseif ((y <= -3.6e-21) || !(y <= 5.5e+96))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.5e+69)
		tmp = z / b;
	elseif (y <= -4.25e-16)
		tmp = x / (((y * b) / t) + 1.0);
	elseif ((y <= -3.6e-21) || ~((y <= 5.5e+96)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.5e+69], N[(z / b), $MachinePrecision], If[LessEqual[y, -4.25e-16], N[(x / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3.6e-21], N[Not[LessEqual[y, 5.5e+96]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.50000000000000018e69 or -4.25e-16 < y < -3.59999999999999989e-21 or 5.5000000000000002e96 < y

   1. Initial program 51.1%

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

      1. associate-/l* 60.4%

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

      2. associate-/l* 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in y around inf 58.4%

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

   if -2.50000000000000018e69 < y < -4.25e-16

   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. associate-/l* 76.1%

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

      2. associate-/l* 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in x around inf 58.8%

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

   6. Taylor expanded in a around 0 56.8%

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

   if -3.59999999999999989e-21 < y < 5.5000000000000002e96

   1. Initial program 90.8%

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

      1. associate-/l* 83.2%

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

      2. associate-/l* 79.5%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in y around 0 53.6%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -4.25 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + 1}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-21} \lor \neg \left(y \leq 5.5 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-178}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 310000:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) a)))
   (if (<= a -2.3e-10)
     t_1
     (if (<= a 4.2e-178)
       (+ x (/ (* y z) t))
       (if (<= a 310000.0) (/ z b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / a;
	double tmp;
	if (a <= -2.3e-10) {
		tmp = t_1;
	} else if (a <= 4.2e-178) {
		tmp = x + ((y * z) / t);
	} else if (a <= 310000.0) {
		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 = (x + (y * (z / t))) / a
    if (a <= (-2.3d-10)) then
        tmp = t_1
    else if (a <= 4.2d-178) then
        tmp = x + ((y * z) / t)
    else if (a <= 310000.0d0) 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 = (x + (y * (z / t))) / a;
	double tmp;
	if (a <= -2.3e-10) {
		tmp = t_1;
	} else if (a <= 4.2e-178) {
		tmp = x + ((y * z) / t);
	} else if (a <= 310000.0) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / a
	tmp = 0
	if a <= -2.3e-10:
		tmp = t_1
	elif a <= 4.2e-178:
		tmp = x + ((y * z) / t)
	elif a <= 310000.0:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / a)
	tmp = 0.0
	if (a <= -2.3e-10)
		tmp = t_1;
	elseif (a <= 4.2e-178)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (a <= 310000.0)
		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 = (x + (y * (z / t))) / a;
	tmp = 0.0;
	if (a <= -2.3e-10)
		tmp = t_1;
	elseif (a <= 4.2e-178)
		tmp = x + ((y * z) / t);
	elseif (a <= 310000.0)
		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[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -2.3e-10], t$95$1, If[LessEqual[a, 4.2e-178], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 310000.0], N[(z / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.30000000000000007e-10 or 3.1e5 < a

   1. Initial program 74.1%

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

      1. associate-/l* 75.2%

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

      2. associate-/l* 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in a around inf 56.9%

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

      1. associate-*r/ 60.2%

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

      2. *-commutative 60.2%

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

   7. Applied egg-rr 60.2%

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

   if -2.30000000000000007e-10 < a < 4.2e-178

   1. Initial program 78.1%

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

      1. associate-/l* 74.5%

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

      2. associate-/l* 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in b around 0 53.9%

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

      1. associate-*r/ 50.3%

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

      2. *-commutative 50.3%

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

      3. div-inv 50.3%

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

      4. associate-*l* 53.9%

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

   7. Applied egg-rr 53.9%

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

   8. Taylor expanded in a around 0 53.3%

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

   if 4.2e-178 < a < 3.1e5

   1. Initial program 62.9%

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

      1. associate-/l* 66.2%

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

      2. associate-/l* 72.6%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in y around inf 52.7%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-178}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 310000:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 220000:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))))
   (if (<= a -2.3e-10)
     (/ t_1 a)
     (if (<= a 1.8e-179)
       t_1
       (if (<= a 220000.0) (/ z b) (/ (+ x (* y (/ z t))) a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double tmp;
	if (a <= -2.3e-10) {
		tmp = t_1 / a;
	} else if (a <= 1.8e-179) {
		tmp = t_1;
	} else if (a <= 220000.0) {
		tmp = z / b;
	} else {
		tmp = (x + (y * (z / t))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    if (a <= (-2.3d-10)) then
        tmp = t_1 / a
    else if (a <= 1.8d-179) then
        tmp = t_1
    else if (a <= 220000.0d0) then
        tmp = z / b
    else
        tmp = (x + (y * (z / t))) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double tmp;
	if (a <= -2.3e-10) {
		tmp = t_1 / a;
	} else if (a <= 1.8e-179) {
		tmp = t_1;
	} else if (a <= 220000.0) {
		tmp = z / b;
	} else {
		tmp = (x + (y * (z / t))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	tmp = 0
	if a <= -2.3e-10:
		tmp = t_1 / a
	elif a <= 1.8e-179:
		tmp = t_1
	elif a <= 220000.0:
		tmp = z / b
	else:
		tmp = (x + (y * (z / t))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (a <= -2.3e-10)
		tmp = Float64(t_1 / a);
	elseif (a <= 1.8e-179)
		tmp = t_1;
	elseif (a <= 220000.0)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	tmp = 0.0;
	if (a <= -2.3e-10)
		tmp = t_1 / a;
	elseif (a <= 1.8e-179)
		tmp = t_1;
	elseif (a <= 220000.0)
		tmp = z / b;
	else
		tmp = (x + (y * (z / t))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e-10], N[(t$95$1 / a), $MachinePrecision], If[LessEqual[a, 1.8e-179], t$95$1, If[LessEqual[a, 220000.0], N[(z / b), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.30000000000000007e-10

   1. Initial program 75.0%

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

      1. associate-/l* 69.4%

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

      2. associate-/l* 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in a around inf 59.6%

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

   if -2.30000000000000007e-10 < a < 1.80000000000000004e-179

   1. Initial program 78.1%

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

      1. associate-/l* 74.5%

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

      2. associate-/l* 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in b around 0 53.9%

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

      1. associate-*r/ 50.3%

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

      2. *-commutative 50.3%

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

      3. div-inv 50.3%

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

      4. associate-*l* 53.9%

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

   7. Applied egg-rr 53.9%

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

   8. Taylor expanded in a around 0 53.3%

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

   if 1.80000000000000004e-179 < a < 2.2e5

   1. Initial program 62.9%

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

      1. associate-/l* 66.2%

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

      2. associate-/l* 72.6%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in y around inf 52.7%

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

   if 2.2e5 < a

   1. Initial program 73.5%

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

      1. associate-/l* 79.2%

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

      2. associate-/l* 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in a around inf 54.9%

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

      1. associate-*r/ 62.0%

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

      2. *-commutative 62.0%

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

   7. Applied egg-rr 62.0%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-179}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 220000:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+32} \lor \neg \left(y \leq 5.5 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.1e+32) (not (<= y 5.5e+96)))
   (+ (/ z b) (* t (/ x (* y b))))
   (/ x (+ (/ (* y b) t) (+ a 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.1e+32) || !(y <= 5.5e+96)) {
		tmp = (z / b) + (t * (x / (y * b)));
	} else {
		tmp = x / (((y * b) / t) + (a + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.1d+32)) .or. (.not. (y <= 5.5d+96))) then
        tmp = (z / b) + (t * (x / (y * b)))
    else
        tmp = x / (((y * b) / t) + (a + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.1e+32) || !(y <= 5.5e+96)) {
		tmp = (z / b) + (t * (x / (y * b)));
	} else {
		tmp = x / (((y * b) / t) + (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.1e+32) or not (y <= 5.5e+96):
		tmp = (z / b) + (t * (x / (y * b)))
	else:
		tmp = x / (((y * b) / t) + (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.1e+32) || !(y <= 5.5e+96))
		tmp = Float64(Float64(z / b) + Float64(t * Float64(x / Float64(y * b))));
	else
		tmp = Float64(x / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.1e+32) || ~((y <= 5.5e+96)))
		tmp = (z / b) + (t * (x / (y * b)));
	else
		tmp = x / (((y * b) / t) + (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.1e+32], N[Not[LessEqual[y, 5.5e+96]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(t * N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.10000000000000004e32 or 5.5000000000000002e96 < y

   1. Initial program 50.8%

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

      1. associate-/l* 59.7%

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

      2. associate-/l* 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in b around inf 32.9%

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

   6. Taylor expanded in t around 0 61.9%

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

      1. associate-/l* 62.0%

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

      2. *-commutative 62.0%

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

   8. Simplified 62.0%

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

   if -5.10000000000000004e32 < y < 5.5000000000000002e96

   1. Initial program 89.9%

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

      1. associate-/l* 83.1%

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

      2. associate-/l* 79.9%

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

   3. Simplified 79.9%

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

   5. Taylor expanded in x around inf 64.8%

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

      1. associate-+r+ 64.8%

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

      2. *-commutative 64.8%

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

   7. Simplified 64.8%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+32} \lor \neg \left(y \leq 5.5 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 63.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+32} \lor \neg \left(y \leq 2.25 \cdot 10^{+170}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.2e+32) (not (<= y 2.25e+170)))
   (+ (/ z b) (* t (/ x (* y b))))
   (/ x (+ (* b (/ y t)) (+ a 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.2e+32) || !(y <= 2.25e+170)) {
		tmp = (z / b) + (t * (x / (y * b)));
	} else {
		tmp = x / ((b * (y / t)) + (a + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-6.2d+32)) .or. (.not. (y <= 2.25d+170))) then
        tmp = (z / b) + (t * (x / (y * b)))
    else
        tmp = x / ((b * (y / t)) + (a + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.2e+32) || !(y <= 2.25e+170)) {
		tmp = (z / b) + (t * (x / (y * b)));
	} else {
		tmp = x / ((b * (y / t)) + (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.2e+32) or not (y <= 2.25e+170):
		tmp = (z / b) + (t * (x / (y * b)))
	else:
		tmp = x / ((b * (y / t)) + (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.2e+32) || !(y <= 2.25e+170))
		tmp = Float64(Float64(z / b) + Float64(t * Float64(x / Float64(y * b))));
	else
		tmp = Float64(x / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.2e+32) || ~((y <= 2.25e+170)))
		tmp = (z / b) + (t * (x / (y * b)));
	else
		tmp = x / ((b * (y / t)) + (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.2e+32], N[Not[LessEqual[y, 2.25e+170]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(t * N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.19999999999999986e32 or 2.25000000000000011e170 < y

   1. Initial program 51.7%

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

      1. associate-/l* 58.2%

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

      2. associate-/l* 64.1%

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

   3. Simplified 64.1%

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

   5. Taylor expanded in b around inf 35.5%

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

   6. Taylor expanded in t around 0 65.8%

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

      1. associate-/l* 67.0%

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

      2. *-commutative 67.0%

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

   8. Simplified 67.0%

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

   if -6.19999999999999986e32 < y < 2.25000000000000011e170

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-/l* 87.1%

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

   4. Applied egg-rr 87.1%

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

      1. *-commutative 85.0%

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

      2. associate-/l* 86.7%

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

   6. Applied egg-rr 89.4%

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

   7. Taylor expanded in x around inf 62.8%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+32} \lor \neg \left(y \leq 2.25 \cdot 10^{+170}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 67.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+72} \lor \neg \left(b \leq 8 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -9.2e+72) (not (<= b 8e+56)))
   (+ (/ z b) (* t (/ x (* y b))))
   (/ (+ x (* z (/ y t))) (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9.2e+72) || !(b <= 8e+56)) {
		tmp = (z / b) + (t * (x / (y * b)));
	} else {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-9.2d+72)) .or. (.not. (b <= 8d+56))) then
        tmp = (z / b) + (t * (x / (y * b)))
    else
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9.2e+72) || !(b <= 8e+56)) {
		tmp = (z / b) + (t * (x / (y * b)));
	} else {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -9.2e+72) or not (b <= 8e+56):
		tmp = (z / b) + (t * (x / (y * b)))
	else:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -9.2e+72) || !(b <= 8e+56))
		tmp = Float64(Float64(z / b) + Float64(t * Float64(x / Float64(y * b))));
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -9.2e+72) || ~((b <= 8e+56)))
		tmp = (z / b) + (t * (x / (y * b)));
	else
		tmp = (x + (z * (y / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -9.2e+72], N[Not[LessEqual[b, 8e+56]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(t * N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.199999999999999e72 or 8.00000000000000074e56 < b

   1. Initial program 60.9%

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

      1. associate-/l* 57.9%

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

      2. associate-/l* 60.8%

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

   3. Simplified 60.8%

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

   5. Taylor expanded in b around inf 45.8%

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

   6. Taylor expanded in t around 0 71.9%

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

      1. associate-/l* 74.6%

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

      2. *-commutative 74.6%

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

   8. Simplified 74.6%

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

   if -9.199999999999999e72 < b < 8.00000000000000074e56

   1. Initial program 82.2%

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

      1. associate-/l* 83.0%

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

      2. associate-/l* 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in b around 0 70.3%

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

      1. *-commutative 82.2%

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

      2. associate-/l* 85.1%

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

   7. Applied egg-rr 74.9%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+72} \lor \neg \left(b \leq 8 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 310000:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.0)
   (/ x a)
   (if (<= a -2.5e-201) x (if (<= a 310000.0) (/ z b) (/ x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.0) {
		tmp = x / a;
	} else if (a <= -2.5e-201) {
		tmp = x;
	} else if (a <= 310000.0) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.0d0)) then
        tmp = x / a
    else if (a <= (-2.5d-201)) then
        tmp = x
    else if (a <= 310000.0d0) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.0) {
		tmp = x / a;
	} else if (a <= -2.5e-201) {
		tmp = x;
	} else if (a <= 310000.0) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.0:
		tmp = x / a
	elif a <= -2.5e-201:
		tmp = x
	elif a <= 310000.0:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.0)
		tmp = Float64(x / a);
	elseif (a <= -2.5e-201)
		tmp = x;
	elseif (a <= 310000.0)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.0)
		tmp = x / a;
	elseif (a <= -2.5e-201)
		tmp = x;
	elseif (a <= 310000.0)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.0], N[(x / a), $MachinePrecision], If[LessEqual[a, -2.5e-201], x, If[LessEqual[a, 310000.0], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1 or 3.1e5 < a

   1. Initial program 74.7%

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

      1. associate-/l* 75.8%

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

      2. associate-/l* 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in y around 0 45.2%

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

   6. Taylor expanded in a around inf 45.2%

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

   if -1 < a < -2.5e-201

   1. Initial program 82.4%

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

      1. associate-/l* 82.5%

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

      2. associate-/l* 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in y around 0 40.7%

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

   6. Taylor expanded in a around 0 39.5%

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

   if -2.5e-201 < a < 3.1e5

   1. Initial program 69.3%

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

      1. associate-/l* 65.9%

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

      2. associate-/l* 70.4%

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

   3. Simplified 70.4%

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

   5. Taylor expanded in y around inf 44.5%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 310000:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 56.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+33} \lor \neg \left(y \leq 6.5 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4e+33) (not (<= y 6.5e+96))) (/ z b) (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4e+33) || !(y <= 6.5e+96)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4d+33)) .or. (.not. (y <= 6.5d+96))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4e+33) || !(y <= 6.5e+96)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4e+33) or not (y <= 6.5e+96):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4e+33) || !(y <= 6.5e+96))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4e+33) || ~((y <= 6.5e+96)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4e+33], N[Not[LessEqual[y, 6.5e+96]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9999999999999998e33 or 6.5e96 < y

   1. Initial program 51.2%

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

      1. associate-/l* 60.3%

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

      2. associate-/l* 68.0%

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

   3. Simplified 68.0%

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

   5. Taylor expanded in y around inf 55.3%

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

   if -3.9999999999999998e33 < y < 6.5e96

   1. Initial program 89.4%

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

      1. associate-/l* 82.6%

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

      2. associate-/l* 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in y around 0 52.1%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+33} \lor \neg \left(y \leq 6.5 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 42.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \lor \neg \left(a \leq 660000\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.0) (not (<= a 660000.0))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.0) || !(a <= 660000.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.0d0)) .or. (.not. (a <= 660000.0d0))) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.0) || !(a <= 660000.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.0) or not (a <= 660000.0):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.0) || !(a <= 660000.0))
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.0) || ~((a <= 660000.0)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.0], N[Not[LessEqual[a, 660000.0]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1 or 6.6e5 < a

   1. Initial program 74.5%

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

      1. associate-/l* 75.6%

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

      2. associate-/l* 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in y around 0 45.6%

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

   6. Taylor expanded in a around inf 45.5%

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

   if -1 < a < 6.6e5

   1. Initial program 74.4%

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

      1. associate-/l* 72.4%

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

      2. associate-/l* 74.5%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in y around 0 31.0%

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

   6. Taylor expanded in a around 0 30.2%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \lor \neg \left(a \leq 660000\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 20.0% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.5%

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

   1. associate-/l* 73.9%

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

   2. associate-/l* 74.9%

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

3. Simplified 74.9%

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

5. Taylor expanded in y around 0 37.9%

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

6. Taylor expanded in a around 0 17.7%

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

7. Final simplification 17.7%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 79.7% 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 2024076 
(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))))