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

Percentage Accurate: 75.5% → 89.9%

Time: 16.8s

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: 75.5% 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: 89.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := \left(a + y \cdot \frac{b}{t}\right) + 1\\ t_3 := \frac{x + \frac{y \cdot z}{t}}{t\_1}\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{-324}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t\_1}\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \left(\frac{x}{b} + \frac{z \cdot \left(-1 - a\right)}{{b}^{2}}\right)}{y}\\ \mathbf{elif}\;t\_3 \leq 10^{+260}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_2} + \frac{y}{t \cdot t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0)))
        (t_2 (+ (+ a (* y (/ b t))) 1.0))
        (t_3 (/ (+ x (/ (* y z) t)) t_1)))
   (if (<= t_3 -5e-324)
     (/ (+ x (* z (/ y t))) t_1)
     (if (<= t_3 0.0)
       (+ (/ z b) (/ (* t (+ (/ x b) (/ (* z (- -1.0 a)) (pow b 2.0)))) y))
       (if (<= t_3 1e+260)
         t_3
         (if (<= t_3 INFINITY)
           (* z (+ (/ x (* z t_2)) (/ y (* t t_2))))
           (/ 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 = (a + (y * (b / t))) + 1.0;
	double t_3 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_3 <= -5e-324) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_3 <= 0.0) {
		tmp = (z / b) + ((t * ((x / b) + ((z * (-1.0 - a)) / pow(b, 2.0)))) / y);
	} else if (t_3 <= 1e+260) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = z * ((x / (z * t_2)) + (y / (t * t_2)));
	} 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 = (a + (y * (b / t))) + 1.0;
	double t_3 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_3 <= -5e-324) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_3 <= 0.0) {
		tmp = (z / b) + ((t * ((x / b) + ((z * (-1.0 - a)) / Math.pow(b, 2.0)))) / y);
	} else if (t_3 <= 1e+260) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = z * ((x / (z * t_2)) + (y / (t * t_2)));
	} 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 = (a + (y * (b / t))) + 1.0
	t_3 = (x + ((y * z) / t)) / t_1
	tmp = 0
	if t_3 <= -5e-324:
		tmp = (x + (z * (y / t))) / t_1
	elif t_3 <= 0.0:
		tmp = (z / b) + ((t * ((x / b) + ((z * (-1.0 - a)) / math.pow(b, 2.0)))) / y)
	elif t_3 <= 1e+260:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = z * ((x / (z * t_2)) + (y / (t * t_2)))
	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(Float64(a + Float64(y * Float64(b / t))) + 1.0)
	t_3 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_3 <= -5e-324)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(Float64(x / b) + Float64(Float64(z * Float64(-1.0 - a)) / (b ^ 2.0)))) / y));
	elseif (t_3 <= 1e+260)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_2)) + Float64(y / Float64(t * t_2))));
	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 = (a + (y * (b / t))) + 1.0;
	t_3 = (x + ((y * z) / t)) / t_1;
	tmp = 0.0;
	if (t_3 <= -5e-324)
		tmp = (x + (z * (y / t))) / t_1;
	elseif (t_3 <= 0.0)
		tmp = (z / b) + ((t * ((x / b) + ((z * (-1.0 - a)) / (b ^ 2.0)))) / y);
	elseif (t_3 <= 1e+260)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = z * ((x / (z * t_2)) + (y / (t * t_2)));
	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[(N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, -5e-324], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(N[(x / b), $MachinePrecision] + N[(N[(z * N[(-1.0 - a), $MachinePrecision]), $MachinePrecision] / N[Power[b, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+260], t$95$3, If[LessEqual[t$95$3, Infinity], N[(z * N[(N[(x / N[(z * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -4.94066e-324

   1. Initial program 93.7%

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

      1. *-commutative 93.7%

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

      2. associate-/l* 98.7%

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

   4. Applied egg-rr 98.7%

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

   if -4.94066e-324 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 56.4%

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

      1. associate-/l* 56.4%

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

      2. associate-/l* 70.1%

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

   3. Simplified 70.1%

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

   5. Taylor expanded in y around -inf 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

      4. distribute-lft-out-- 66.4%

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

      5. mul-1-neg 66.4%

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

      6. associate-/l* 66.8%

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

      7. associate-/l* 76.1%

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

      8. distribute-lft-out-- 76.1%

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

   7. Simplified 76.1%

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

   if 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.00000000000000007e260

   1. Initial program 99.8%

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

   if 1.00000000000000007e260 < (/.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 52.5%

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

      1. associate-/l* 57.4%

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

      2. associate-/l* 57.4%

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

   3. Simplified 57.4%

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

   5. Taylor expanded in z around inf 87.7%

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

      1. associate-*l/ 87.7%

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

      2. *-commutative 87.7%

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

      3. associate-*l/ 87.7%

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

      4. *-commutative 87.7%

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

   7. Simplified 87.7%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.4%

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

      2. associate-/l* 4.4%

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

   3. Simplified 4.4%

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

   5. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-324}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \left(\frac{x}{b} + \frac{z \cdot \left(-1 - a\right)}{{b}^{2}}\right)}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+260}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(\left(a + y \cdot \frac{b}{t}\right) + 1\right)} + \frac{y}{t \cdot \left(\left(a + y \cdot \frac{b}{t}\right) + 1\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t\_2}{t\_1}\\ t_4 := \left(a + y \cdot \frac{b}{t}\right) + 1\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{-189}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t\_1}\\ \mathbf{elif}\;t\_3 \leq 10^{+260}:\\ \;\;\;\;\frac{t\_2}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_4} + \frac{y}{t \cdot t\_4}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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))
        (t_4 (+ (+ a (* y (/ b t))) 1.0)))
   (if (<= t_3 -2e-189)
     (/ (+ x (* z (/ y t))) t_1)
     (if (<= t_3 1e+260)
       (/ t_2 (+ (+ a 1.0) (* b (/ y t))))
       (if (<= t_3 INFINITY)
         (* z (+ (/ x (* z t_4)) (/ y (* t t_4))))
         (/ 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 t_4 = (a + (y * (b / t))) + 1.0;
	double tmp;
	if (t_3 <= -2e-189) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_3 <= 1e+260) {
		tmp = t_2 / ((a + 1.0) + (b * (y / t)));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = z * ((x / (z * t_4)) + (y / (t * t_4)));
	} 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 t_4 = (a + (y * (b / t))) + 1.0;
	double tmp;
	if (t_3 <= -2e-189) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_3 <= 1e+260) {
		tmp = t_2 / ((a + 1.0) + (b * (y / t)));
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = z * ((x / (z * t_4)) + (y / (t * t_4)));
	} 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
	t_4 = (a + (y * (b / t))) + 1.0
	tmp = 0
	if t_3 <= -2e-189:
		tmp = (x + (z * (y / t))) / t_1
	elif t_3 <= 1e+260:
		tmp = t_2 / ((a + 1.0) + (b * (y / t)))
	elif t_3 <= math.inf:
		tmp = z * ((x / (z * t_4)) + (y / (t * t_4)))
	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)
	t_4 = Float64(Float64(a + Float64(y * Float64(b / t))) + 1.0)
	tmp = 0.0
	if (t_3 <= -2e-189)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	elseif (t_3 <= 1e+260)
		tmp = Float64(t_2 / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	elseif (t_3 <= Inf)
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_4)) + Float64(y / Float64(t * t_4))));
	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;
	t_4 = (a + (y * (b / t))) + 1.0;
	tmp = 0.0;
	if (t_3 <= -2e-189)
		tmp = (x + (z * (y / t))) / t_1;
	elseif (t_3 <= 1e+260)
		tmp = t_2 / ((a + 1.0) + (b * (y / t)));
	elseif (t_3 <= Inf)
		tmp = z * ((x / (z * t_4)) + (y / (t * t_4)));
	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]}, Block[{t$95$4 = N[(N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[t$95$3, -2e-189], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$3, 1e+260], N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(z * N[(N[(x / N[(z * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -2.00000000000000014e-189

   1. Initial program 92.9%

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

      1. *-commutative 92.9%

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

      2. associate-/l* 98.6%

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

   4. Applied egg-rr 98.6%

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

   if -2.00000000000000014e-189 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.00000000000000007e260

   1. Initial program 85.5%

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

      1. *-commutative 85.5%

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

      2. associate-/l* 88.4%

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

   4. Applied egg-rr 88.4%

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

   if 1.00000000000000007e260 < (/.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 52.5%

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

      1. associate-/l* 57.4%

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

      2. associate-/l* 57.4%

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

   3. Simplified 57.4%

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

   5. Taylor expanded in z around inf 87.7%

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

      1. associate-*l/ 87.7%

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

      2. *-commutative 87.7%

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

      3. associate-*l/ 87.7%

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

      4. *-commutative 87.7%

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

   7. Simplified 87.7%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.4%

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

      2. associate-/l* 4.4%

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

   3. Simplified 4.4%

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

   5. Taylor expanded in y around inf 100.0%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-189}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+260}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(\left(a + y \cdot \frac{b}{t}\right) + 1\right)} + \frac{y}{t \cdot \left(\left(a + y \cdot \frac{b}{t}\right) + 1\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t\_2}{t\_1}\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{-189}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t\_1}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{t\_2}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0)))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (/ t_2 t_1)))
   (if (<= t_3 -2e-189)
     (/ (+ x (* z (/ y t))) t_1)
     (if (<= t_3 5e+301) (/ t_2 (+ (+ a 1.0) (* b (/ y t)))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((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 <= -2e-189) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_3 <= 5e+301) {
		tmp = t_2 / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = ((y * b) / t) + (a + 1.0d0)
    t_2 = x + ((y * z) / t)
    t_3 = t_2 / t_1
    if (t_3 <= (-2d-189)) then
        tmp = (x + (z * (y / t))) / t_1
    else if (t_3 <= 5d+301) then
        tmp = t_2 / ((a + 1.0d0) + (b * (y / t)))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double 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 <= -2e-189) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_3 <= 5e+301) {
		tmp = t_2 / ((a + 1.0) + (b * (y / t)));
	} 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 <= -2e-189:
		tmp = (x + (z * (y / t))) / t_1
	elif t_3 <= 5e+301:
		tmp = t_2 / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(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 <= -2e-189)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	elseif (t_3 <= 5e+301)
		tmp = Float64(t_2 / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * b) / t) + (a + 1.0);
	t_2 = x + ((y * z) / t);
	t_3 = t_2 / t_1;
	tmp = 0.0;
	if (t_3 <= -2e-189)
		tmp = (x + (z * (y / t))) / t_1;
	elseif (t_3 <= 5e+301)
		tmp = t_2 / ((a + 1.0) + (b * (y / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(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, -2e-189], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$3, 5e+301], N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $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))) < -2.00000000000000014e-189

   1. Initial program 92.9%

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

      1. *-commutative 92.9%

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

      2. associate-/l* 98.6%

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

   4. Applied egg-rr 98.6%

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

   if -2.00000000000000014e-189 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.0000000000000004e301

   1. Initial program 86.3%

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

      1. *-commutative 86.3%

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

      2. associate-/l* 89.1%

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

   4. Applied egg-rr 89.1%

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

   if 5.0000000000000004e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.6%

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

      1. associate-/l* 23.8%

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

      2. associate-/l* 26.2%

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

   3. Simplified 26.2%

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

   5. Taylor expanded in y around inf 78.5%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-189}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{if}\;b \leq -4.6 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+103}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+133} \lor \neg \left(b \leq 1.66 \cdot 10^{+165}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ (+ a (/ (* y b) t)) 1.0))))
   (if (<= b -4.6e+77)
     t_1
     (if (<= b -4.6e+22)
       (/ z b)
       (if (<= b 3.6e+103)
         (/ (+ x (* y (/ z t))) (+ a 1.0))
         (if (or (<= b 8.8e+133) (not (<= b 1.66e+165))) (/ z b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a + ((y * b) / t)) + 1.0);
	double tmp;
	if (b <= -4.6e+77) {
		tmp = t_1;
	} else if (b <= -4.6e+22) {
		tmp = z / b;
	} else if (b <= 3.6e+103) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if ((b <= 8.8e+133) || !(b <= 1.66e+165)) {
		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 / ((a + ((y * b) / t)) + 1.0d0)
    if (b <= (-4.6d+77)) then
        tmp = t_1
    else if (b <= (-4.6d+22)) then
        tmp = z / b
    else if (b <= 3.6d+103) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else if ((b <= 8.8d+133) .or. (.not. (b <= 1.66d+165))) 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 / ((a + ((y * b) / t)) + 1.0);
	double tmp;
	if (b <= -4.6e+77) {
		tmp = t_1;
	} else if (b <= -4.6e+22) {
		tmp = z / b;
	} else if (b <= 3.6e+103) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if ((b <= 8.8e+133) || !(b <= 1.66e+165)) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a + ((y * b) / t)) + 1.0)
	tmp = 0
	if b <= -4.6e+77:
		tmp = t_1
	elif b <= -4.6e+22:
		tmp = z / b
	elif b <= 3.6e+103:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	elif (b <= 8.8e+133) or not (b <= 1.66e+165):
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a + Float64(Float64(y * b) / t)) + 1.0))
	tmp = 0.0
	if (b <= -4.6e+77)
		tmp = t_1;
	elseif (b <= -4.6e+22)
		tmp = Float64(z / b);
	elseif (b <= 3.6e+103)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	elseif ((b <= 8.8e+133) || !(b <= 1.66e+165))
		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 / ((a + ((y * b) / t)) + 1.0);
	tmp = 0.0;
	if (b <= -4.6e+77)
		tmp = t_1;
	elseif (b <= -4.6e+22)
		tmp = z / b;
	elseif (b <= 3.6e+103)
		tmp = (x + (y * (z / t))) / (a + 1.0);
	elseif ((b <= 8.8e+133) || ~((b <= 1.66e+165)))
		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[(x / N[(N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.6e+77], t$95$1, If[LessEqual[b, -4.6e+22], N[(z / b), $MachinePrecision], If[LessEqual[b, 3.6e+103], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 8.8e+133], N[Not[LessEqual[b, 1.66e+165]], $MachinePrecision]], N[(z / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.5999999999999999e77 or 8.8e133 < b < 1.66e165

   1. Initial program 69.7%

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

      1. associate-/l* 69.6%

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

      2. associate-/l* 65.3%

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

   3. Simplified 65.3%

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

   5. Taylor expanded in x around inf 70.5%

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

   if -4.5999999999999999e77 < b < -4.6000000000000004e22 or 3.60000000000000017e103 < b < 8.8e133 or 1.66e165 < b

   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* 54.0%

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

      2. associate-/l* 53.6%

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

   3. Simplified 53.6%

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

   5. Taylor expanded in y around inf 67.4%

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

   if -4.6000000000000004e22 < b < 3.60000000000000017e103

   1. Initial program 85.9%

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

      1. associate-/l* 86.6%

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

      2. associate-/l* 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in y around 0 76.5%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+103}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+133} \lor \neg \left(b \leq 1.66 \cdot 10^{+165}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{if}\;b \leq -2.35 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+105}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+134} \lor \neg \left(b \leq 1.4 \cdot 10^{+165}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ (+ a (/ (* y b) t)) 1.0))))
   (if (<= b -2.35e+79)
     t_1
     (if (<= b -6.5e+22)
       (/ z b)
       (if (<= b 1.25e+105)
         (/ (+ x (* z (/ y t))) (+ a 1.0))
         (if (or (<= b 4.4e+134) (not (<= b 1.4e+165))) (/ z b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a + ((y * b) / t)) + 1.0);
	double tmp;
	if (b <= -2.35e+79) {
		tmp = t_1;
	} else if (b <= -6.5e+22) {
		tmp = z / b;
	} else if (b <= 1.25e+105) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if ((b <= 4.4e+134) || !(b <= 1.4e+165)) {
		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 / ((a + ((y * b) / t)) + 1.0d0)
    if (b <= (-2.35d+79)) then
        tmp = t_1
    else if (b <= (-6.5d+22)) then
        tmp = z / b
    else if (b <= 1.25d+105) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else if ((b <= 4.4d+134) .or. (.not. (b <= 1.4d+165))) 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 / ((a + ((y * b) / t)) + 1.0);
	double tmp;
	if (b <= -2.35e+79) {
		tmp = t_1;
	} else if (b <= -6.5e+22) {
		tmp = z / b;
	} else if (b <= 1.25e+105) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if ((b <= 4.4e+134) || !(b <= 1.4e+165)) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a + ((y * b) / t)) + 1.0)
	tmp = 0
	if b <= -2.35e+79:
		tmp = t_1
	elif b <= -6.5e+22:
		tmp = z / b
	elif b <= 1.25e+105:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	elif (b <= 4.4e+134) or not (b <= 1.4e+165):
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a + Float64(Float64(y * b) / t)) + 1.0))
	tmp = 0.0
	if (b <= -2.35e+79)
		tmp = t_1;
	elseif (b <= -6.5e+22)
		tmp = Float64(z / b);
	elseif (b <= 1.25e+105)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	elseif ((b <= 4.4e+134) || !(b <= 1.4e+165))
		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 / ((a + ((y * b) / t)) + 1.0);
	tmp = 0.0;
	if (b <= -2.35e+79)
		tmp = t_1;
	elseif (b <= -6.5e+22)
		tmp = z / b;
	elseif (b <= 1.25e+105)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	elseif ((b <= 4.4e+134) || ~((b <= 1.4e+165)))
		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[(x / N[(N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.35e+79], t$95$1, If[LessEqual[b, -6.5e+22], N[(z / b), $MachinePrecision], If[LessEqual[b, 1.25e+105], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 4.4e+134], N[Not[LessEqual[b, 1.4e+165]], $MachinePrecision]], N[(z / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.35000000000000011e79 or 4.4e134 < b < 1.3999999999999999e165

   1. Initial program 69.7%

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

      1. associate-/l* 69.6%

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

      2. associate-/l* 65.3%

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

   3. Simplified 65.3%

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

   5. Taylor expanded in x around inf 70.5%

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

   if -2.35000000000000011e79 < b < -6.49999999999999979e22 or 1.25000000000000011e105 < b < 4.4e134 or 1.3999999999999999e165 < b

   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* 54.0%

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

      2. associate-/l* 53.6%

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

   3. Simplified 53.6%

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

   5. Taylor expanded in y around inf 67.4%

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

   if -6.49999999999999979e22 < b < 1.25000000000000011e105

   1. Initial program 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-/l* 89.5%

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

   4. Applied egg-rr 89.5%

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

   5. Taylor expanded in y around 0 80.3%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.35 \cdot 10^{+79}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+105}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+134} \lor \neg \left(b \leq 1.4 \cdot 10^{+165}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{+20}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+103}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+134} \lor \neg \left(b \leq 3.1 \cdot 10^{+156}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ (+ a (/ (* y b) t)) 1.0))))
   (if (<= b -8.5e+77)
     t_1
     (if (<= b -2.8e+20)
       (/ z b)
       (if (<= b 6.2e+103)
         (/ (+ x (/ z (/ t y))) (+ a 1.0))
         (if (or (<= b 1.75e+134) (not (<= b 3.1e+156))) (/ z b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a + ((y * b) / t)) + 1.0);
	double tmp;
	if (b <= -8.5e+77) {
		tmp = t_1;
	} else if (b <= -2.8e+20) {
		tmp = z / b;
	} else if (b <= 6.2e+103) {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	} else if ((b <= 1.75e+134) || !(b <= 3.1e+156)) {
		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 / ((a + ((y * b) / t)) + 1.0d0)
    if (b <= (-8.5d+77)) then
        tmp = t_1
    else if (b <= (-2.8d+20)) then
        tmp = z / b
    else if (b <= 6.2d+103) then
        tmp = (x + (z / (t / y))) / (a + 1.0d0)
    else if ((b <= 1.75d+134) .or. (.not. (b <= 3.1d+156))) 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 / ((a + ((y * b) / t)) + 1.0);
	double tmp;
	if (b <= -8.5e+77) {
		tmp = t_1;
	} else if (b <= -2.8e+20) {
		tmp = z / b;
	} else if (b <= 6.2e+103) {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	} else if ((b <= 1.75e+134) || !(b <= 3.1e+156)) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a + ((y * b) / t)) + 1.0)
	tmp = 0
	if b <= -8.5e+77:
		tmp = t_1
	elif b <= -2.8e+20:
		tmp = z / b
	elif b <= 6.2e+103:
		tmp = (x + (z / (t / y))) / (a + 1.0)
	elif (b <= 1.75e+134) or not (b <= 3.1e+156):
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a + Float64(Float64(y * b) / t)) + 1.0))
	tmp = 0.0
	if (b <= -8.5e+77)
		tmp = t_1;
	elseif (b <= -2.8e+20)
		tmp = Float64(z / b);
	elseif (b <= 6.2e+103)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + 1.0));
	elseif ((b <= 1.75e+134) || !(b <= 3.1e+156))
		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 / ((a + ((y * b) / t)) + 1.0);
	tmp = 0.0;
	if (b <= -8.5e+77)
		tmp = t_1;
	elseif (b <= -2.8e+20)
		tmp = z / b;
	elseif (b <= 6.2e+103)
		tmp = (x + (z / (t / y))) / (a + 1.0);
	elseif ((b <= 1.75e+134) || ~((b <= 3.1e+156)))
		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[(x / N[(N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.5e+77], t$95$1, If[LessEqual[b, -2.8e+20], N[(z / b), $MachinePrecision], If[LessEqual[b, 6.2e+103], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 1.75e+134], N[Not[LessEqual[b, 3.1e+156]], $MachinePrecision]], N[(z / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.50000000000000018e77 or 1.75000000000000001e134 < b < 3.1000000000000002e156

   1. Initial program 69.7%

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

      1. associate-/l* 69.6%

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

      2. associate-/l* 65.3%

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

   3. Simplified 65.3%

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

   5. Taylor expanded in x around inf 70.5%

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

   if -8.50000000000000018e77 < b < -2.8e20 or 6.2000000000000003e103 < b < 1.75000000000000001e134 or 3.1000000000000002e156 < b

   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* 54.0%

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

      2. associate-/l* 53.6%

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

   3. Simplified 53.6%

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

   5. Taylor expanded in y around inf 67.4%

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

   if -2.8e20 < b < 6.2000000000000003e103

   1. Initial program 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-/l* 89.5%

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

   4. Applied egg-rr 89.5%

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

   5. Taylor expanded in y around 0 80.3%

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

      1. clear-num 80.2%

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

      2. un-div-inv 80.9%

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

   7. Applied egg-rr 80.9%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{+20}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+103}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+134} \lor \neg \left(b \leq 3.1 \cdot 10^{+156}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{\left(a + y \cdot \frac{b}{t}\right) + 1}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-209}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-125}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-66}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y}{\frac{t}{b}}\right) + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.8e-84)
   (/ x (+ (+ a (* y (/ b t))) 1.0))
   (if (<= t 3.7e-209)
     (/ z b)
     (if (<= t 7e-125)
       (/ x (+ (+ a (/ (* y b) t)) 1.0))
       (if (<= t 5.8e-66) (/ z b) (/ x (+ (+ a (/ y (/ t b))) 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.8e-84) {
		tmp = x / ((a + (y * (b / t))) + 1.0);
	} else if (t <= 3.7e-209) {
		tmp = z / b;
	} else if (t <= 7e-125) {
		tmp = x / ((a + ((y * b) / t)) + 1.0);
	} else if (t <= 5.8e-66) {
		tmp = z / b;
	} else {
		tmp = x / ((a + (y / (t / b))) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.8d-84)) then
        tmp = x / ((a + (y * (b / t))) + 1.0d0)
    else if (t <= 3.7d-209) then
        tmp = z / b
    else if (t <= 7d-125) then
        tmp = x / ((a + ((y * b) / t)) + 1.0d0)
    else if (t <= 5.8d-66) then
        tmp = z / b
    else
        tmp = x / ((a + (y / (t / b))) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.8e-84) {
		tmp = x / ((a + (y * (b / t))) + 1.0);
	} else if (t <= 3.7e-209) {
		tmp = z / b;
	} else if (t <= 7e-125) {
		tmp = x / ((a + ((y * b) / t)) + 1.0);
	} else if (t <= 5.8e-66) {
		tmp = z / b;
	} else {
		tmp = x / ((a + (y / (t / b))) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.8e-84:
		tmp = x / ((a + (y * (b / t))) + 1.0)
	elif t <= 3.7e-209:
		tmp = z / b
	elif t <= 7e-125:
		tmp = x / ((a + ((y * b) / t)) + 1.0)
	elif t <= 5.8e-66:
		tmp = z / b
	else:
		tmp = x / ((a + (y / (t / b))) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.8e-84)
		tmp = Float64(x / Float64(Float64(a + Float64(y * Float64(b / t))) + 1.0));
	elseif (t <= 3.7e-209)
		tmp = Float64(z / b);
	elseif (t <= 7e-125)
		tmp = Float64(x / Float64(Float64(a + Float64(Float64(y * b) / t)) + 1.0));
	elseif (t <= 5.8e-66)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(Float64(a + Float64(y / Float64(t / b))) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.8e-84)
		tmp = x / ((a + (y * (b / t))) + 1.0);
	elseif (t <= 3.7e-209)
		tmp = z / b;
	elseif (t <= 7e-125)
		tmp = x / ((a + ((y * b) / t)) + 1.0);
	elseif (t <= 5.8e-66)
		tmp = z / b;
	else
		tmp = x / ((a + (y / (t / b))) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.8e-84], N[(x / N[(N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e-209], N[(z / b), $MachinePrecision], If[LessEqual[t, 7e-125], N[(x / N[(N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e-66], N[(z / b), $MachinePrecision], N[(x / N[(N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.80000000000000035e-84

   1. Initial program 83.9%

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

      1. associate-/l* 88.4%

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

      2. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in x around inf 67.5%

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

      1. associate-*l/ 68.5%

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

      2. *-commutative 68.5%

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

   7. Simplified 68.5%

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

   if -4.80000000000000035e-84 < t < 3.6999999999999998e-209 or 6.99999999999999995e-125 < t < 5.80000000000000023e-66

   1. Initial program 56.8%

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

      1. associate-/l* 47.7%

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

      2. associate-/l* 43.7%

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

   3. Simplified 43.7%

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

   5. Taylor expanded in y around inf 60.8%

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

   if 3.6999999999999998e-209 < t < 6.99999999999999995e-125

   1. Initial program 88.4%

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

      1. associate-/l* 71.5%

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

      2. associate-/l* 48.9%

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

   3. Simplified 48.9%

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

   5. Taylor expanded in x around inf 60.4%

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

   if 5.80000000000000023e-66 < t

   1. Initial program 85.0%

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

      1. associate-/l* 90.0%

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

      2. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in x around inf 65.6%

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

      1. associate-*l/ 68.0%

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

      2. *-commutative 68.0%

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

   7. Simplified 68.0%

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

      1. clear-num 42.3%

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

      2. un-div-inv 43.1%

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

   9. Applied egg-rr 68.8%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{\left(a + y \cdot \frac{b}{t}\right) + 1}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-209}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-125}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-66}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y}{\frac{t}{b}}\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{\left(a + y \cdot \frac{b}{t}\right) + 1}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-209}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{\frac{1}{\frac{t}{y \cdot b}} + 1}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y}{\frac{t}{b}}\right) + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.2e-85)
   (/ x (+ (+ a (* y (/ b t))) 1.0))
   (if (<= t 3.7e-209)
     (/ z b)
     (if (<= t 1.9e-108)
       (/ x (+ (/ 1.0 (/ t (* y b))) 1.0))
       (if (<= t 3.5e-68) (/ z b) (/ x (+ (+ a (/ y (/ t b))) 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.2e-85) {
		tmp = x / ((a + (y * (b / t))) + 1.0);
	} else if (t <= 3.7e-209) {
		tmp = z / b;
	} else if (t <= 1.9e-108) {
		tmp = x / ((1.0 / (t / (y * b))) + 1.0);
	} else if (t <= 3.5e-68) {
		tmp = z / b;
	} else {
		tmp = x / ((a + (y / (t / b))) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.2d-85)) then
        tmp = x / ((a + (y * (b / t))) + 1.0d0)
    else if (t <= 3.7d-209) then
        tmp = z / b
    else if (t <= 1.9d-108) then
        tmp = x / ((1.0d0 / (t / (y * b))) + 1.0d0)
    else if (t <= 3.5d-68) then
        tmp = z / b
    else
        tmp = x / ((a + (y / (t / b))) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.2e-85) {
		tmp = x / ((a + (y * (b / t))) + 1.0);
	} else if (t <= 3.7e-209) {
		tmp = z / b;
	} else if (t <= 1.9e-108) {
		tmp = x / ((1.0 / (t / (y * b))) + 1.0);
	} else if (t <= 3.5e-68) {
		tmp = z / b;
	} else {
		tmp = x / ((a + (y / (t / b))) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.2e-85:
		tmp = x / ((a + (y * (b / t))) + 1.0)
	elif t <= 3.7e-209:
		tmp = z / b
	elif t <= 1.9e-108:
		tmp = x / ((1.0 / (t / (y * b))) + 1.0)
	elif t <= 3.5e-68:
		tmp = z / b
	else:
		tmp = x / ((a + (y / (t / b))) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.2e-85)
		tmp = Float64(x / Float64(Float64(a + Float64(y * Float64(b / t))) + 1.0));
	elseif (t <= 3.7e-209)
		tmp = Float64(z / b);
	elseif (t <= 1.9e-108)
		tmp = Float64(x / Float64(Float64(1.0 / Float64(t / Float64(y * b))) + 1.0));
	elseif (t <= 3.5e-68)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(Float64(a + Float64(y / Float64(t / b))) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.2e-85)
		tmp = x / ((a + (y * (b / t))) + 1.0);
	elseif (t <= 3.7e-209)
		tmp = z / b;
	elseif (t <= 1.9e-108)
		tmp = x / ((1.0 / (t / (y * b))) + 1.0);
	elseif (t <= 3.5e-68)
		tmp = z / b;
	else
		tmp = x / ((a + (y / (t / b))) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.2e-85], N[(x / N[(N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e-209], N[(z / b), $MachinePrecision], If[LessEqual[t, 1.9e-108], N[(x / N[(N[(1.0 / N[(t / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-68], N[(z / b), $MachinePrecision], N[(x / N[(N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.20000000000000027e-85

   1. Initial program 83.9%

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

      1. associate-/l* 88.4%

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

      2. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in x around inf 67.5%

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

      1. associate-*l/ 68.5%

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

      2. *-commutative 68.5%

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

   7. Simplified 68.5%

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

   if -3.20000000000000027e-85 < t < 3.6999999999999998e-209 or 1.89999999999999987e-108 < t < 3.50000000000000013e-68

   1. Initial program 55.6%

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

      1. associate-/l* 46.3%

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

      2. associate-/l* 42.1%

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

   3. Simplified 42.1%

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

   5. Taylor expanded in y around inf 62.4%

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

   if 3.6999999999999998e-209 < t < 1.89999999999999987e-108

   1. Initial program 89.5%

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

      1. associate-/l* 74.4%

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

      2. associate-/l* 54.2%

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

   3. Simplified 54.2%

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

   5. Taylor expanded in x around inf 54.3%

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

      1. associate-*l/ 29.1%

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

      2. *-commutative 29.1%

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

   7. Simplified 29.1%

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

   8. Taylor expanded in a around 0 54.5%

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

      1. *-commutative 54.5%

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

      2. associate-*r/ 29.1%

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

   10. Simplified 29.1%

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

       1. associate-*r/ 54.5%

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

       2. clear-num 54.5%

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

   12. Applied egg-rr 54.5%

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

   if 3.50000000000000013e-68 < t

   1. Initial program 85.0%

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

      1. associate-/l* 90.0%

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

      2. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in x around inf 65.6%

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

      1. associate-*l/ 68.0%

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

      2. *-commutative 68.0%

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

   7. Simplified 68.0%

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

      1. clear-num 42.3%

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

      2. un-div-inv 43.1%

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

   9. Applied egg-rr 68.8%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{\left(a + y \cdot \frac{b}{t}\right) + 1}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-209}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{\frac{1}{\frac{t}{y \cdot b}} + 1}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y}{\frac{t}{b}}\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{y}{\frac{t}{b}} + 1}\\ t_2 := \frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{if}\;a \leq -62000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.56 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-212}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ (/ y (/ t b)) 1.0))) (t_2 (/ (+ x (* y (/ z t))) a)))
   (if (<= a -62000.0)
     t_2
     (if (<= a 1.56e-273)
       t_1
       (if (<= a 1.6e-212) (/ z b) (if (<= a 7e-12) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((y / (t / b)) + 1.0);
	double t_2 = (x + (y * (z / t))) / a;
	double tmp;
	if (a <= -62000.0) {
		tmp = t_2;
	} else if (a <= 1.56e-273) {
		tmp = t_1;
	} else if (a <= 1.6e-212) {
		tmp = z / b;
	} else if (a <= 7e-12) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((y / (t / b)) + 1.0d0)
    t_2 = (x + (y * (z / t))) / a
    if (a <= (-62000.0d0)) then
        tmp = t_2
    else if (a <= 1.56d-273) then
        tmp = t_1
    else if (a <= 1.6d-212) then
        tmp = z / b
    else if (a <= 7d-12) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((y / (t / b)) + 1.0);
	double t_2 = (x + (y * (z / t))) / a;
	double tmp;
	if (a <= -62000.0) {
		tmp = t_2;
	} else if (a <= 1.56e-273) {
		tmp = t_1;
	} else if (a <= 1.6e-212) {
		tmp = z / b;
	} else if (a <= 7e-12) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((y / (t / b)) + 1.0)
	t_2 = (x + (y * (z / t))) / a
	tmp = 0
	if a <= -62000.0:
		tmp = t_2
	elif a <= 1.56e-273:
		tmp = t_1
	elif a <= 1.6e-212:
		tmp = z / b
	elif a <= 7e-12:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(y / Float64(t / b)) + 1.0))
	t_2 = Float64(Float64(x + Float64(y * Float64(z / t))) / a)
	tmp = 0.0
	if (a <= -62000.0)
		tmp = t_2;
	elseif (a <= 1.56e-273)
		tmp = t_1;
	elseif (a <= 1.6e-212)
		tmp = Float64(z / b);
	elseif (a <= 7e-12)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / ((y / (t / b)) + 1.0);
	t_2 = (x + (y * (z / t))) / a;
	tmp = 0.0;
	if (a <= -62000.0)
		tmp = t_2;
	elseif (a <= 1.56e-273)
		tmp = t_1;
	elseif (a <= 1.6e-212)
		tmp = z / b;
	elseif (a <= 7e-12)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -62000.0], t$95$2, If[LessEqual[a, 1.56e-273], t$95$1, If[LessEqual[a, 1.6e-212], N[(z / b), $MachinePrecision], If[LessEqual[a, 7e-12], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -62000 or 7.0000000000000001e-12 < a

   1. Initial program 79.7%

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

      1. associate-/l* 78.3%

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

      2. associate-/l* 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in a around inf 68.0%

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

   if -62000 < a < 1.55999999999999994e-273 or 1.5999999999999999e-212 < a < 7.0000000000000001e-12

   1. Initial program 76.3%

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

      1. associate-/l* 76.3%

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

      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 x around inf 61.3%

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

      1. associate-*l/ 57.8%

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

      2. *-commutative 57.8%

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

   7. Simplified 57.8%

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

   8. Taylor expanded in a around 0 60.8%

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

      1. *-commutative 60.8%

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

      2. associate-*r/ 57.2%

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

   10. Simplified 57.2%

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

       1. clear-num 57.2%

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

       2. un-div-inv 57.8%

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

   12. Applied egg-rr 57.8%

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

   if 1.55999999999999994e-273 < a < 1.5999999999999999e-212

   1. Initial program 62.4%

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

      1. associate-/l* 62.7%

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

      2. associate-/l* 67.4%

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

   3. Simplified 67.4%

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

   5. Taylor expanded in y around inf 51.8%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -62000:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a \leq 1.56 \cdot 10^{-273}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{t}{b}} + 1}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-212}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{t}{b}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{y}{\frac{t}{b}} + 1}\\ \mathbf{if}\;a \leq -86:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-212}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ (/ y (/ t b)) 1.0))))
   (if (<= a -86.0)
     (/ (+ x (/ (* y z) t)) a)
     (if (<= a 2.3e-273)
       t_1
       (if (<= a 1.8e-212)
         (/ z b)
         (if (<= a 7e-12) t_1 (/ (+ 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 / (t / b)) + 1.0);
	double tmp;
	if (a <= -86.0) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (a <= 2.3e-273) {
		tmp = t_1;
	} else if (a <= 1.8e-212) {
		tmp = z / b;
	} else if (a <= 7e-12) {
		tmp = t_1;
	} 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 / (t / b)) + 1.0d0)
    if (a <= (-86.0d0)) then
        tmp = (x + ((y * z) / t)) / a
    else if (a <= 2.3d-273) then
        tmp = t_1
    else if (a <= 1.8d-212) then
        tmp = z / b
    else if (a <= 7d-12) then
        tmp = t_1
    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 / (t / b)) + 1.0);
	double tmp;
	if (a <= -86.0) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (a <= 2.3e-273) {
		tmp = t_1;
	} else if (a <= 1.8e-212) {
		tmp = z / b;
	} else if (a <= 7e-12) {
		tmp = t_1;
	} else {
		tmp = (x + (y * (z / t))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((y / (t / b)) + 1.0)
	tmp = 0
	if a <= -86.0:
		tmp = (x + ((y * z) / t)) / a
	elif a <= 2.3e-273:
		tmp = t_1
	elif a <= 1.8e-212:
		tmp = z / b
	elif a <= 7e-12:
		tmp = t_1
	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 / Float64(t / b)) + 1.0))
	tmp = 0.0
	if (a <= -86.0)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	elseif (a <= 2.3e-273)
		tmp = t_1;
	elseif (a <= 1.8e-212)
		tmp = Float64(z / b);
	elseif (a <= 7e-12)
		tmp = t_1;
	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 / (t / b)) + 1.0);
	tmp = 0.0;
	if (a <= -86.0)
		tmp = (x + ((y * z) / t)) / a;
	elseif (a <= 2.3e-273)
		tmp = t_1;
	elseif (a <= 1.8e-212)
		tmp = z / b;
	elseif (a <= 7e-12)
		tmp = t_1;
	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 / N[(t / b), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -86.0], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 2.3e-273], t$95$1, If[LessEqual[a, 1.8e-212], N[(z / b), $MachinePrecision], If[LessEqual[a, 7e-12], t$95$1, N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -86

   1. Initial program 83.4%

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

      1. associate-/l* 77.9%

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

      2. associate-/l* 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 a around inf 67.1%

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

   if -86 < a < 2.29999999999999981e-273 or 1.8e-212 < a < 7.0000000000000001e-12

   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* 77.0%

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

      2. associate-/l* 75.9%

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

   3. Simplified 75.9%

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

   5. Taylor expanded in x around inf 61.0%

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

      1. associate-*l/ 58.3%

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

      2. *-commutative 58.3%

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

   7. Simplified 58.3%

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

   8. Taylor expanded in a around 0 60.4%

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

      1. *-commutative 60.4%

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

      2. associate-*r/ 57.7%

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

   10. Simplified 57.7%

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

       1. clear-num 57.7%

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

       2. un-div-inv 58.3%

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

   12. Applied egg-rr 58.3%

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

   if 2.29999999999999981e-273 < a < 1.8e-212

   1. Initial program 62.4%

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

      1. associate-/l* 62.7%

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

      2. associate-/l* 67.4%

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

   3. Simplified 67.4%

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

   5. Taylor expanded in y around inf 51.8%

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

   if 7.0000000000000001e-12 < a

   1. Initial program 77.2%

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

      1. associate-/l* 77.4%

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

      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 a around inf 69.3%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -86:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-273}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{t}{b}} + 1}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-212}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{t}{b}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+100}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{x}{y \cdot b} + \frac{z}{t \cdot b}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.6e+77)
   (/ x (+ (+ a (/ (* y b) t)) 1.0))
   (if (<= b -6.5e+22)
     (/ z b)
     (if (<= b 5.5e+100)
       (/ (+ x (/ z (/ t y))) (+ a 1.0))
       (* t (+ (/ x (* y b)) (/ z (* t b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.6e+77) {
		tmp = x / ((a + ((y * b) / t)) + 1.0);
	} else if (b <= -6.5e+22) {
		tmp = z / b;
	} else if (b <= 5.5e+100) {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	} else {
		tmp = t * ((x / (y * b)) + (z / (t * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.6d+77)) then
        tmp = x / ((a + ((y * b) / t)) + 1.0d0)
    else if (b <= (-6.5d+22)) then
        tmp = z / b
    else if (b <= 5.5d+100) then
        tmp = (x + (z / (t / y))) / (a + 1.0d0)
    else
        tmp = t * ((x / (y * b)) + (z / (t * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.6e+77) {
		tmp = x / ((a + ((y * b) / t)) + 1.0);
	} else if (b <= -6.5e+22) {
		tmp = z / b;
	} else if (b <= 5.5e+100) {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	} else {
		tmp = t * ((x / (y * b)) + (z / (t * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.6e+77:
		tmp = x / ((a + ((y * b) / t)) + 1.0)
	elif b <= -6.5e+22:
		tmp = z / b
	elif b <= 5.5e+100:
		tmp = (x + (z / (t / y))) / (a + 1.0)
	else:
		tmp = t * ((x / (y * b)) + (z / (t * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.6e+77)
		tmp = Float64(x / Float64(Float64(a + Float64(Float64(y * b) / t)) + 1.0));
	elseif (b <= -6.5e+22)
		tmp = Float64(z / b);
	elseif (b <= 5.5e+100)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + 1.0));
	else
		tmp = Float64(t * Float64(Float64(x / Float64(y * b)) + Float64(z / Float64(t * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.6e+77)
		tmp = x / ((a + ((y * b) / t)) + 1.0);
	elseif (b <= -6.5e+22)
		tmp = z / b;
	elseif (b <= 5.5e+100)
		tmp = (x + (z / (t / y))) / (a + 1.0);
	else
		tmp = t * ((x / (y * b)) + (z / (t * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.6e+77], N[(x / N[(N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.5e+22], N[(z / b), $MachinePrecision], If[LessEqual[b, 5.5e+100], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.5999999999999999e77

   1. Initial program 68.3%

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

      1. associate-/l* 65.8%

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

      2. associate-/l* 63.4%

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

   3. Simplified 63.4%

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

   5. Taylor expanded in x around inf 66.8%

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

   if -4.5999999999999999e77 < b < -6.49999999999999979e22

   1. Initial program 53.3%

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

      1. associate-/l* 58.3%

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

      2. associate-/l* 58.1%

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

   3. Simplified 58.1%

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

   5. Taylor expanded in y around inf 66.8%

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

   if -6.49999999999999979e22 < b < 5.5000000000000002e100

   1. Initial program 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-/l* 89.5%

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

   4. Applied egg-rr 89.5%

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

   5. Taylor expanded in y around 0 80.3%

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

      1. clear-num 80.2%

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

      2. un-div-inv 80.9%

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

   7. Applied egg-rr 80.9%

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

   if 5.5000000000000002e100 < 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* 57.4%

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

      2. associate-/l* 54.7%

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

   3. Simplified 54.7%

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

   5. Taylor expanded in b around inf 39.7%

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

   6. Taylor expanded in t around inf 65.5%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+100}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{x}{y \cdot b} + \frac{z}{t \cdot b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 81.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-188} \lor \neg \left(t \leq 2.05 \cdot 10^{-170}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{1}{b} + \frac{\frac{x \cdot t}{b}}{y \cdot z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -9.5e-188) (not (<= t 2.05e-170)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (* z (+ (/ 1.0 b) (/ (/ (* x t) b) (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9.5e-188) || !(t <= 2.05e-170)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = z * ((1.0 / b) + (((x * t) / b) / (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-9.5d-188)) .or. (.not. (t <= 2.05d-170))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = z * ((1.0d0 / b) + (((x * t) / b) / (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9.5e-188) || !(t <= 2.05e-170)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = z * ((1.0 / b) + (((x * t) / b) / (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -9.5e-188) or not (t <= 2.05e-170):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = z * ((1.0 / b) + (((x * t) / b) / (y * z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -9.5e-188) || !(t <= 2.05e-170))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(z * Float64(Float64(1.0 / b) + Float64(Float64(Float64(x * t) / b) / Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -9.5e-188) || ~((t <= 2.05e-170)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	else
		tmp = z * ((1.0 / b) + (((x * t) / b) / (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -9.5e-188], N[Not[LessEqual[t, 2.05e-170]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(1.0 / b), $MachinePrecision] + N[(N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.50000000000000063e-188 or 2.04999999999999983e-170 < t

   1. Initial program 82.3%

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

      1. associate-/l* 84.5%

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

      2. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

   if -9.50000000000000063e-188 < t < 2.04999999999999983e-170

   1. Initial program 49.8%

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

      1. associate-/l* 34.5%

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

      2. associate-/l* 25.4%

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

   3. Simplified 25.4%

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

   5. Taylor expanded in b around inf 50.7%

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

   6. Taylor expanded in z around inf 71.8%

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

      1. associate-/r* 76.3%

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

   8. Simplified 76.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-188} \lor \neg \left(t \leq 2.05 \cdot 10^{-170}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{1}{b} + \frac{\frac{x \cdot t}{b}}{y \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 80.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+205}:\\ \;\;\;\;z \cdot \left(\frac{1}{b} + \frac{\frac{x \cdot t}{b}}{y \cdot z}\right)\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+164}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\frac{t}{y} \cdot \frac{x}{z} + 1}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.1e+205)
   (* z (+ (/ 1.0 b) (/ (/ (* x t) b) (* y z))))
   (if (<= y 1.06e+164)
     (/ (+ x (* z (/ y t))) (+ (/ (* y b) t) (+ a 1.0)))
     (* z (/ (+ (* (/ t y) (/ x z)) 1.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.1e+205) {
		tmp = z * ((1.0 / b) + (((x * t) / b) / (y * z)));
	} else if (y <= 1.06e+164) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else {
		tmp = z * ((((t / y) * (x / z)) + 1.0) / 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 <= (-3.1d+205)) then
        tmp = z * ((1.0d0 / b) + (((x * t) / b) / (y * z)))
    else if (y <= 1.06d+164) then
        tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0d0))
    else
        tmp = z * ((((t / y) * (x / z)) + 1.0d0) / 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 <= -3.1e+205) {
		tmp = z * ((1.0 / b) + (((x * t) / b) / (y * z)));
	} else if (y <= 1.06e+164) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else {
		tmp = z * ((((t / y) * (x / z)) + 1.0) / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.1e+205:
		tmp = z * ((1.0 / b) + (((x * t) / b) / (y * z)))
	elif y <= 1.06e+164:
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0))
	else:
		tmp = z * ((((t / y) * (x / z)) + 1.0) / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.1e+205)
		tmp = Float64(z * Float64(Float64(1.0 / b) + Float64(Float64(Float64(x * t) / b) / Float64(y * z))));
	elseif (y <= 1.06e+164)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	else
		tmp = Float64(z * Float64(Float64(Float64(Float64(t / y) * Float64(x / z)) + 1.0) / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.1e+205)
		tmp = z * ((1.0 / b) + (((x * t) / b) / (y * z)));
	elseif (y <= 1.06e+164)
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	else
		tmp = z * ((((t / y) * (x / z)) + 1.0) / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.1e+205], N[(z * N[(N[(1.0 / b), $MachinePrecision] + N[(N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e+164], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(N[(N[(t / y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.10000000000000017e205

   1. Initial program 50.4%

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

      1. associate-/l* 55.9%

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

      2. associate-/l* 61.0%

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

   3. Simplified 61.0%

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

   5. Taylor expanded in b around inf 40.5%

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

   6. Taylor expanded in z around inf 78.2%

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

      1. associate-/r* 78.3%

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

   8. Simplified 78.3%

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

   if -3.10000000000000017e205 < y < 1.05999999999999997e164

   1. Initial program 85.8%

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

      1. *-commutative 85.8%

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

      2. associate-/l* 88.9%

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

   4. Applied egg-rr 88.9%

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

   if 1.05999999999999997e164 < y

   1. Initial program 33.7%

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

      1. *-commutative 33.7%

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

      2. associate-/l* 37.0%

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

   4. Applied egg-rr 37.0%

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

   5. Taylor expanded in z around inf 35.5%

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

   6. Taylor expanded in b around inf 75.6%

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

      1. associate-/l* 72.5%

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

      2. times-frac 75.6%

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

   8. Simplified 75.6%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+205}:\\ \;\;\;\;z \cdot \left(\frac{1}{b} + \frac{\frac{x \cdot t}{b}}{y \cdot z}\right)\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+164}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\frac{t}{y} \cdot \frac{x}{z} + 1}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 55.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1150:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+142}:\\ \;\;\;\;y \cdot \frac{\frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1150.0)
   (/ z b)
   (if (<= y 1.8e+40)
     (/ x (+ a 1.0))
     (if (<= y 1.4e+142) (* y (/ (/ z t) (+ a 1.0))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1150.0) {
		tmp = z / b;
	} else if (y <= 1.8e+40) {
		tmp = x / (a + 1.0);
	} else if (y <= 1.4e+142) {
		tmp = y * ((z / t) / (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1150.0d0)) then
        tmp = z / b
    else if (y <= 1.8d+40) then
        tmp = x / (a + 1.0d0)
    else if (y <= 1.4d+142) then
        tmp = y * ((z / t) / (a + 1.0d0))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1150.0) {
		tmp = z / b;
	} else if (y <= 1.8e+40) {
		tmp = x / (a + 1.0);
	} else if (y <= 1.4e+142) {
		tmp = y * ((z / t) / (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1150.0:
		tmp = z / b
	elif y <= 1.8e+40:
		tmp = x / (a + 1.0)
	elif y <= 1.4e+142:
		tmp = y * ((z / t) / (a + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1150.0)
		tmp = Float64(z / b);
	elseif (y <= 1.8e+40)
		tmp = Float64(x / Float64(a + 1.0));
	elseif (y <= 1.4e+142)
		tmp = Float64(y * Float64(Float64(z / t) / Float64(a + 1.0)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1150.0)
		tmp = z / b;
	elseif (y <= 1.8e+40)
		tmp = x / (a + 1.0);
	elseif (y <= 1.4e+142)
		tmp = y * ((z / t) / (a + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1150.0], N[(z / b), $MachinePrecision], If[LessEqual[y, 1.8e+40], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+142], N[(y * N[(N[(z / t), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1150 or 1.4e142 < y

   1. Initial program 50.1%

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

      1. associate-/l* 56.6%

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

      2. associate-/l* 62.8%

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

   3. Simplified 62.8%

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

   5. Taylor expanded in y around inf 54.3%

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

   if -1150 < y < 1.79999999999999998e40

   1. Initial program 96.3%

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

      1. associate-/l* 88.7%

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

      2. associate-/l* 82.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in y around 0 60.3%

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

   if 1.79999999999999998e40 < y < 1.4e142

   1. Initial program 86.0%

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

      1. *-commutative 86.0%

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

      2. associate-/l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0 79.1%

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

   6. Taylor expanded in x around 0 51.7%

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

      1. associate-/l* 51.9%

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

      2. associate-/r* 65.8%

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

   8. Simplified 65.8%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1150:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+142}:\\ \;\;\;\;y \cdot \frac{\frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 65.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \left(\frac{\frac{z}{b}}{x} + \frac{\frac{t}{y}}{b}\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+104}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{x}{y \cdot b} + \frac{z}{t \cdot b}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.5e+22)
   (* x (+ (/ (/ z b) x) (/ (/ t y) b)))
   (if (<= b 8.5e+104)
     (/ (+ x (/ z (/ t y))) (+ a 1.0))
     (* t (+ (/ x (* y b)) (/ z (* t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.5e+22) {
		tmp = x * (((z / b) / x) + ((t / y) / b));
	} else if (b <= 8.5e+104) {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	} else {
		tmp = t * ((x / (y * b)) + (z / (t * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.5d+22)) then
        tmp = x * (((z / b) / x) + ((t / y) / b))
    else if (b <= 8.5d+104) then
        tmp = (x + (z / (t / y))) / (a + 1.0d0)
    else
        tmp = t * ((x / (y * b)) + (z / (t * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.5e+22) {
		tmp = x * (((z / b) / x) + ((t / y) / b));
	} else if (b <= 8.5e+104) {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	} else {
		tmp = t * ((x / (y * b)) + (z / (t * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.5e+22:
		tmp = x * (((z / b) / x) + ((t / y) / b))
	elif b <= 8.5e+104:
		tmp = (x + (z / (t / y))) / (a + 1.0)
	else:
		tmp = t * ((x / (y * b)) + (z / (t * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.5e+22)
		tmp = Float64(x * Float64(Float64(Float64(z / b) / x) + Float64(Float64(t / y) / b)));
	elseif (b <= 8.5e+104)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + 1.0));
	else
		tmp = Float64(t * Float64(Float64(x / Float64(y * b)) + Float64(z / Float64(t * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.5e+22)
		tmp = x * (((z / b) / x) + ((t / y) / b));
	elseif (b <= 8.5e+104)
		tmp = (x + (z / (t / y))) / (a + 1.0);
	else
		tmp = t * ((x / (y * b)) + (z / (t * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.5e+22], N[(x * N[(N[(N[(z / b), $MachinePrecision] / x), $MachinePrecision] + N[(N[(t / y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e+104], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.49999999999999979e22

   1. Initial program 63.4%

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

      1. associate-/l* 63.4%

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

      2. associate-/l* 61.7%

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

   3. Simplified 61.7%

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

   5. Taylor expanded in b around inf 42.4%

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

   6. Taylor expanded in x around inf 61.9%

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

      1. +-commutative 61.9%

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

      2. associate-/r* 63.7%

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

      3. *-commutative 63.7%

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

      4. associate-/r* 66.9%

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

   8. Simplified 66.9%

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

   if -6.49999999999999979e22 < b < 8.4999999999999999e104

   1. Initial program 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-/l* 89.5%

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

   4. Applied egg-rr 89.5%

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

   5. Taylor expanded in y around 0 80.3%

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

      1. clear-num 80.2%

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

      2. un-div-inv 80.9%

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

   7. Applied egg-rr 80.9%

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

   if 8.4999999999999999e104 < 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* 57.4%

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

      2. associate-/l* 54.7%

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

   3. Simplified 54.7%

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

   5. Taylor expanded in b around inf 39.7%

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

   6. Taylor expanded in t around inf 65.5%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \left(\frac{\frac{z}{b}}{x} + \frac{\frac{t}{y}}{b}\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+104}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{x}{y \cdot b} + \frac{z}{t \cdot b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-83} \lor \neg \left(t \leq 5.8 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{x}{\left(a + y \cdot \frac{b}{t}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1e-83) (not (<= t 5.8e-67)))
   (/ x (+ (+ a (* y (/ b t))) 1.0))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1e-83) || !(t <= 5.8e-67)) {
		tmp = x / ((a + (y * (b / t))) + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1d-83)) .or. (.not. (t <= 5.8d-67))) then
        tmp = x / ((a + (y * (b / t))) + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1e-83) || !(t <= 5.8e-67)) {
		tmp = x / ((a + (y * (b / t))) + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1e-83) or not (t <= 5.8e-67):
		tmp = x / ((a + (y * (b / t))) + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1e-83) || !(t <= 5.8e-67))
		tmp = Float64(x / Float64(Float64(a + Float64(y * Float64(b / t))) + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1e-83) || ~((t <= 5.8e-67)))
		tmp = x / ((a + (y * (b / t))) + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1e-83], N[Not[LessEqual[t, 5.8e-67]], $MachinePrecision]], N[(x / N[(N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1e-83 or 5.8000000000000001e-67 < t

   1. Initial program 84.4%

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

      1. associate-/l* 89.1%

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

      2. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in x around inf 66.6%

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

      1. associate-*l/ 68.3%

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

      2. *-commutative 68.3%

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

   7. Simplified 68.3%

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

   if -1e-83 < t < 5.8000000000000001e-67

   1. Initial program 62.8%

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

      1. associate-/l* 52.2%

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

      2. associate-/l* 44.7%

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

   3. Simplified 44.7%

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

   5. Taylor expanded in y around inf 55.2%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-83} \lor \neg \left(t \leq 5.8 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{x}{\left(a + y \cdot \frac{b}{t}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 62.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{\left(a + y \cdot \frac{b}{t}\right) + 1}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-70}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y}{\frac{t}{b}}\right) + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2e-85)
   (/ x (+ (+ a (* y (/ b t))) 1.0))
   (if (<= t 7.2e-70) (/ z b) (/ x (+ (+ a (/ y (/ t b))) 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2e-85) {
		tmp = x / ((a + (y * (b / t))) + 1.0);
	} else if (t <= 7.2e-70) {
		tmp = z / b;
	} else {
		tmp = x / ((a + (y / (t / b))) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2d-85)) then
        tmp = x / ((a + (y * (b / t))) + 1.0d0)
    else if (t <= 7.2d-70) then
        tmp = z / b
    else
        tmp = x / ((a + (y / (t / b))) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2e-85) {
		tmp = x / ((a + (y * (b / t))) + 1.0);
	} else if (t <= 7.2e-70) {
		tmp = z / b;
	} else {
		tmp = x / ((a + (y / (t / b))) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2e-85:
		tmp = x / ((a + (y * (b / t))) + 1.0)
	elif t <= 7.2e-70:
		tmp = z / b
	else:
		tmp = x / ((a + (y / (t / b))) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2e-85)
		tmp = Float64(x / Float64(Float64(a + Float64(y * Float64(b / t))) + 1.0));
	elseif (t <= 7.2e-70)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(Float64(a + Float64(y / Float64(t / b))) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2e-85)
		tmp = x / ((a + (y * (b / t))) + 1.0);
	elseif (t <= 7.2e-70)
		tmp = z / b;
	else
		tmp = x / ((a + (y / (t / b))) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2e-85], N[(x / N[(N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e-70], N[(z / b), $MachinePrecision], N[(x / N[(N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2e-85

   1. Initial program 83.9%

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

      1. associate-/l* 88.4%

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

      2. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in x around inf 67.5%

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

      1. associate-*l/ 68.5%

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

      2. *-commutative 68.5%

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

   7. Simplified 68.5%

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

   if -2e-85 < t < 7.2000000000000004e-70

   1. Initial program 62.8%

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

      1. associate-/l* 52.2%

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

      2. associate-/l* 44.7%

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

   3. Simplified 44.7%

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

   5. Taylor expanded in y around inf 55.2%

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

   if 7.2000000000000004e-70 < t

   1. Initial program 85.0%

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

      1. associate-/l* 90.0%

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

      2. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in x around inf 65.6%

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

      1. associate-*l/ 68.0%

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

      2. *-commutative 68.0%

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

   7. Simplified 68.0%

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

      1. clear-num 42.3%

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

      2. un-div-inv 43.1%

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

   9. Applied egg-rr 68.8%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{\left(a + y \cdot \frac{b}{t}\right) + 1}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-70}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y}{\frac{t}{b}}\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{+79}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+57}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+270}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.08e+79)
   (/ x a)
   (if (<= t 4.8e+57) (/ z b) (if (<= t 5.8e+270) (/ x a) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.08e+79) {
		tmp = x / a;
	} else if (t <= 4.8e+57) {
		tmp = z / b;
	} else if (t <= 5.8e+270) {
		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 (t <= (-1.08d+79)) then
        tmp = x / a
    else if (t <= 4.8d+57) then
        tmp = z / b
    else if (t <= 5.8d+270) 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 (t <= -1.08e+79) {
		tmp = x / a;
	} else if (t <= 4.8e+57) {
		tmp = z / b;
	} else if (t <= 5.8e+270) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.08e+79:
		tmp = x / a
	elif t <= 4.8e+57:
		tmp = z / b
	elif t <= 5.8e+270:
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.08e+79)
		tmp = Float64(x / a);
	elseif (t <= 4.8e+57)
		tmp = Float64(z / b);
	elseif (t <= 5.8e+270)
		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 (t <= -1.08e+79)
		tmp = x / a;
	elseif (t <= 4.8e+57)
		tmp = z / b;
	elseif (t <= 5.8e+270)
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.08e+79], N[(x / a), $MachinePrecision], If[LessEqual[t, 4.8e+57], N[(z / b), $MachinePrecision], If[LessEqual[t, 5.8e+270], N[(x / a), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.08000000000000002e79 or 4.80000000000000009e57 < t < 5.7999999999999998e270

   1. Initial program 82.7%

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

      1. associate-/l* 90.9%

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

      2. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in x around inf 74.1%

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

      1. associate-*l/ 78.0%

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

      2. *-commutative 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in a around inf 43.5%

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

   if -1.08000000000000002e79 < t < 4.80000000000000009e57

   1. Initial program 72.2%

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

      1. associate-/l* 65.2%

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

      2. associate-/l* 60.0%

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

   3. Simplified 60.0%

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

   5. Taylor expanded in y around inf 48.0%

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

   if 5.7999999999999998e270 < t

   1. Initial program 90.5%

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

      1. associate-/l* 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 80.4%

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

      1. associate-*l/ 80.4%

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

      2. *-commutative 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in a around 0 69.6%

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

      1. *-commutative 69.6%

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

      2. associate-*r/ 69.6%

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

   10. Simplified 69.6%

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

   11. Taylor expanded in y around 0 69.6%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{+79}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+57}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+270}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 56.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1150 \lor \neg \left(y \leq 2.4 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1150.0) (not (<= y 2.4e+54))) (/ 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 <= -1150.0) || !(y <= 2.4e+54)) {
		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 <= (-1150.0d0)) .or. (.not. (y <= 2.4d+54))) 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 <= -1150.0) || !(y <= 2.4e+54)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1150.0) or not (y <= 2.4e+54):
		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 <= -1150.0) || !(y <= 2.4e+54))
		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 <= -1150.0) || ~((y <= 2.4e+54)))
		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, -1150.0], N[Not[LessEqual[y, 2.4e+54]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1150 or 2.39999999999999998e54 < y

   1. Initial program 53.6%

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

      1. associate-/l* 60.4%

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

      2. associate-/l* 66.0%

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

   3. Simplified 66.0%

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

   5. Taylor expanded in y around inf 51.5%

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

   if -1150 < y < 2.39999999999999998e54

   1. Initial program 95.8%

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

      1. associate-/l* 89.0%

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

      2. associate-/l* 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in y around 0 60.1%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1150 \lor \neg \left(y \leq 2.4 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 41.5% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if a < -1 or 1 < a

   1. Initial program 79.5%

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

      1. associate-/l* 78.0%

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

      2. associate-/l* 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in x around inf 52.7%

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

      1. associate-*l/ 51.1%

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

      2. *-commutative 51.1%

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

   7. Simplified 51.1%

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

   8. Taylor expanded in a around inf 47.3%

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

   if -1 < a < 1

   1. Initial program 74.3%

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

      1. associate-/l* 74.4%

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

      2. associate-/l* 74.2%

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

   3. Simplified 74.2%

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

   5. Taylor expanded in x around inf 54.6%

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

      1. associate-*l/ 53.1%

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

      2. *-commutative 53.1%

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

   7. Simplified 53.1%

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

   8. Taylor expanded in a around 0 54.1%

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

      1. *-commutative 54.1%

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

      2. associate-*r/ 52.7%

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

   10. Simplified 52.7%

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

   11. Taylor expanded in y around 0 36.1%

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

4. Final simplification 41.5%

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

Alternative 21: 19.8% 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 76.8%

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

   1. associate-/l* 76.1%

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

   2. associate-/l* 75.3%

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

3. Simplified 75.3%

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

5. Taylor expanded in x around inf 53.7%

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

   1. associate-*l/ 52.2%

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

   2. *-commutative 52.2%

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

7. Simplified 52.2%

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

8. Taylor expanded in a around 0 33.7%

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

   1. *-commutative 33.7%

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

   2. associate-*r/ 32.2%

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

10. Simplified 32.2%

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

11. Taylor expanded in y around 0 20.8%

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

12. Final simplification 20.8%

    \[\leadsto x \]
13. Add Preprocessing

Developer target: 79.4% 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 2024115 
(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))))