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

Percentage Accurate: 75.9% → 89.9%

Time: 17.7s

Alternatives: 17

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.9% 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

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_2 := 1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{t\_2} + \frac{\frac{y}{t}}{t\_2}\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;t\_1 \leq 10^{+301}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0))))
        (t_2 (+ 1.0 (fma y (/ b t) a))))
   (if (<= t_1 (- INFINITY))
     (* z (+ (/ (/ x z) t_2) (/ (/ y t) t_2)))
     (if (<= t_1 -2e-275)
       t_1
       (if (<= t_1 0.0)
         (/ (* x (+ (/ t y) (/ z x))) b)
         (if (<= t_1 1e+301) t_1 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = 1.0 + fma(y, (b / t), a);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z * (((x / z) / t_2) + ((y / t) / t_2));
	} else if (t_1 <= -2e-275) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (t_1 <= 1e+301) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	t_2 = Float64(1.0 + fma(y, Float64(b / t), a))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(Float64(x / z) / t_2) + Float64(Float64(y / t) / t_2)));
	elseif (t_1 <= -2e-275)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(x * Float64(Float64(t / y) + Float64(z / x))) / b);
	elseif (t_1 <= 1e+301)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(y * N[(b / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z * N[(N[(N[(x / z), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-275], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(x * N[(N[(t / y), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$1, 1e+301], t$95$1, N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 24.6%

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

      1. associate-/l* 50.3%

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

      2. associate-/l* 50.3%

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

   3. Simplified 50.3%

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

   5. Taylor expanded in z around inf 74.2%

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

      1. associate-/r* 87.1%

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

      2. +-commutative 87.1%

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

      3. associate-*l/ 87.1%

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

      4. *-commutative 87.1%

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

      5. fma-define 87.1%

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

      6. associate-/r* 93.4%

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

      7. +-commutative 93.4%

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

      8. associate-*l/ 93.2%

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

      9. *-commutative 93.2%

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

      10. fma-define 93.2%

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

   7. Simplified 93.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999987e-275 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.00000000000000005e301

   1. Initial program 99.7%

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

   if -1.99999999999999987e-275 < (/.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 42.0%

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

      1. associate-/l* 42.0%

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

      2. associate-/l* 63.3%

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

   3. Simplified 63.3%

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

   5. Taylor expanded in x around inf 42.0%

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

   6. Taylor expanded in b around inf 71.5%

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

   if 1.00000000000000005e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 18.2%

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

      1. associate-/l* 29.4%

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

      2. associate-/l* 34.9%

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

   3. Simplified 34.9%

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

   5. Taylor expanded in y around inf 86.3%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)} + \frac{\frac{y}{t}}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-275}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+301}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1 + \left(a + 1\right)}\\ t_3 := 1 + \left(a + t\_1\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_3} + \frac{y}{t \cdot t\_3}\right)\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-275}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;t\_2 \leq 10^{+301}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (/ (+ x (/ (* y z) t)) (+ t_1 (+ a 1.0))))
        (t_3 (+ 1.0 (+ a t_1))))
   (if (<= t_2 (- INFINITY))
     (* z (+ (/ x (* z t_3)) (/ y (* t t_3))))
     (if (<= t_2 -2e-275)
       t_2
       (if (<= t_2 0.0)
         (/ (* x (+ (/ t y) (/ z x))) b)
         (if (<= t_2 1e+301) 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;
	double t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double t_3 = 1.0 + (a + t_1);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	} else if (t_2 <= -2e-275) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (t_2 <= 1e+301) {
		tmp = 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;
	double t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double t_3 = 1.0 + (a + t_1);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	} else if (t_2 <= -2e-275) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (t_2 <= 1e+301) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0))
	t_3 = 1.0 + (a + t_1)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)))
	elif t_2 <= -2e-275:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (x * ((t / y) + (z / x))) / b
	elif t_2 <= 1e+301:
		tmp = t_2
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(t_1 + Float64(a + 1.0)))
	t_3 = Float64(1.0 + Float64(a + t_1))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_3)) + Float64(y / Float64(t * t_3))));
	elseif (t_2 <= -2e-275)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(x * Float64(Float64(t / y) + Float64(z / x))) / b);
	elseif (t_2 <= 1e+301)
		tmp = 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;
	t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	t_3 = 1.0 + (a + t_1);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	elseif (t_2 <= -2e-275)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (x * ((t / y) + (z / x))) / b;
	elseif (t_2 <= 1e+301)
		tmp = 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[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z * N[(N[(x / N[(z * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-275], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(x * N[(N[(t / y), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$2, 1e+301], t$95$2, N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 24.6%

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

      1. associate-/l* 50.3%

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

      2. associate-/l* 50.3%

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

   3. Simplified 50.3%

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

   5. Taylor expanded in z around inf 74.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999987e-275 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.00000000000000005e301

   1. Initial program 99.7%

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

   if -1.99999999999999987e-275 < (/.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 42.0%

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

      1. associate-/l* 42.0%

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

      2. associate-/l* 63.3%

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

   3. Simplified 63.3%

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

   5. Taylor expanded in x around inf 42.0%

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

   6. Taylor expanded in b around inf 71.5%

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

   if 1.00000000000000005e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 18.2%

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

      1. associate-/l* 29.4%

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

      2. associate-/l* 34.9%

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

   3. Simplified 34.9%

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

   5. Taylor expanded in y around inf 86.3%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-275}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+301}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-275}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;t\_2 \leq 10^{+301}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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_1)))
   (if (<= t_2 -2e-275)
     (/ (+ x (* z (/ y t))) t_1)
     (if (<= t_2 0.0)
       (/ (* x (+ (/ t y) (/ z x))) b)
       (if (<= t_2 1e+301) 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 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -2e-275) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (t_2 <= 1e+301) {
		tmp = t_2;
	} 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) :: tmp
    t_1 = ((y * b) / t) + (a + 1.0d0)
    t_2 = (x + ((y * z) / t)) / t_1
    if (t_2 <= (-2d-275)) then
        tmp = (x + (z * (y / t))) / t_1
    else if (t_2 <= 0.0d0) then
        tmp = (x * ((t / y) + (z / x))) / b
    else if (t_2 <= 1d+301) then
        tmp = t_2
    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)) / t_1;
	double tmp;
	if (t_2 <= -2e-275) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (t_2 <= 1e+301) {
		tmp = 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 = (x + ((y * z) / t)) / t_1
	tmp = 0
	if t_2 <= -2e-275:
		tmp = (x + (z * (y / t))) / t_1
	elif t_2 <= 0.0:
		tmp = (x * ((t / y) + (z / x))) / b
	elif t_2 <= 1e+301:
		tmp = 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(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_2 <= -2e-275)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(x * Float64(Float64(t / y) + Float64(z / x))) / b);
	elseif (t_2 <= 1e+301)
		tmp = 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 = (x + ((y * z) / t)) / t_1;
	tmp = 0.0;
	if (t_2 <= -2e-275)
		tmp = (x + (z * (y / t))) / t_1;
	elseif (t_2 <= 0.0)
		tmp = (x * ((t / y) + (z / x))) / b;
	elseif (t_2 <= 1e+301)
		tmp = 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[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-275], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(N[(x * N[(N[(t / y), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$2, 1e+301], t$95$2, 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))) < -1.99999999999999987e-275

   1. Initial program 88.6%

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

      1. *-commutative 88.6%

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

      2. associate-/l* 89.6%

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

   4. Applied egg-rr 89.6%

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

   if -1.99999999999999987e-275 < (/.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 42.0%

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

      1. associate-/l* 42.0%

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

      2. associate-/l* 63.3%

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

   3. Simplified 63.3%

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

   5. Taylor expanded in x around inf 42.0%

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

   6. Taylor expanded in b around inf 71.5%

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

   if -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.00000000000000005e301

   1. Initial program 99.7%

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

   if 1.00000000000000005e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 18.2%

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

      1. associate-/l* 29.4%

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

      2. associate-/l* 34.9%

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

   3. Simplified 34.9%

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

   5. Taylor expanded in y around inf 86.3%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-275}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+301}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ t_2 := \frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-182}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-247}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-259}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ (* y (/ b t)) (+ a 1.0))))
        (t_2 (/ (+ z (/ (* x t) y)) b)))
   (if (<= t -1.45e-21)
     t_1
     (if (<= t -2.7e-182)
       t_2
       (if (<= t -5.5e-247)
         (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
         (if (<= t 1.9e-259) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	double t_2 = (z + ((x * t) / y)) / b;
	double tmp;
	if (t <= -1.45e-21) {
		tmp = t_1;
	} else if (t <= -2.7e-182) {
		tmp = t_2;
	} else if (t <= -5.5e-247) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t <= 1.9e-259) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0d0))
    t_2 = (z + ((x * t) / y)) / b
    if (t <= (-1.45d-21)) then
        tmp = t_1
    else if (t <= (-2.7d-182)) then
        tmp = t_2
    else if (t <= (-5.5d-247)) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else if (t <= 1.9d-259) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	double t_2 = (z + ((x * t) / y)) / b;
	double tmp;
	if (t <= -1.45e-21) {
		tmp = t_1;
	} else if (t <= -2.7e-182) {
		tmp = t_2;
	} else if (t <= -5.5e-247) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t <= 1.9e-259) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0))
	t_2 = (z + ((x * t) / y)) / b
	tmp = 0
	if t <= -1.45e-21:
		tmp = t_1
	elif t <= -2.7e-182:
		tmp = t_2
	elif t <= -5.5e-247:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	elif t <= 1.9e-259:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)))
	t_2 = Float64(Float64(z + Float64(Float64(x * t) / y)) / b)
	tmp = 0.0
	if (t <= -1.45e-21)
		tmp = t_1;
	elseif (t <= -2.7e-182)
		tmp = t_2;
	elseif (t <= -5.5e-247)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	elseif (t <= 1.9e-259)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	t_2 = (z + ((x * t) / y)) / b;
	tmp = 0.0;
	if (t <= -1.45e-21)
		tmp = t_1;
	elseif (t <= -2.7e-182)
		tmp = t_2;
	elseif (t <= -5.5e-247)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	elseif (t <= 1.9e-259)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[t, -1.45e-21], t$95$1, If[LessEqual[t, -2.7e-182], t$95$2, If[LessEqual[t, -5.5e-247], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-259], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.45e-21 or 1.9e-259 < t

   1. Initial program 81.0%

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

      1. associate-/l* 83.6%

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

      2. associate-/l* 86.8%

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

   3. Simplified 86.8%

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

   if -1.45e-21 < t < -2.69999999999999999e-182 or -5.49999999999999995e-247 < t < 1.9e-259

   1. Initial program 60.5%

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

      1. associate-/l* 55.5%

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

      2. associate-/l* 50.1%

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

   3. Simplified 50.1%

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

   5. Taylor expanded in x around inf 57.4%

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

   6. Taylor expanded in b around inf 73.9%

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

   7. Taylor expanded in x around 0 84.0%

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

   if -2.69999999999999999e-182 < t < -5.49999999999999995e-247

   1. Initial program 74.0%

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

      1. associate-/l* 54.9%

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

      2. associate-/l* 52.5%

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

   3. Simplified 52.5%

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

   5. Taylor expanded in t around 0 54.9%

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

   6. Taylor expanded in x around 0 70.6%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-21}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-182}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-247}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-259}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{if}\;t \leq -3 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-227}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-95}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y (/ t z))) (+ a 1.0))))
   (if (<= t -3e-21)
     t_1
     (if (<= t 5e-227)
       (/ (+ z (/ (* x t) y)) b)
       (if (<= t 4.6e-131)
         t_1
         (if (<= t 1.25e-95)
           (/ z b)
           (if (<= t 7.5e-73) (/ x (+ 1.0 (+ a (/ (* y b) t)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / (a + 1.0);
	double tmp;
	if (t <= -3e-21) {
		tmp = t_1;
	} else if (t <= 5e-227) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 4.6e-131) {
		tmp = t_1;
	} else if (t <= 1.25e-95) {
		tmp = z / b;
	} else if (t <= 7.5e-73) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / (t / z))) / (a + 1.0d0)
    if (t <= (-3d-21)) then
        tmp = t_1
    else if (t <= 5d-227) then
        tmp = (z + ((x * t) / y)) / b
    else if (t <= 4.6d-131) then
        tmp = t_1
    else if (t <= 1.25d-95) then
        tmp = z / b
    else if (t <= 7.5d-73) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / (a + 1.0);
	double tmp;
	if (t <= -3e-21) {
		tmp = t_1;
	} else if (t <= 5e-227) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 4.6e-131) {
		tmp = t_1;
	} else if (t <= 1.25e-95) {
		tmp = z / b;
	} else if (t <= 7.5e-73) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y / (t / z))) / (a + 1.0)
	tmp = 0
	if t <= -3e-21:
		tmp = t_1
	elif t <= 5e-227:
		tmp = (z + ((x * t) / y)) / b
	elif t <= 4.6e-131:
		tmp = t_1
	elif t <= 1.25e-95:
		tmp = z / b
	elif t <= 7.5e-73:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -3e-21)
		tmp = t_1;
	elseif (t <= 5e-227)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (t <= 4.6e-131)
		tmp = t_1;
	elseif (t <= 1.25e-95)
		tmp = Float64(z / b);
	elseif (t <= 7.5e-73)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y / (t / z))) / (a + 1.0);
	tmp = 0.0;
	if (t <= -3e-21)
		tmp = t_1;
	elseif (t <= 5e-227)
		tmp = (z + ((x * t) / y)) / b;
	elseif (t <= 4.6e-131)
		tmp = t_1;
	elseif (t <= 1.25e-95)
		tmp = z / b;
	elseif (t <= 7.5e-73)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e-21], t$95$1, If[LessEqual[t, 5e-227], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t, 4.6e-131], t$95$1, If[LessEqual[t, 1.25e-95], N[(z / b), $MachinePrecision], If[LessEqual[t, 7.5e-73], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.99999999999999991e-21 or 4.99999999999999961e-227 < t < 4.60000000000000044e-131 or 7.5e-73 < t

   1. Initial program 80.5%

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

      1. associate-/l* 83.4%

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

      2. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in y around 0 76.0%

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

      1. clear-num 87.6%

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

      2. un-div-inv 87.6%

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

   7. Applied egg-rr 76.0%

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

   if -2.99999999999999991e-21 < t < 4.99999999999999961e-227

   1. Initial program 65.8%

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

      1. associate-/l* 58.6%

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

      2. associate-/l* 54.3%

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

   3. Simplified 54.3%

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

   5. Taylor expanded in x around inf 62.3%

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

   6. Taylor expanded in b around inf 67.8%

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

   7. Taylor expanded in x around 0 76.2%

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

   if 4.60000000000000044e-131 < t < 1.2499999999999999e-95

   1. Initial program 68.1%

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

      1. associate-/l* 68.1%

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

      2. associate-/l* 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in y around inf 83.6%

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

   if 1.2499999999999999e-95 < t < 7.5e-73

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

      2. associate-/l* 83.9%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in x around inf 99.7%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-21}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-227}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-131}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-95}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-227}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-95}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ a 1.0))))
   (if (<= t -1.45e-21)
     t_1
     (if (<= t 5e-227)
       (/ (+ z (/ (* x t) y)) b)
       (if (<= t 2.35e-130)
         t_1
         (if (<= t 8.5e-95)
           (/ z b)
           (if (<= t 1.35e-70) (/ x (+ 1.0 (+ a (/ (* y b) t)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / (a + 1.0);
	double tmp;
	if (t <= -1.45e-21) {
		tmp = t_1;
	} else if (t <= 5e-227) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 2.35e-130) {
		tmp = t_1;
	} else if (t <= 8.5e-95) {
		tmp = z / b;
	} else if (t <= 1.35e-70) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / (a + 1.0d0)
    if (t <= (-1.45d-21)) then
        tmp = t_1
    else if (t <= 5d-227) then
        tmp = (z + ((x * t) / y)) / b
    else if (t <= 2.35d-130) then
        tmp = t_1
    else if (t <= 8.5d-95) then
        tmp = z / b
    else if (t <= 1.35d-70) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / (a + 1.0);
	double tmp;
	if (t <= -1.45e-21) {
		tmp = t_1;
	} else if (t <= 5e-227) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 2.35e-130) {
		tmp = t_1;
	} else if (t <= 8.5e-95) {
		tmp = z / b;
	} else if (t <= 1.35e-70) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / (a + 1.0)
	tmp = 0
	if t <= -1.45e-21:
		tmp = t_1
	elif t <= 5e-227:
		tmp = (z + ((x * t) / y)) / b
	elif t <= 2.35e-130:
		tmp = t_1
	elif t <= 8.5e-95:
		tmp = z / b
	elif t <= 1.35e-70:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -1.45e-21)
		tmp = t_1;
	elseif (t <= 5e-227)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (t <= 2.35e-130)
		tmp = t_1;
	elseif (t <= 8.5e-95)
		tmp = Float64(z / b);
	elseif (t <= 1.35e-70)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / (a + 1.0);
	tmp = 0.0;
	if (t <= -1.45e-21)
		tmp = t_1;
	elseif (t <= 5e-227)
		tmp = (z + ((x * t) / y)) / b;
	elseif (t <= 2.35e-130)
		tmp = t_1;
	elseif (t <= 8.5e-95)
		tmp = z / b;
	elseif (t <= 1.35e-70)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e-21], t$95$1, If[LessEqual[t, 5e-227], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t, 2.35e-130], t$95$1, If[LessEqual[t, 8.5e-95], N[(z / b), $MachinePrecision], If[LessEqual[t, 1.35e-70], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.45e-21 or 4.99999999999999961e-227 < t < 2.34999999999999984e-130 or 1.3500000000000001e-70 < t

   1. Initial program 80.5%

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

      1. associate-/l* 83.4%

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

      2. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in y around 0 76.0%

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

   if -1.45e-21 < t < 4.99999999999999961e-227

   1. Initial program 65.8%

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

      1. associate-/l* 58.6%

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

      2. associate-/l* 54.3%

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

   3. Simplified 54.3%

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

   5. Taylor expanded in x around inf 62.3%

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

   6. Taylor expanded in b around inf 67.8%

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

   7. Taylor expanded in x around 0 76.2%

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

   if 2.34999999999999984e-130 < t < 8.4999999999999995e-95

   1. Initial program 68.1%

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

      1. associate-/l* 68.1%

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

      2. associate-/l* 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in y around inf 83.6%

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

   if 8.4999999999999995e-95 < t < 1.3500000000000001e-70

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

      2. associate-/l* 83.9%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in x around inf 99.7%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-21}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-227}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-130}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-95}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a}\\ t_2 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -1.16 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-46}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-232}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.65:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) a)) (t_2 (+ x (/ (* y z) t))))
   (if (<= a -1.16e+166)
     t_1
     (if (<= a -7.8e-46)
       (/ z b)
       (if (<= a -5e-88)
         t_2
         (if (<= a -5.1e-232) (/ z b) (if (<= a 1.65) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / a;
	double t_2 = x + ((y * z) / t);
	double tmp;
	if (a <= -1.16e+166) {
		tmp = t_1;
	} else if (a <= -7.8e-46) {
		tmp = z / b;
	} else if (a <= -5e-88) {
		tmp = t_2;
	} else if (a <= -5.1e-232) {
		tmp = z / b;
	} else if (a <= 1.65) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / a
    t_2 = x + ((y * z) / t)
    if (a <= (-1.16d+166)) then
        tmp = t_1
    else if (a <= (-7.8d-46)) then
        tmp = z / b
    else if (a <= (-5d-88)) then
        tmp = t_2
    else if (a <= (-5.1d-232)) then
        tmp = z / b
    else if (a <= 1.65d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / a;
	double t_2 = x + ((y * z) / t);
	double tmp;
	if (a <= -1.16e+166) {
		tmp = t_1;
	} else if (a <= -7.8e-46) {
		tmp = z / b;
	} else if (a <= -5e-88) {
		tmp = t_2;
	} else if (a <= -5.1e-232) {
		tmp = z / b;
	} else if (a <= 1.65) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / a
	t_2 = x + ((y * z) / t)
	tmp = 0
	if a <= -1.16e+166:
		tmp = t_1
	elif a <= -7.8e-46:
		tmp = z / b
	elif a <= -5e-88:
		tmp = t_2
	elif a <= -5.1e-232:
		tmp = z / b
	elif a <= 1.65:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / a)
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (a <= -1.16e+166)
		tmp = t_1;
	elseif (a <= -7.8e-46)
		tmp = Float64(z / b);
	elseif (a <= -5e-88)
		tmp = t_2;
	elseif (a <= -5.1e-232)
		tmp = Float64(z / b);
	elseif (a <= 1.65)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / a;
	t_2 = x + ((y * z) / t);
	tmp = 0.0;
	if (a <= -1.16e+166)
		tmp = t_1;
	elseif (a <= -7.8e-46)
		tmp = z / b;
	elseif (a <= -5e-88)
		tmp = t_2;
	elseif (a <= -5.1e-232)
		tmp = z / b;
	elseif (a <= 1.65)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.16e+166], t$95$1, If[LessEqual[a, -7.8e-46], N[(z / b), $MachinePrecision], If[LessEqual[a, -5e-88], t$95$2, If[LessEqual[a, -5.1e-232], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.65], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.16000000000000002e166 or 1.6499999999999999 < a

   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* 80.8%

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

      2. associate-/l* 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in a around inf 70.5%

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

   if -1.16000000000000002e166 < a < -7.8000000000000005e-46 or -5.00000000000000009e-88 < a < -5.10000000000000029e-232

   1. Initial program 70.1%

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

      1. associate-/l* 65.1%

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

      2. associate-/l* 59.7%

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

   3. Simplified 59.7%

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

   5. Taylor expanded in y around inf 61.0%

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

   if -7.8000000000000005e-46 < a < -5.00000000000000009e-88 or -5.10000000000000029e-232 < a < 1.6499999999999999

   1. Initial program 78.8%

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

      1. associate-/l* 76.9%

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

      2. associate-/l* 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in y around 0 60.1%

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

   6. Taylor expanded in a around 0 59.6%

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

Alternative 8: 81.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+68}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+229}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.6e+68)
   (/ (+ z (/ (* x t) y)) b)
   (if (<= y 3e+24)
     (/ (+ x (* z (/ y t))) (+ (/ (* y b) t) (+ a 1.0)))
     (if (<= y 1.6e+229)
       (/ (+ x (/ y (/ t z))) (+ (* y (/ b t)) (+ a 1.0)))
       (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.6e+68) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 3e+24) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else if (y <= 1.6e+229) {
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4.6d+68)) then
        tmp = (z + ((x * t) / y)) / b
    else if (y <= 3d+24) then
        tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0d0))
    else if (y <= 1.6d+229) then
        tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0d0))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.6e+68) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 3e+24) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else if (y <= 1.6e+229) {
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.6e+68:
		tmp = (z + ((x * t) / y)) / b
	elif y <= 3e+24:
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0))
	elif y <= 1.6e+229:
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.6e+68)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (y <= 3e+24)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	elseif (y <= 1.6e+229)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.6e+68)
		tmp = (z + ((x * t) / y)) / b;
	elseif (y <= 3e+24)
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	elseif (y <= 1.6e+229)
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.6e+68], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 3e+24], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+229], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.6e68

   1. Initial program 54.8%

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

      1. associate-/l* 52.5%

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

      2. associate-/l* 63.8%

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

   3. Simplified 63.8%

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

   5. Taylor expanded in x around inf 50.2%

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

   6. Taylor expanded in b around inf 70.5%

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

   7. Taylor expanded in x around 0 70.5%

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

   if -4.6e68 < y < 2.99999999999999995e24

   1. Initial program 94.1%

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

      1. *-commutative 94.1%

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

      2. associate-/l* 93.5%

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

   4. Applied egg-rr 93.5%

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

   if 2.99999999999999995e24 < y < 1.5999999999999999e229

   1. Initial program 55.9%

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

      1. associate-/l* 68.6%

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

      2. associate-/l* 77.0%

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

   3. Simplified 77.0%

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

      1. clear-num 77.1%

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

      2. un-div-inv 77.0%

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

   6. Applied egg-rr 77.0%

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

   if 1.5999999999999999e229 < y

   1. Initial program 15.1%

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

      1. associate-/l* 27.9%

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

      2. associate-/l* 34.5%

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

   3. Simplified 34.5%

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

   5. Taylor expanded in y around inf 67.6%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+68}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+229}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+69}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+26}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 10^{+229}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.15e+69)
   (/ (+ z (/ (* x t) y)) b)
   (if (<= y 5e+26)
     (/ (+ x (* z (/ y t))) (+ (/ (* y b) t) (+ a 1.0)))
     (if (<= y 1e+229)
       (/ (+ x (* y (/ z t))) (+ (* y (/ b t)) (+ a 1.0)))
       (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.15e+69) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 5e+26) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else if (y <= 1e+229) {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.15d+69)) then
        tmp = (z + ((x * t) / y)) / b
    else if (y <= 5d+26) then
        tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0d0))
    else if (y <= 1d+229) then
        tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0d0))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.15e+69) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 5e+26) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else if (y <= 1e+229) {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.15e+69:
		tmp = (z + ((x * t) / y)) / b
	elif y <= 5e+26:
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0))
	elif y <= 1e+229:
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.15e+69)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (y <= 5e+26)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	elseif (y <= 1e+229)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.15e+69)
		tmp = (z + ((x * t) / y)) / b;
	elseif (y <= 5e+26)
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	elseif (y <= 1e+229)
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.15e+69], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 5e+26], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+229], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.15000000000000008e69

   1. Initial program 54.8%

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

      1. associate-/l* 52.5%

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

      2. associate-/l* 63.8%

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

   3. Simplified 63.8%

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

   5. Taylor expanded in x around inf 50.2%

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

   6. Taylor expanded in b around inf 70.5%

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

   7. Taylor expanded in x around 0 70.5%

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

   if -1.15000000000000008e69 < y < 5.0000000000000001e26

   1. Initial program 94.2%

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

      1. *-commutative 94.2%

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

      2. associate-/l* 93.6%

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

   4. Applied egg-rr 93.6%

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

   if 5.0000000000000001e26 < y < 9.9999999999999999e228

   1. Initial program 54.9%

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

      1. associate-/l* 68.0%

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

      2. associate-/l* 76.5%

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

   3. Simplified 76.5%

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

   if 9.9999999999999999e228 < y

   1. Initial program 15.1%

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

      1. associate-/l* 27.9%

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

      2. associate-/l* 34.5%

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

   3. Simplified 34.5%

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

   5. Taylor expanded in y around inf 67.6%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+69}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+26}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 10^{+229}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{if}\;b \leq -1.08 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-19}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+36} \lor \neg \left(b \leq 2 \cdot 10^{+94}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ (* x t) y)) b)))
   (if (<= b -1.08e+86)
     t_1
     (if (<= b 2.6e-19)
       (/ (+ x (/ y (/ t z))) (+ a 1.0))
       (if (or (<= b 4.4e+36) (not (<= b 2e+94)))
         t_1
         (/ (+ x (/ (* y z) t)) (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double tmp;
	if (b <= -1.08e+86) {
		tmp = t_1;
	} else if (b <= 2.6e-19) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else if ((b <= 4.4e+36) || !(b <= 2e+94)) {
		tmp = t_1;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + ((x * t) / y)) / b
    if (b <= (-1.08d+86)) then
        tmp = t_1
    else if (b <= 2.6d-19) then
        tmp = (x + (y / (t / z))) / (a + 1.0d0)
    else if ((b <= 4.4d+36) .or. (.not. (b <= 2d+94))) then
        tmp = t_1
    else
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double tmp;
	if (b <= -1.08e+86) {
		tmp = t_1;
	} else if (b <= 2.6e-19) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else if ((b <= 4.4e+36) || !(b <= 2e+94)) {
		tmp = t_1;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + ((x * t) / y)) / b
	tmp = 0
	if b <= -1.08e+86:
		tmp = t_1
	elif b <= 2.6e-19:
		tmp = (x + (y / (t / z))) / (a + 1.0)
	elif (b <= 4.4e+36) or not (b <= 2e+94):
		tmp = t_1
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(Float64(x * t) / y)) / b)
	tmp = 0.0
	if (b <= -1.08e+86)
		tmp = t_1;
	elseif (b <= 2.6e-19)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0));
	elseif ((b <= 4.4e+36) || !(b <= 2e+94))
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + ((x * t) / y)) / b;
	tmp = 0.0;
	if (b <= -1.08e+86)
		tmp = t_1;
	elseif (b <= 2.6e-19)
		tmp = (x + (y / (t / z))) / (a + 1.0);
	elseif ((b <= 4.4e+36) || ~((b <= 2e+94)))
		tmp = t_1;
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[b, -1.08e+86], t$95$1, If[LessEqual[b, 2.6e-19], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 4.4e+36], N[Not[LessEqual[b, 2e+94]], $MachinePrecision]], t$95$1, N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.07999999999999993e86 or 2.60000000000000013e-19 < b < 4.40000000000000001e36 or 2e94 < b

   1. Initial program 56.3%

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

      1. associate-/l* 54.1%

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

      2. associate-/l* 55.9%

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

   3. Simplified 55.9%

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

   5. Taylor expanded in x around inf 56.4%

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

   6. Taylor expanded in b around inf 61.6%

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

   7. Taylor expanded in x around 0 68.5%

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

   if -1.07999999999999993e86 < b < 2.60000000000000013e-19

   1. Initial program 86.0%

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

      1. associate-/l* 88.4%

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

      2. associate-/l* 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in y around 0 77.4%

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

      1. clear-num 89.0%

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

      2. un-div-inv 89.0%

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

   7. Applied egg-rr 77.5%

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

   if 4.40000000000000001e36 < b < 2e94

   1. Initial program 89.7%

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

      1. associate-/l* 60.8%

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

      2. associate-/l* 60.1%

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

   3. Simplified 60.1%

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

   5. Taylor expanded in b around 0 81.0%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.08 \cdot 10^{+86}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-19}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+36} \lor \neg \left(b \leq 2 \cdot 10^{+94}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{x \cdot t}{y}}{b}\\ t_2 := \frac{x}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-195}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ (* x t) y)) b))
        (t_2 (/ x (+ (+ a 1.0) (/ y (/ t b))))))
   (if (<= t -3.1e-21)
     t_2
     (if (<= t 4.5e-231)
       t_1
       (if (<= t 2.9e-195)
         (/ (+ x (/ (* y z) t)) a)
         (if (<= t 1.35e-34) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double t_2 = x / ((a + 1.0) + (y / (t / b)));
	double tmp;
	if (t <= -3.1e-21) {
		tmp = t_2;
	} else if (t <= 4.5e-231) {
		tmp = t_1;
	} else if (t <= 2.9e-195) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (t <= 1.35e-34) {
		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 = (z + ((x * t) / y)) / b
    t_2 = x / ((a + 1.0d0) + (y / (t / b)))
    if (t <= (-3.1d-21)) then
        tmp = t_2
    else if (t <= 4.5d-231) then
        tmp = t_1
    else if (t <= 2.9d-195) then
        tmp = (x + ((y * z) / t)) / a
    else if (t <= 1.35d-34) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double t_2 = x / ((a + 1.0) + (y / (t / b)));
	double tmp;
	if (t <= -3.1e-21) {
		tmp = t_2;
	} else if (t <= 4.5e-231) {
		tmp = t_1;
	} else if (t <= 2.9e-195) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (t <= 1.35e-34) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + ((x * t) / y)) / b
	t_2 = x / ((a + 1.0) + (y / (t / b)))
	tmp = 0
	if t <= -3.1e-21:
		tmp = t_2
	elif t <= 4.5e-231:
		tmp = t_1
	elif t <= 2.9e-195:
		tmp = (x + ((y * z) / t)) / a
	elif t <= 1.35e-34:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(Float64(x * t) / y)) / b)
	t_2 = Float64(x / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))))
	tmp = 0.0
	if (t <= -3.1e-21)
		tmp = t_2;
	elseif (t <= 4.5e-231)
		tmp = t_1;
	elseif (t <= 2.9e-195)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	elseif (t <= 1.35e-34)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + ((x * t) / y)) / b;
	t_2 = x / ((a + 1.0) + (y / (t / b)));
	tmp = 0.0;
	if (t <= -3.1e-21)
		tmp = t_2;
	elseif (t <= 4.5e-231)
		tmp = t_1;
	elseif (t <= 2.9e-195)
		tmp = (x + ((y * z) / t)) / a;
	elseif (t <= 1.35e-34)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e-21], t$95$2, If[LessEqual[t, 4.5e-231], t$95$1, If[LessEqual[t, 2.9e-195], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 1.35e-34], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.0999999999999998e-21 or 1.35000000000000008e-34 < t

   1. Initial program 80.1%

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

      1. associate-/l* 85.2%

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

      2. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

      1. clear-num 92.5%

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

      2. un-div-inv 92.5%

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

   6. Applied egg-rr 92.5%

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

   7. Taylor expanded in x around inf 70.0%

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

   if -3.0999999999999998e-21 < t < 4.4999999999999998e-231 or 2.9000000000000002e-195 < t < 1.35000000000000008e-34

   1. Initial program 69.3%

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

      1. associate-/l* 63.4%

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

      2. associate-/l* 57.9%

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

   3. Simplified 57.9%

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

   5. Taylor expanded in x around inf 64.3%

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

   6. Taylor expanded in b around inf 61.3%

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

   7. Taylor expanded in x around 0 68.8%

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

   if 4.4999999999999998e-231 < t < 2.9000000000000002e-195

   1. Initial program 99.7%

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

      1. associate-/l* 90.2%

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

      2. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in a around inf 80.8%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-195}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-34}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{x \cdot t}{y}}{b}\\ t_2 := \frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-195}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ (* x t) y)) b))
        (t_2 (/ x (+ 1.0 (+ a (/ (* y b) t))))))
   (if (<= t -1.45e-21)
     t_2
     (if (<= t 4.5e-231)
       t_1
       (if (<= t 3.25e-195)
         (/ (+ x (/ (* y z) t)) a)
         (if (<= t 4.6e-95) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double t_2 = x / (1.0 + (a + ((y * b) / t)));
	double tmp;
	if (t <= -1.45e-21) {
		tmp = t_2;
	} else if (t <= 4.5e-231) {
		tmp = t_1;
	} else if (t <= 3.25e-195) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (t <= 4.6e-95) {
		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 = (z + ((x * t) / y)) / b
    t_2 = x / (1.0d0 + (a + ((y * b) / t)))
    if (t <= (-1.45d-21)) then
        tmp = t_2
    else if (t <= 4.5d-231) then
        tmp = t_1
    else if (t <= 3.25d-195) then
        tmp = (x + ((y * z) / t)) / a
    else if (t <= 4.6d-95) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double t_2 = x / (1.0 + (a + ((y * b) / t)));
	double tmp;
	if (t <= -1.45e-21) {
		tmp = t_2;
	} else if (t <= 4.5e-231) {
		tmp = t_1;
	} else if (t <= 3.25e-195) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (t <= 4.6e-95) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + ((x * t) / y)) / b
	t_2 = x / (1.0 + (a + ((y * b) / t)))
	tmp = 0
	if t <= -1.45e-21:
		tmp = t_2
	elif t <= 4.5e-231:
		tmp = t_1
	elif t <= 3.25e-195:
		tmp = (x + ((y * z) / t)) / a
	elif t <= 4.6e-95:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(Float64(x * t) / y)) / b)
	t_2 = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))))
	tmp = 0.0
	if (t <= -1.45e-21)
		tmp = t_2;
	elseif (t <= 4.5e-231)
		tmp = t_1;
	elseif (t <= 3.25e-195)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	elseif (t <= 4.6e-95)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + ((x * t) / y)) / b;
	t_2 = x / (1.0 + (a + ((y * b) / t)));
	tmp = 0.0;
	if (t <= -1.45e-21)
		tmp = t_2;
	elseif (t <= 4.5e-231)
		tmp = t_1;
	elseif (t <= 3.25e-195)
		tmp = (x + ((y * z) / t)) / a;
	elseif (t <= 4.6e-95)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e-21], t$95$2, If[LessEqual[t, 4.5e-231], t$95$1, If[LessEqual[t, 3.25e-195], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 4.6e-95], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.45e-21 or 4.59999999999999998e-95 < t

   1. Initial program 80.3%

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

      1. associate-/l* 84.9%

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

      2. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x around inf 64.1%

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

   if -1.45e-21 < t < 4.4999999999999998e-231 or 3.25000000000000002e-195 < t < 4.59999999999999998e-95

   1. Initial program 67.1%

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

      1. associate-/l* 60.3%

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

      2. associate-/l* 55.8%

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

   3. Simplified 55.8%

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

   5. Taylor expanded in x around inf 62.3%

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

   6. Taylor expanded in b around inf 64.8%

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

   7. Taylor expanded in x around 0 72.6%

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

   if 4.4999999999999998e-231 < t < 3.25000000000000002e-195

   1. Initial program 99.7%

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

      1. associate-/l* 90.2%

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

      2. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in a around inf 80.8%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-195}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-95}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3400000000000:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;a \leq 0.00115:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y (/ t z))) (+ a 1.0))))
   (if (<= a -1.3e+124)
     t_1
     (if (<= a -3400000000000.0)
       (/ (+ z (/ (* x t) y)) b)
       (if (<= a 0.00115)
         (/ (+ x (* y (/ z t))) (+ 1.0 (* y (/ b t))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / (a + 1.0);
	double tmp;
	if (a <= -1.3e+124) {
		tmp = t_1;
	} else if (a <= -3400000000000.0) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (a <= 0.00115) {
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / (t / z))) / (a + 1.0d0)
    if (a <= (-1.3d+124)) then
        tmp = t_1
    else if (a <= (-3400000000000.0d0)) then
        tmp = (z + ((x * t) / y)) / b
    else if (a <= 0.00115d0) then
        tmp = (x + (y * (z / t))) / (1.0d0 + (y * (b / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / (a + 1.0);
	double tmp;
	if (a <= -1.3e+124) {
		tmp = t_1;
	} else if (a <= -3400000000000.0) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (a <= 0.00115) {
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y / (t / z))) / (a + 1.0)
	tmp = 0
	if a <= -1.3e+124:
		tmp = t_1
	elif a <= -3400000000000.0:
		tmp = (z + ((x * t) / y)) / b
	elif a <= 0.00115:
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0))
	tmp = 0.0
	if (a <= -1.3e+124)
		tmp = t_1;
	elseif (a <= -3400000000000.0)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (a <= 0.00115)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(1.0 + Float64(y * Float64(b / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y / (t / z))) / (a + 1.0);
	tmp = 0.0;
	if (a <= -1.3e+124)
		tmp = t_1;
	elseif (a <= -3400000000000.0)
		tmp = (z + ((x * t) / y)) / b;
	elseif (a <= 0.00115)
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.3e+124], t$95$1, If[LessEqual[a, -3400000000000.0], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[a, 0.00115], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.3e124 or 0.00115 < a

   1. Initial program 76.7%

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

      1. associate-/l* 79.5%

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

      2. associate-/l* 80.2%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in y around 0 70.6%

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

      1. clear-num 80.2%

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

      2. un-div-inv 80.3%

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

   7. Applied egg-rr 70.7%

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

   if -1.3e124 < a < -3.4e12

   1. Initial program 54.7%

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

      1. associate-/l* 48.3%

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

      2. associate-/l* 41.9%

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

   3. Simplified 41.9%

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

   5. Taylor expanded in x around inf 61.5%

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

   6. Taylor expanded in b around inf 57.3%

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

   7. Taylor expanded in x around 0 67.3%

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

   if -3.4e12 < a < 0.00115

   1. Initial program 77.9%

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

      1. associate-/l* 75.8%

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

      2. associate-/l* 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in a around 0 74.7%

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

      1. associate-*l/ 76.6%

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

      2. *-commutative 76.6%

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

   7. Simplified 76.6%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+124}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;a \leq -3400000000000:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;a \leq 0.00115:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{x \cdot t}{y}}{b}\\ t_2 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-195}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ (* x t) y)) b)) (t_2 (/ x (+ a 1.0))))
   (if (<= t -3.5e-20)
     t_2
     (if (<= t 4.5e-231)
       t_1
       (if (<= t 2.9e-195)
         (/ (+ x (/ (* y z) t)) a)
         (if (<= t 6.2e-33) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double t_2 = x / (a + 1.0);
	double tmp;
	if (t <= -3.5e-20) {
		tmp = t_2;
	} else if (t <= 4.5e-231) {
		tmp = t_1;
	} else if (t <= 2.9e-195) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (t <= 6.2e-33) {
		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 = (z + ((x * t) / y)) / b
    t_2 = x / (a + 1.0d0)
    if (t <= (-3.5d-20)) then
        tmp = t_2
    else if (t <= 4.5d-231) then
        tmp = t_1
    else if (t <= 2.9d-195) then
        tmp = (x + ((y * z) / t)) / a
    else if (t <= 6.2d-33) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double t_2 = x / (a + 1.0);
	double tmp;
	if (t <= -3.5e-20) {
		tmp = t_2;
	} else if (t <= 4.5e-231) {
		tmp = t_1;
	} else if (t <= 2.9e-195) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (t <= 6.2e-33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + ((x * t) / y)) / b
	t_2 = x / (a + 1.0)
	tmp = 0
	if t <= -3.5e-20:
		tmp = t_2
	elif t <= 4.5e-231:
		tmp = t_1
	elif t <= 2.9e-195:
		tmp = (x + ((y * z) / t)) / a
	elif t <= 6.2e-33:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(Float64(x * t) / y)) / b)
	t_2 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -3.5e-20)
		tmp = t_2;
	elseif (t <= 4.5e-231)
		tmp = t_1;
	elseif (t <= 2.9e-195)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	elseif (t <= 6.2e-33)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + ((x * t) / y)) / b;
	t_2 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -3.5e-20)
		tmp = t_2;
	elseif (t <= 4.5e-231)
		tmp = t_1;
	elseif (t <= 2.9e-195)
		tmp = (x + ((y * z) / t)) / a;
	elseif (t <= 6.2e-33)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e-20], t$95$2, If[LessEqual[t, 4.5e-231], t$95$1, If[LessEqual[t, 2.9e-195], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 6.2e-33], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.50000000000000003e-20 or 6.19999999999999994e-33 < t

   1. Initial program 80.1%

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

      1. associate-/l* 85.2%

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

      2. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in y around 0 62.2%

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

   if -3.50000000000000003e-20 < t < 4.4999999999999998e-231 or 2.9000000000000002e-195 < t < 6.19999999999999994e-33

   1. Initial program 69.3%

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

      1. associate-/l* 63.4%

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

      2. associate-/l* 57.9%

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

   3. Simplified 57.9%

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

   5. Taylor expanded in x around inf 64.3%

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

   6. Taylor expanded in b around inf 61.3%

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

   7. Taylor expanded in x around 0 68.8%

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

   if 4.4999999999999998e-231 < t < 2.9000000000000002e-195

   1. Initial program 99.7%

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

      1. associate-/l* 90.2%

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

      2. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in a around inf 80.8%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-195}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-33}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 54.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-21} \lor \neg \left(t \leq 5 \cdot 10^{-227} \lor \neg \left(t \leq 1.25 \cdot 10^{-181}\right) \land t \leq 4.6 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.2e-21)
         (not (or (<= t 5e-227) (and (not (<= t 1.25e-181)) (<= t 4.6e-29)))))
   (/ x (+ a 1.0))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.2e-21) || !((t <= 5e-227) || (!(t <= 1.25e-181) && (t <= 4.6e-29)))) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.2d-21)) .or. (.not. (t <= 5d-227) .or. (.not. (t <= 1.25d-181)) .and. (t <= 4.6d-29))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.2e-21) || !((t <= 5e-227) || (!(t <= 1.25e-181) && (t <= 4.6e-29)))) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.2e-21) or not ((t <= 5e-227) or (not (t <= 1.25e-181) and (t <= 4.6e-29))):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.2e-21) || !((t <= 5e-227) || (!(t <= 1.25e-181) && (t <= 4.6e-29))))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.2e-21) || ~(((t <= 5e-227) || (~((t <= 1.25e-181)) && (t <= 4.6e-29)))))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.2e-21], N[Not[Or[LessEqual[t, 5e-227], And[N[Not[LessEqual[t, 1.25e-181]], $MachinePrecision], LessEqual[t, 4.6e-29]]]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2000000000000001e-21 or 4.99999999999999961e-227 < t < 1.25e-181 or 4.59999999999999982e-29 < t

   1. Initial program 80.9%

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

      1. associate-/l* 85.0%

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

      2. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in y around 0 62.4%

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

   if -2.2000000000000001e-21 < t < 4.99999999999999961e-227 or 1.25e-181 < t < 4.59999999999999982e-29

   1. Initial program 69.8%

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

      1. associate-/l* 63.9%

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

      2. associate-/l* 58.4%

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

   3. Simplified 58.4%

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

   5. Taylor expanded in y around inf 60.3%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-21} \lor \neg \left(t \leq 5 \cdot 10^{-227} \lor \neg \left(t \leq 1.25 \cdot 10^{-181}\right) \land t \leq 4.6 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+123} \lor \neg \left(a \leq 5.8 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -6e+123) (not (<= a 5.8e+33))) (/ x a) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -6e+123) || !(a <= 5.8e+33)) {
		tmp = x / a;
	} 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 ((a <= (-6d+123)) .or. (.not. (a <= 5.8d+33))) then
        tmp = x / a
    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 ((a <= -6e+123) || !(a <= 5.8e+33)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -6e+123) or not (a <= 5.8e+33):
		tmp = x / a
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -6e+123) || !(a <= 5.8e+33))
		tmp = Float64(x / a);
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -6e+123) || ~((a <= 5.8e+33)))
		tmp = x / a;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -6e+123], N[Not[LessEqual[a, 5.8e+33]], $MachinePrecision]], N[(x / a), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.00000000000000016e123 or 5.80000000000000049e33 < a

   1. Initial program 77.6%

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

      1. associate-/l* 79.6%

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

      2. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in t around 0 54.7%

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

   6. Taylor expanded in x around inf 37.3%

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

   7. Taylor expanded in a around inf 53.4%

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

   if -6.00000000000000016e123 < a < 5.80000000000000049e33

   1. Initial program 75.1%

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

      1. associate-/l* 73.3%

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

      2. associate-/l* 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in y around inf 43.1%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+123} \lor \neg \left(a \leq 5.8 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 25.8% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.0%

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

   1. associate-/l* 75.7%

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

   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 t around 0 65.2%

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

6. Taylor expanded in x around inf 39.0%

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

7. Taylor expanded in a around inf 24.1%

   \[\leadsto \color{blue}{\frac{x}{a}} \]
8. 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 2024110 
(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))))