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

Percentage Accurate: 75.1% → 88.7%

Time: 14.5s

Alternatives: 16

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-171}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;t\_2 \leq 10^{+285}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x}{b} \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (/ (* y b) t))) (t_2 (/ (+ x (/ (* y z) t)) t_1)))
   (if (<= t_2 (- INFINITY))
     (/ (+ z (* t (/ x y))) b)
     (if (<= t_2 -1e-171)
       t_2
       (if (<= t_2 -5e-310)
         (/ (+ x (* y (/ z t))) t_1)
         (if (<= t_2 0.0)
           (+ (/ z b) (/ (* t (/ x b)) y))
           (if (<= t_2 1e+285) t_2 (+ (/ z b) (* (/ x b) (/ t y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + ((y * b) / t);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (z + (t * (x / y))) / b;
	} else if (t_2 <= -1e-171) {
		tmp = t_2;
	} else if (t_2 <= -5e-310) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = (z / b) + ((t * (x / b)) / y);
	} else if (t_2 <= 1e+285) {
		tmp = t_2;
	} else {
		tmp = (z / b) + ((x / b) * (t / y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + ((y * b) / t);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (z + (t * (x / y))) / b;
	} else if (t_2 <= -1e-171) {
		tmp = t_2;
	} else if (t_2 <= -5e-310) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = (z / b) + ((t * (x / b)) / y);
	} else if (t_2 <= 1e+285) {
		tmp = t_2;
	} else {
		tmp = (z / b) + ((x / b) * (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + ((y * b) / t)
	t_2 = (x + ((y * z) / t)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (z + (t * (x / y))) / b
	elif t_2 <= -1e-171:
		tmp = t_2
	elif t_2 <= -5e-310:
		tmp = (x + (y * (z / t))) / t_1
	elif t_2 <= 0.0:
		tmp = (z / b) + ((t * (x / b)) / y)
	elif t_2 <= 1e+285:
		tmp = t_2
	else:
		tmp = (z / b) + ((x / b) * (t / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	elseif (t_2 <= -1e-171)
		tmp = t_2;
	elseif (t_2 <= -5e-310)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / t_1);
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y));
	elseif (t_2 <= 1e+285)
		tmp = t_2;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x / b) * Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + ((y * b) / t);
	t_2 = (x + ((y * z) / t)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (z + (t * (x / y))) / b;
	elseif (t_2 <= -1e-171)
		tmp = t_2;
	elseif (t_2 <= -5e-310)
		tmp = (x + (y * (z / t))) / t_1;
	elseif (t_2 <= 0.0)
		tmp = (z / b) + ((t * (x / b)) / y);
	elseif (t_2 <= 1e+285)
		tmp = t_2;
	else
		tmp = (z / b) + ((x / b) * (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $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, (-Infinity)], N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$2, -1e-171], t$95$2, If[LessEqual[t$95$2, -5e-310], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+285], t$95$2, N[(N[(z / b), $MachinePrecision] + N[(N[(x / b), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 36.6%

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

   3. Taylor expanded in y around -inf 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

      4. sub-neg 50.6%

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

      5. mul-1-neg 50.6%

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

      6. associate-/l* 50.6%

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

      7. distribute-rgt-neg-in 50.6%

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

      8. mul-1-neg 50.6%

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

      9. remove-double-neg 50.6%

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

      10. associate-/l* 42.9%

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

   5. Simplified 42.9%

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

   6. Taylor expanded in x around inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. associate-*r/ 59.6%

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

      3. *-commutative 59.6%

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

      4. distribute-rgt-neg-in 59.6%

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

   8. Simplified 59.6%

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

   9. Taylor expanded in b around 0 68.0%

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

       1. sub-neg 68.0%

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

       2. mul-1-neg 68.0%

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

       3. remove-double-neg 68.0%

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

       4. associate-/l* 78.7%

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

   11. Simplified 78.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -9.9999999999999998e-172 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999998e284

   1. Initial program 99.1%

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

   if -9.9999999999999998e-172 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -4.999999999999985e-310

   1. Initial program 92.5%

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

      1. associate-/l* 99.9%

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

      2. *-commutative 99.9%

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

   4. Applied egg-rr 99.9%

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

   if -4.999999999999985e-310 < (/.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 45.6%

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

   3. Taylor expanded in y around -inf 71.8%

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

      1. +-commutative 71.8%

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

      2. mul-1-neg 71.8%

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

      3. unsub-neg 71.8%

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

      4. sub-neg 71.8%

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

      5. mul-1-neg 71.8%

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

      6. associate-/l* 74.4%

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

      7. distribute-rgt-neg-in 74.4%

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

      8. mul-1-neg 74.4%

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

      9. remove-double-neg 74.4%

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

      10. associate-/l* 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in x around inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. associate-*r/ 77.7%

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

      3. *-commutative 77.7%

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

      4. distribute-rgt-neg-in 77.7%

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

   8. Simplified 77.7%

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

   if 9.9999999999999998e284 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 14.8%

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

   3. Taylor expanded in y around -inf 58.8%

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

      1. +-commutative 58.8%

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

      2. mul-1-neg 58.8%

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

      3. unsub-neg 58.8%

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

      4. sub-neg 58.8%

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

      5. mul-1-neg 58.8%

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

      6. associate-/l* 58.8%

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

      7. distribute-rgt-neg-in 58.8%

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

      8. mul-1-neg 58.8%

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

      9. remove-double-neg 58.8%

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

      10. associate-/l* 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in x around inf 83.2%

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

      1. mul-1-neg 83.2%

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

      2. associate-*r/ 83.4%

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

      3. *-commutative 83.4%

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

      4. distribute-rgt-neg-in 83.4%

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

   8. Simplified 83.4%

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

      1. associate-/l* 83.5%

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

   10. Applied egg-rr 83.5%

       \[\leadsto \frac{z}{b} - \color{blue}{\frac{x}{b} \cdot \frac{-t}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-171}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+285}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x}{b} \cdot \frac{t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + t\_1}\\ t_3 := \left(a + t\_1\right) + 1\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_3} + \frac{y}{t \cdot t\_3}\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-310}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;t\_2 \leq 10^{+285}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x}{b} \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) t_1)))
        (t_3 (+ (+ a t_1) 1.0)))
   (if (<= t_2 (- INFINITY))
     (* z (+ (/ x (* z t_3)) (/ y (* t t_3))))
     (if (<= t_2 -5e-310)
       t_2
       (if (<= t_2 0.0)
         (+ (/ z b) (/ (* t (/ x b)) y))
         (if (<= t_2 1e+285) t_2 (+ (/ z b) (* (/ x b) (/ t y)))))))))

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)) / ((a + 1.0) + t_1);
	double t_3 = (a + t_1) + 1.0;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	} else if (t_2 <= -5e-310) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (z / b) + ((t * (x / b)) / y);
	} else if (t_2 <= 1e+285) {
		tmp = t_2;
	} else {
		tmp = (z / b) + ((x / b) * (t / y));
	}
	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)) / ((a + 1.0) + t_1);
	double t_3 = (a + t_1) + 1.0;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	} else if (t_2 <= -5e-310) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (z / b) + ((t * (x / b)) / y);
	} else if (t_2 <= 1e+285) {
		tmp = t_2;
	} else {
		tmp = (z / b) + ((x / b) * (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = (x + ((y * z) / t)) / ((a + 1.0) + t_1)
	t_3 = (a + t_1) + 1.0
	tmp = 0
	if t_2 <= -math.inf:
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)))
	elif t_2 <= -5e-310:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (z / b) + ((t * (x / b)) / y)
	elif t_2 <= 1e+285:
		tmp = t_2
	else:
		tmp = (z / b) + ((x / b) * (t / y))
	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(Float64(a + 1.0) + t_1))
	t_3 = Float64(Float64(a + t_1) + 1.0)
	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 <= -5e-310)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y));
	elseif (t_2 <= 1e+285)
		tmp = t_2;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x / b) * Float64(t / y)));
	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)) / ((a + 1.0) + t_1);
	t_3 = (a + t_1) + 1.0;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	elseif (t_2 <= -5e-310)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (z / b) + ((t * (x / b)) / y);
	elseif (t_2 <= 1e+285)
		tmp = t_2;
	else
		tmp = (z / b) + ((x / b) * (t / y));
	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[(N[(a + 1.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a + t$95$1), $MachinePrecision] + 1.0), $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, -5e-310], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+285], t$95$2, N[(N[(z / b), $MachinePrecision] + N[(N[(x / b), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]), $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 36.6%

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

   3. Taylor expanded in z around inf 91.3%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -4.999999999999985e-310 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999998e284

   1. Initial program 98.3%

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

   if -4.999999999999985e-310 < (/.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 45.6%

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

   3. Taylor expanded in y around -inf 71.8%

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

      1. +-commutative 71.8%

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

      2. mul-1-neg 71.8%

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

      3. unsub-neg 71.8%

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

      4. sub-neg 71.8%

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

      5. mul-1-neg 71.8%

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

      6. associate-/l* 74.4%

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

      7. distribute-rgt-neg-in 74.4%

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

      8. mul-1-neg 74.4%

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

      9. remove-double-neg 74.4%

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

      10. associate-/l* 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in x around inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. associate-*r/ 77.7%

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

      3. *-commutative 77.7%

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

      4. distribute-rgt-neg-in 77.7%

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

   8. Simplified 77.7%

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

   if 9.9999999999999998e284 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 14.8%

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

   3. Taylor expanded in y around -inf 58.8%

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

      1. +-commutative 58.8%

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

      2. mul-1-neg 58.8%

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

      3. unsub-neg 58.8%

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

      4. sub-neg 58.8%

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

      5. mul-1-neg 58.8%

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

      6. associate-/l* 58.8%

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

      7. distribute-rgt-neg-in 58.8%

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

      8. mul-1-neg 58.8%

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

      9. remove-double-neg 58.8%

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

      10. associate-/l* 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in x around inf 83.2%

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

      1. mul-1-neg 83.2%

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

      2. associate-*r/ 83.4%

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

      3. *-commutative 83.4%

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

      4. distribute-rgt-neg-in 83.4%

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

   8. Simplified 83.4%

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

      1. associate-/l* 83.5%

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

   10. Applied egg-rr 83.5%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(\left(a + \frac{y \cdot b}{t}\right) + 1\right)} + \frac{y}{t \cdot \left(\left(a + \frac{y \cdot b}{t}\right) + 1\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+285}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x}{b} \cdot \frac{t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;a + 1 \leq -5 \cdot 10^{+48}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{elif}\;a + 1 \leq 1:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;a + 1 \leq 5 \cdot 10^{+36}:\\ \;\;\;\;\frac{t\_1}{\frac{y \cdot b}{t} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= (+ a 1.0) -5e+48)
     (/ t_1 a)
     (if (<= (+ a 1.0) 1.0)
       (/ (* x (+ (/ t y) (/ z x))) b)
       (if (<= (+ a 1.0) 5e+36)
         (/ t_1 (+ (/ (* y b) t) 1.0))
         (/ (+ x (/ (* y z) t)) a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if ((a + 1.0) <= -5e+48) {
		tmp = t_1 / a;
	} else if ((a + 1.0) <= 1.0) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if ((a + 1.0) <= 5e+36) {
		tmp = t_1 / (((y * b) / t) + 1.0);
	} else {
		tmp = (x + ((y * z) / t)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    if ((a + 1.0d0) <= (-5d+48)) then
        tmp = t_1 / a
    else if ((a + 1.0d0) <= 1.0d0) then
        tmp = (x * ((t / y) + (z / x))) / b
    else if ((a + 1.0d0) <= 5d+36) then
        tmp = t_1 / (((y * b) / t) + 1.0d0)
    else
        tmp = (x + ((y * z) / t)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if ((a + 1.0) <= -5e+48) {
		tmp = t_1 / a;
	} else if ((a + 1.0) <= 1.0) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if ((a + 1.0) <= 5e+36) {
		tmp = t_1 / (((y * b) / t) + 1.0);
	} else {
		tmp = (x + ((y * z) / t)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * (z / t))
	tmp = 0
	if (a + 1.0) <= -5e+48:
		tmp = t_1 / a
	elif (a + 1.0) <= 1.0:
		tmp = (x * ((t / y) + (z / x))) / b
	elif (a + 1.0) <= 5e+36:
		tmp = t_1 / (((y * b) / t) + 1.0)
	else:
		tmp = (x + ((y * z) / t)) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (Float64(a + 1.0) <= -5e+48)
		tmp = Float64(t_1 / a);
	elseif (Float64(a + 1.0) <= 1.0)
		tmp = Float64(Float64(x * Float64(Float64(t / y) + Float64(z / x))) / b);
	elseif (Float64(a + 1.0) <= 5e+36)
		tmp = Float64(t_1 / Float64(Float64(Float64(y * b) / t) + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * (z / t));
	tmp = 0.0;
	if ((a + 1.0) <= -5e+48)
		tmp = t_1 / a;
	elseif ((a + 1.0) <= 1.0)
		tmp = (x * ((t / y) + (z / x))) / b;
	elseif ((a + 1.0) <= 5e+36)
		tmp = t_1 / (((y * b) / t) + 1.0);
	else
		tmp = (x + ((y * z) / t)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a + 1.0), $MachinePrecision], -5e+48], N[(t$95$1 / a), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], 1.0], N[(N[(x * N[(N[(t / y), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], 5e+36], N[(t$95$1 / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 a #s(literal 1 binary64)) < -4.99999999999999973e48

   1. Initial program 83.5%

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

      1. associate-/l* 83.2%

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

      2. *-commutative 83.2%

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

   4. Applied egg-rr 83.2%

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

   5. Taylor expanded in a around inf 81.4%

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

   if -4.99999999999999973e48 < (+.f64 a #s(literal 1 binary64)) < 1

   1. Initial program 75.5%

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

   3. Taylor expanded in x around inf 71.4%

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

   4. Taylor expanded in b around inf 46.0%

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

   if 1 < (+.f64 a #s(literal 1 binary64)) < 4.99999999999999977e36

   1. Initial program 90.1%

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

      1. associate-/l* 90.2%

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

      2. *-commutative 90.2%

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

   4. Applied egg-rr 90.2%

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

   5. Taylor expanded in a around 0 62.5%

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

   if 4.99999999999999977e36 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 81.0%

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

   3. Taylor expanded in a around inf 75.2%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -5 \cdot 10^{+48}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a + 1 \leq 1:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;a + 1 \leq 5 \cdot 10^{+36}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\frac{y \cdot b}{t} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+47}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-136}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + 1}\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-277}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (* t (/ x y))) b)))
   (if (<= a -1.35e+47)
     (/ (+ x (* y (/ z t))) a)
     (if (<= a -1.9e-38)
       t_1
       (if (<= a -8e-136)
         (/ x (+ (* y (/ b t)) 1.0))
         (if (<= a -1.42e-277)
           (+ x (* z (/ y t)))
           (if (<= a 7e+76) t_1 (/ (+ x (/ (* y z) t)) a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (t * (x / y))) / b;
	double tmp;
	if (a <= -1.35e+47) {
		tmp = (x + (y * (z / t))) / a;
	} else if (a <= -1.9e-38) {
		tmp = t_1;
	} else if (a <= -8e-136) {
		tmp = x / ((y * (b / t)) + 1.0);
	} else if (a <= -1.42e-277) {
		tmp = x + (z * (y / t));
	} else if (a <= 7e+76) {
		tmp = t_1;
	} else {
		tmp = (x + ((y * z) / t)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + (t * (x / y))) / b
    if (a <= (-1.35d+47)) then
        tmp = (x + (y * (z / t))) / a
    else if (a <= (-1.9d-38)) then
        tmp = t_1
    else if (a <= (-8d-136)) then
        tmp = x / ((y * (b / t)) + 1.0d0)
    else if (a <= (-1.42d-277)) then
        tmp = x + (z * (y / t))
    else if (a <= 7d+76) then
        tmp = t_1
    else
        tmp = (x + ((y * z) / t)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (t * (x / y))) / b;
	double tmp;
	if (a <= -1.35e+47) {
		tmp = (x + (y * (z / t))) / a;
	} else if (a <= -1.9e-38) {
		tmp = t_1;
	} else if (a <= -8e-136) {
		tmp = x / ((y * (b / t)) + 1.0);
	} else if (a <= -1.42e-277) {
		tmp = x + (z * (y / t));
	} else if (a <= 7e+76) {
		tmp = t_1;
	} else {
		tmp = (x + ((y * z) / t)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + (t * (x / y))) / b
	tmp = 0
	if a <= -1.35e+47:
		tmp = (x + (y * (z / t))) / a
	elif a <= -1.9e-38:
		tmp = t_1
	elif a <= -8e-136:
		tmp = x / ((y * (b / t)) + 1.0)
	elif a <= -1.42e-277:
		tmp = x + (z * (y / t))
	elif a <= 7e+76:
		tmp = t_1
	else:
		tmp = (x + ((y * z) / t)) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(t * Float64(x / y))) / b)
	tmp = 0.0
	if (a <= -1.35e+47)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / a);
	elseif (a <= -1.9e-38)
		tmp = t_1;
	elseif (a <= -8e-136)
		tmp = Float64(x / Float64(Float64(y * Float64(b / t)) + 1.0));
	elseif (a <= -1.42e-277)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (a <= 7e+76)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + (t * (x / y))) / b;
	tmp = 0.0;
	if (a <= -1.35e+47)
		tmp = (x + (y * (z / t))) / a;
	elseif (a <= -1.9e-38)
		tmp = t_1;
	elseif (a <= -8e-136)
		tmp = x / ((y * (b / t)) + 1.0);
	elseif (a <= -1.42e-277)
		tmp = x + (z * (y / t));
	elseif (a <= 7e+76)
		tmp = t_1;
	else
		tmp = (x + ((y * z) / t)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[a, -1.35e+47], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -1.9e-38], t$95$1, If[LessEqual[a, -8e-136], N[(x / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.42e-277], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e+76], t$95$1, N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.34999999999999998e47

   1. Initial program 83.5%

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

      1. associate-/l* 83.2%

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

      2. *-commutative 83.2%

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

   4. Applied egg-rr 83.2%

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

   5. Taylor expanded in a around inf 81.4%

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

   if -1.34999999999999998e47 < a < -1.9e-38 or -1.4199999999999999e-277 < a < 7.00000000000000001e76

   1. Initial program 73.2%

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

   3. Taylor expanded in y around -inf 51.0%

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

      1. +-commutative 51.0%

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

      2. mul-1-neg 51.0%

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

      3. unsub-neg 51.0%

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

      4. sub-neg 51.0%

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

      5. mul-1-neg 51.0%

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

      6. associate-/l* 51.8%

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

      7. distribute-rgt-neg-in 51.8%

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

      8. mul-1-neg 51.8%

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

      9. remove-double-neg 51.8%

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

      10. associate-/l* 52.0%

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

   5. Simplified 52.0%

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

   6. Taylor expanded in x around inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. associate-*r/ 56.3%

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

      3. *-commutative 56.3%

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

      4. distribute-rgt-neg-in 56.3%

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

   8. Simplified 56.3%

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

   9. Taylor expanded in b around 0 57.7%

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

       1. sub-neg 57.7%

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

       2. mul-1-neg 57.7%

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

       3. remove-double-neg 57.7%

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

       4. associate-/l* 58.0%

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

   11. Simplified 58.0%

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

   if -1.9e-38 < a < -8.00000000000000001e-136

   1. Initial program 88.0%

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

   3. Taylor expanded in x around inf 72.8%

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

   4. Taylor expanded in a around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-*r/ 72.9%

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

   6. Simplified 72.9%

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

   if -8.00000000000000001e-136 < a < -1.4199999999999999e-277

   1. Initial program 78.3%

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

   3. Taylor expanded in b around 0 78.6%

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

   4. Taylor expanded in a around 0 78.6%

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

      1. *-commutative 78.3%

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

      2. associate-/l* 83.6%

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

   6. Applied egg-rr 83.9%

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

   if 7.00000000000000001e76 < a

   1. Initial program 83.1%

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

   3. Taylor expanded in a around inf 78.7%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z}{t}}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+47}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-38}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-136}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + 1}\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-277}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+76}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 42.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-38}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-281}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-114}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+77}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.6e+43)
   (/ x a)
   (if (<= a -1.85e-38)
     (/ z b)
     (if (<= a 4e-281)
       x
       (if (<= a 6.2e-114)
         (/ z b)
         (if (<= a 6e-90) x (if (<= a 1.1e+77) (/ z b) (/ x a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.6e+43) {
		tmp = x / a;
	} else if (a <= -1.85e-38) {
		tmp = z / b;
	} else if (a <= 4e-281) {
		tmp = x;
	} else if (a <= 6.2e-114) {
		tmp = z / b;
	} else if (a <= 6e-90) {
		tmp = x;
	} else if (a <= 1.1e+77) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.6d+43)) then
        tmp = x / a
    else if (a <= (-1.85d-38)) then
        tmp = z / b
    else if (a <= 4d-281) then
        tmp = x
    else if (a <= 6.2d-114) then
        tmp = z / b
    else if (a <= 6d-90) then
        tmp = x
    else if (a <= 1.1d+77) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.6e+43) {
		tmp = x / a;
	} else if (a <= -1.85e-38) {
		tmp = z / b;
	} else if (a <= 4e-281) {
		tmp = x;
	} else if (a <= 6.2e-114) {
		tmp = z / b;
	} else if (a <= 6e-90) {
		tmp = x;
	} else if (a <= 1.1e+77) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.6e+43:
		tmp = x / a
	elif a <= -1.85e-38:
		tmp = z / b
	elif a <= 4e-281:
		tmp = x
	elif a <= 6.2e-114:
		tmp = z / b
	elif a <= 6e-90:
		tmp = x
	elif a <= 1.1e+77:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.6e+43)
		tmp = Float64(x / a);
	elseif (a <= -1.85e-38)
		tmp = Float64(z / b);
	elseif (a <= 4e-281)
		tmp = x;
	elseif (a <= 6.2e-114)
		tmp = Float64(z / b);
	elseif (a <= 6e-90)
		tmp = x;
	elseif (a <= 1.1e+77)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.6e+43)
		tmp = x / a;
	elseif (a <= -1.85e-38)
		tmp = z / b;
	elseif (a <= 4e-281)
		tmp = x;
	elseif (a <= 6.2e-114)
		tmp = z / b;
	elseif (a <= 6e-90)
		tmp = x;
	elseif (a <= 1.1e+77)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.6e+43], N[(x / a), $MachinePrecision], If[LessEqual[a, -1.85e-38], N[(z / b), $MachinePrecision], If[LessEqual[a, 4e-281], x, If[LessEqual[a, 6.2e-114], N[(z / b), $MachinePrecision], If[LessEqual[a, 6e-90], x, If[LessEqual[a, 1.1e+77], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.60000000000000021e43 or 1.1e77 < a

   1. Initial program 83.7%

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

   3. Taylor expanded in y around 0 61.0%

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

   4. Taylor expanded in a around inf 61.0%

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

   if -2.60000000000000021e43 < a < -1.85e-38 or 4.0000000000000001e-281 < a < 6.2e-114 or 6.00000000000000041e-90 < a < 1.1e77

   1. Initial program 71.5%

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

   3. Taylor expanded in y around inf 49.5%

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

   if -1.85e-38 < a < 4.0000000000000001e-281 or 6.2e-114 < a < 6.00000000000000041e-90

   1. Initial program 82.6%

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

   3. Taylor expanded in y around 0 47.2%

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

   4. Taylor expanded in a around 0 47.2%

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

Alternative 6: 68.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+39}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+52} \lor \neg \left(y \leq 3.65 \cdot 10^{+174}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x}{y} \cdot \frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.3e+39)
   (/ (+ z (* t (/ x y))) b)
   (if (<= y 6.8e+24)
     (/ (+ x (/ (* y z) t)) (+ a 1.0))
     (if (or (<= y 1.9e+52) (not (<= y 3.65e+174)))
       (+ (/ z b) (* (/ x y) (/ t b)))
       (/ (+ x (* y (/ z t))) (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.3e+39) {
		tmp = (z + (t * (x / y))) / b;
	} else if (y <= 6.8e+24) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if ((y <= 1.9e+52) || !(y <= 3.65e+174)) {
		tmp = (z / b) + ((x / y) * (t / b));
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.3d+39)) then
        tmp = (z + (t * (x / y))) / b
    else if (y <= 6.8d+24) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if ((y <= 1.9d+52) .or. (.not. (y <= 3.65d+174))) then
        tmp = (z / b) + ((x / y) * (t / b))
    else
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.3e+39) {
		tmp = (z + (t * (x / y))) / b;
	} else if (y <= 6.8e+24) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if ((y <= 1.9e+52) || !(y <= 3.65e+174)) {
		tmp = (z / b) + ((x / y) * (t / b));
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.3e+39:
		tmp = (z + (t * (x / y))) / b
	elif y <= 6.8e+24:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif (y <= 1.9e+52) or not (y <= 3.65e+174):
		tmp = (z / b) + ((x / y) * (t / b))
	else:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.3e+39)
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	elseif (y <= 6.8e+24)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif ((y <= 1.9e+52) || !(y <= 3.65e+174))
		tmp = Float64(Float64(z / b) + Float64(Float64(x / y) * Float64(t / b)));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.3e+39)
		tmp = (z + (t * (x / y))) / b;
	elseif (y <= 6.8e+24)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif ((y <= 1.9e+52) || ~((y <= 3.65e+174)))
		tmp = (z / b) + ((x / y) * (t / b));
	else
		tmp = (x + (y * (z / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.3e+39], N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 6.8e+24], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.9e+52], N[Not[LessEqual[y, 3.65e+174]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] * N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3e39

   1. Initial program 65.6%

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

   3. Taylor expanded in y around -inf 52.4%

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

      1. +-commutative 52.4%

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

      2. mul-1-neg 52.4%

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

      3. unsub-neg 52.4%

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

      4. sub-neg 52.4%

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

      5. mul-1-neg 52.4%

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

      6. associate-/l* 54.1%

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

      7. distribute-rgt-neg-in 54.1%

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

      8. mul-1-neg 54.1%

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

      9. remove-double-neg 54.1%

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

      10. associate-/l* 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in x around inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. associate-*r/ 60.4%

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

      3. *-commutative 60.4%

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

      4. distribute-rgt-neg-in 60.4%

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

   8. Simplified 60.4%

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

   9. Taylor expanded in b around 0 63.0%

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

       1. sub-neg 63.0%

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

       2. mul-1-neg 63.0%

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

       3. remove-double-neg 63.0%

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

       4. associate-/l* 68.6%

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

   11. Simplified 68.6%

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

   if -1.3e39 < y < 6.8000000000000001e24

   1. Initial program 92.6%

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

   3. Taylor expanded in b around 0 78.1%

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

   if 6.8000000000000001e24 < y < 1.9e52 or 3.6500000000000002e174 < y

   1. Initial program 39.6%

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

   3. Taylor expanded in y around -inf 68.3%

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

      1. +-commutative 68.3%

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

      2. mul-1-neg 68.3%

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

      3. unsub-neg 68.3%

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

      4. sub-neg 68.3%

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

      5. mul-1-neg 68.3%

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

      6. associate-/l* 68.2%

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

      7. distribute-rgt-neg-in 68.2%

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

      8. mul-1-neg 68.2%

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

      9. remove-double-neg 68.2%

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

      10. associate-/l* 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in x around inf 80.1%

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

      1. mul-1-neg 80.1%

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

      2. times-frac 89.3%

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

      3. distribute-lft-neg-in 89.3%

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

      4. mul-1-neg 89.3%

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

      5. associate-*r/ 89.3%

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

      6. neg-mul-1 89.3%

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

   8. Simplified 89.3%

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

   if 1.9e52 < y < 3.6500000000000002e174

   1. Initial program 80.1%

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

      1. associate-/l* 84.4%

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

      2. *-commutative 84.4%

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

   4. Applied egg-rr 84.4%

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

   5. Taylor expanded in y around 0 67.3%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+39}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+52} \lor \neg \left(y \leq 3.65 \cdot 10^{+174}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x}{y} \cdot \frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+52} \lor \neg \left(y \leq 1.2 \cdot 10^{+177}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (* t (/ x y))) b)))
   (if (<= y -1.3e+40)
     t_1
     (if (<= y 2.7e+24)
       (/ (+ x (/ (* y z) t)) (+ a 1.0))
       (if (or (<= y 2.3e+52) (not (<= y 1.2e+177)))
         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 + (t * (x / y))) / b;
	double tmp;
	if (y <= -1.3e+40) {
		tmp = t_1;
	} else if (y <= 2.7e+24) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if ((y <= 2.3e+52) || !(y <= 1.2e+177)) {
		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 + (t * (x / y))) / b
    if (y <= (-1.3d+40)) then
        tmp = t_1
    else if (y <= 2.7d+24) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if ((y <= 2.3d+52) .or. (.not. (y <= 1.2d+177))) 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 + (t * (x / y))) / b;
	double tmp;
	if (y <= -1.3e+40) {
		tmp = t_1;
	} else if (y <= 2.7e+24) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if ((y <= 2.3e+52) || !(y <= 1.2e+177)) {
		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 + (t * (x / y))) / b
	tmp = 0
	if y <= -1.3e+40:
		tmp = t_1
	elif y <= 2.7e+24:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif (y <= 2.3e+52) or not (y <= 1.2e+177):
		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(t * Float64(x / y))) / b)
	tmp = 0.0
	if (y <= -1.3e+40)
		tmp = t_1;
	elseif (y <= 2.7e+24)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif ((y <= 2.3e+52) || !(y <= 1.2e+177))
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + (t * (x / y))) / b;
	tmp = 0.0;
	if (y <= -1.3e+40)
		tmp = t_1;
	elseif (y <= 2.7e+24)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif ((y <= 2.3e+52) || ~((y <= 1.2e+177)))
		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[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -1.3e+40], t$95$1, If[LessEqual[y, 2.7e+24], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.3e+52], N[Not[LessEqual[y, 1.2e+177]], $MachinePrecision]], t$95$1, N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3e40 or 2.7e24 < y < 2.3e52 or 1.2e177 < y

   1. Initial program 55.6%

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

   3. Taylor expanded in y around -inf 58.5%

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

      1. +-commutative 58.5%

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

      2. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

      4. sub-neg 58.5%

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

      5. mul-1-neg 58.5%

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

      6. associate-/l* 59.6%

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

      7. distribute-rgt-neg-in 59.6%

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

      8. mul-1-neg 59.6%

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

      9. remove-double-neg 59.6%

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

      10. associate-/l* 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in x around inf 70.6%

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

      1. mul-1-neg 70.6%

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

      2. associate-*r/ 69.1%

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

      3. *-commutative 69.1%

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

      4. distribute-rgt-neg-in 69.1%

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

   8. Simplified 69.1%

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

   9. Taylor expanded in b around 0 71.8%

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

       1. sub-neg 71.8%

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

       2. mul-1-neg 71.8%

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

       3. remove-double-neg 71.8%

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

       4. associate-/l* 75.5%

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

   11. Simplified 75.5%

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

   if -1.3e40 < y < 2.7e24

   1. Initial program 92.6%

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

   3. Taylor expanded in b around 0 78.1%

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

   if 2.3e52 < y < 1.2e177

   1. Initial program 80.1%

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

      1. associate-/l* 84.4%

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

      2. *-commutative 84.4%

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

   4. Applied egg-rr 84.4%

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

   5. Taylor expanded in y around 0 67.3%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+40}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+52} \lor \neg \left(y \leq 1.2 \cdot 10^{+177}\right):\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + t \cdot \frac{x}{y}}{b}\\ t_2 := \frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{-117}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 18000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + \frac{b}{\frac{t}{y}}\right) + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (* t (/ x y))) b))
        (t_2 (/ (+ x (* y (/ z t))) (+ a 1.0))))
   (if (<= t -1.85e-117)
     t_2
     (if (<= t 2.25e-73)
       t_1
       (if (<= t 1.15e-43)
         t_2
         (if (<= t 18000.0) t_1 (/ x (+ (+ a (/ b (/ t y))) 1.0))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (t * (x / y))) / b;
	double t_2 = (x + (y * (z / t))) / (a + 1.0);
	double tmp;
	if (t <= -1.85e-117) {
		tmp = t_2;
	} else if (t <= 2.25e-73) {
		tmp = t_1;
	} else if (t <= 1.15e-43) {
		tmp = t_2;
	} else if (t <= 18000.0) {
		tmp = t_1;
	} else {
		tmp = x / ((a + (b / (t / y))) + 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) :: t_2
    real(8) :: tmp
    t_1 = (z + (t * (x / y))) / b
    t_2 = (x + (y * (z / t))) / (a + 1.0d0)
    if (t <= (-1.85d-117)) then
        tmp = t_2
    else if (t <= 2.25d-73) then
        tmp = t_1
    else if (t <= 1.15d-43) then
        tmp = t_2
    else if (t <= 18000.0d0) then
        tmp = t_1
    else
        tmp = x / ((a + (b / (t / y))) + 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 + (t * (x / y))) / b;
	double t_2 = (x + (y * (z / t))) / (a + 1.0);
	double tmp;
	if (t <= -1.85e-117) {
		tmp = t_2;
	} else if (t <= 2.25e-73) {
		tmp = t_1;
	} else if (t <= 1.15e-43) {
		tmp = t_2;
	} else if (t <= 18000.0) {
		tmp = t_1;
	} else {
		tmp = x / ((a + (b / (t / y))) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + (t * (x / y))) / b
	t_2 = (x + (y * (z / t))) / (a + 1.0)
	tmp = 0
	if t <= -1.85e-117:
		tmp = t_2
	elif t <= 2.25e-73:
		tmp = t_1
	elif t <= 1.15e-43:
		tmp = t_2
	elif t <= 18000.0:
		tmp = t_1
	else:
		tmp = x / ((a + (b / (t / y))) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(t * Float64(x / y))) / b)
	t_2 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -1.85e-117)
		tmp = t_2;
	elseif (t <= 2.25e-73)
		tmp = t_1;
	elseif (t <= 1.15e-43)
		tmp = t_2;
	elseif (t <= 18000.0)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(Float64(a + Float64(b / Float64(t / y))) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + (t * (x / y))) / b;
	t_2 = (x + (y * (z / t))) / (a + 1.0);
	tmp = 0.0;
	if (t <= -1.85e-117)
		tmp = t_2;
	elseif (t <= 2.25e-73)
		tmp = t_1;
	elseif (t <= 1.15e-43)
		tmp = t_2;
	elseif (t <= 18000.0)
		tmp = t_1;
	else
		tmp = x / ((a + (b / (t / y))) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.85e-117], t$95$2, If[LessEqual[t, 2.25e-73], t$95$1, If[LessEqual[t, 1.15e-43], t$95$2, If[LessEqual[t, 18000.0], t$95$1, N[(x / N[(N[(a + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8500000000000001e-117 or 2.25e-73 < t < 1.1499999999999999e-43

   1. Initial program 85.2%

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

      1. associate-/l* 85.6%

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

      2. *-commutative 85.6%

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

   4. Applied egg-rr 85.6%

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

   5. Taylor expanded in y around 0 77.8%

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

   if -1.8500000000000001e-117 < t < 2.25e-73 or 1.1499999999999999e-43 < t < 18000

   1. Initial program 66.5%

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

   3. Taylor expanded in y around -inf 58.7%

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

      1. +-commutative 58.7%

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

      2. mul-1-neg 58.7%

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

      3. unsub-neg 58.7%

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

      4. sub-neg 58.7%

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

      5. mul-1-neg 58.7%

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

      6. associate-/l* 57.8%

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

      7. distribute-rgt-neg-in 57.8%

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

      8. mul-1-neg 57.8%

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

      9. remove-double-neg 57.8%

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

      10. associate-/l* 57.8%

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

   5. Simplified 57.8%

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

   6. Taylor expanded in x around inf 69.2%

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

      1. mul-1-neg 69.2%

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

      2. associate-*r/ 66.0%

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

      3. *-commutative 66.0%

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

      4. distribute-rgt-neg-in 66.0%

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

   8. Simplified 66.0%

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

   9. Taylor expanded in b around 0 69.9%

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

       1. sub-neg 69.9%

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

       2. mul-1-neg 69.9%

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

       3. remove-double-neg 69.9%

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

       4. associate-/l* 68.0%

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

   11. Simplified 68.0%

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

   if 18000 < t

   1. Initial program 89.5%

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

   3. Taylor expanded in x around inf 74.6%

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

      1. associate-/l* 81.3%

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

      2. clear-num 81.3%

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

      3. un-div-inv 81.3%

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

   5. Applied egg-rr 81.3%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-117}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-73}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-43}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 18000:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + \frac{b}{\frac{t}{y}}\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a + 1 \leq -1 \cdot 10^{+44}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a + 1 \leq 1:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a + 1 \leq 5 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ a 1.0) -1e+44)
   (/ (+ x (* y (/ z t))) a)
   (if (<= (+ a 1.0) 1.0)
     (/ z b)
     (if (<= (+ a 1.0) 5e+36)
       (/ x (+ (* y (/ b t)) 1.0))
       (/ (+ x (/ (* y z) t)) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a + 1.0) <= -1e+44) {
		tmp = (x + (y * (z / t))) / a;
	} else if ((a + 1.0) <= 1.0) {
		tmp = z / b;
	} else if ((a + 1.0) <= 5e+36) {
		tmp = x / ((y * (b / t)) + 1.0);
	} else {
		tmp = (x + ((y * z) / t)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a + 1.0d0) <= (-1d+44)) then
        tmp = (x + (y * (z / t))) / a
    else if ((a + 1.0d0) <= 1.0d0) then
        tmp = z / b
    else if ((a + 1.0d0) <= 5d+36) then
        tmp = x / ((y * (b / t)) + 1.0d0)
    else
        tmp = (x + ((y * z) / t)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a + 1.0) <= -1e+44) {
		tmp = (x + (y * (z / t))) / a;
	} else if ((a + 1.0) <= 1.0) {
		tmp = z / b;
	} else if ((a + 1.0) <= 5e+36) {
		tmp = x / ((y * (b / t)) + 1.0);
	} else {
		tmp = (x + ((y * z) / t)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a + 1.0) <= -1e+44:
		tmp = (x + (y * (z / t))) / a
	elif (a + 1.0) <= 1.0:
		tmp = z / b
	elif (a + 1.0) <= 5e+36:
		tmp = x / ((y * (b / t)) + 1.0)
	else:
		tmp = (x + ((y * z) / t)) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(a + 1.0) <= -1e+44)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / a);
	elseif (Float64(a + 1.0) <= 1.0)
		tmp = Float64(z / b);
	elseif (Float64(a + 1.0) <= 5e+36)
		tmp = Float64(x / Float64(Float64(y * Float64(b / t)) + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a + 1.0) <= -1e+44)
		tmp = (x + (y * (z / t))) / a;
	elseif ((a + 1.0) <= 1.0)
		tmp = z / b;
	elseif ((a + 1.0) <= 5e+36)
		tmp = x / ((y * (b / t)) + 1.0);
	else
		tmp = (x + ((y * z) / t)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(a + 1.0), $MachinePrecision], -1e+44], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], 1.0], N[(z / b), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], 5e+36], N[(x / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 a #s(literal 1 binary64)) < -1.0000000000000001e44

   1. Initial program 84.1%

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

      1. associate-/l* 83.8%

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

      2. *-commutative 83.8%

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

   4. Applied egg-rr 83.8%

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

   5. Taylor expanded in a around inf 80.3%

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

   if -1.0000000000000001e44 < (+.f64 a #s(literal 1 binary64)) < 1

   1. Initial program 75.2%

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

   3. Taylor expanded in y around inf 39.0%

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

   if 1 < (+.f64 a #s(literal 1 binary64)) < 4.99999999999999977e36

   1. Initial program 90.1%

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

   3. Taylor expanded in x around inf 71.6%

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

   4. Taylor expanded in a around 0 50.3%

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

      1. *-commutative 50.3%

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

      2. associate-*r/ 50.1%

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

   6. Simplified 50.1%

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

   if 4.99999999999999977e36 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 81.0%

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

   3. Taylor expanded in a around inf 75.2%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -1 \cdot 10^{+44}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a + 1 \leq 1:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a + 1 \leq 5 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{if}\;a + 1 \leq -1 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a + 1 \leq 1:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a + 1 \leq 5 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) a)))
   (if (<= (+ a 1.0) -1e+44)
     t_1
     (if (<= (+ a 1.0) 1.0)
       (/ z b)
       (if (<= (+ a 1.0) 5e+36) (/ x (+ (* y (/ b t)) 1.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / a;
	double tmp;
	if ((a + 1.0) <= -1e+44) {
		tmp = t_1;
	} else if ((a + 1.0) <= 1.0) {
		tmp = z / b;
	} else if ((a + 1.0) <= 5e+36) {
		tmp = x / ((y * (b / t)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / a
    if ((a + 1.0d0) <= (-1d+44)) then
        tmp = t_1
    else if ((a + 1.0d0) <= 1.0d0) then
        tmp = z / b
    else if ((a + 1.0d0) <= 5d+36) then
        tmp = x / ((y * (b / t)) + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / a;
	double tmp;
	if ((a + 1.0) <= -1e+44) {
		tmp = t_1;
	} else if ((a + 1.0) <= 1.0) {
		tmp = z / b;
	} else if ((a + 1.0) <= 5e+36) {
		tmp = x / ((y * (b / t)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / a
	tmp = 0
	if (a + 1.0) <= -1e+44:
		tmp = t_1
	elif (a + 1.0) <= 1.0:
		tmp = z / b
	elif (a + 1.0) <= 5e+36:
		tmp = x / ((y * (b / t)) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / a)
	tmp = 0.0
	if (Float64(a + 1.0) <= -1e+44)
		tmp = t_1;
	elseif (Float64(a + 1.0) <= 1.0)
		tmp = Float64(z / b);
	elseif (Float64(a + 1.0) <= 5e+36)
		tmp = Float64(x / Float64(Float64(y * Float64(b / t)) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / a;
	tmp = 0.0;
	if ((a + 1.0) <= -1e+44)
		tmp = t_1;
	elseif ((a + 1.0) <= 1.0)
		tmp = z / b;
	elseif ((a + 1.0) <= 5e+36)
		tmp = x / ((y * (b / t)) + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[N[(a + 1.0), $MachinePrecision], -1e+44], t$95$1, If[LessEqual[N[(a + 1.0), $MachinePrecision], 1.0], N[(z / b), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], 5e+36], N[(x / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 a #s(literal 1 binary64)) < -1.0000000000000001e44 or 4.99999999999999977e36 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 82.7%

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

      1. associate-/l* 79.6%

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

      2. *-commutative 79.6%

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

   4. Applied egg-rr 79.6%

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

   5. Taylor expanded in a around inf 76.1%

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

   if -1.0000000000000001e44 < (+.f64 a #s(literal 1 binary64)) < 1

   1. Initial program 75.2%

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

   3. Taylor expanded in y around inf 39.0%

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

   if 1 < (+.f64 a #s(literal 1 binary64)) < 4.99999999999999977e36

   1. Initial program 90.1%

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

   3. Taylor expanded in x around inf 71.6%

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

   4. Taylor expanded in a around 0 50.3%

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

      1. *-commutative 50.3%

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

      2. associate-*r/ 50.1%

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

   6. Simplified 50.1%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -1 \cdot 10^{+44}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a + 1 \leq 1:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a + 1 \leq 5 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 81.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+109}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+175}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x}{y} \cdot \frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.2e+109)
   (/ (+ z (* t (/ x y))) b)
   (if (<= y 4e+175)
     (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (* b (/ y t))))
     (+ (/ z b) (* (/ x y) (/ t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.2e+109) {
		tmp = (z + (t * (x / y))) / b;
	} else if (y <= 4e+175) {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z / b) + ((x / y) * (t / b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.2d+109)) then
        tmp = (z + (t * (x / y))) / b
    else if (y <= 4d+175) then
        tmp = (x + ((y * z) / t)) / ((a + 1.0d0) + (b * (y / t)))
    else
        tmp = (z / b) + ((x / y) * (t / b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.2e+109) {
		tmp = (z + (t * (x / y))) / b;
	} else if (y <= 4e+175) {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z / b) + ((x / y) * (t / b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.2e+109:
		tmp = (z + (t * (x / y))) / b
	elif y <= 4e+175:
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = (z / b) + ((x / y) * (t / b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.2e+109)
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	elseif (y <= 4e+175)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x / y) * Float64(t / b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.2e+109)
		tmp = (z + (t * (x / y))) / b;
	elseif (y <= 4e+175)
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	else
		tmp = (z / b) + ((x / y) * (t / b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.2e+109], N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 4e+175], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] * N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2000000000000001e109

   1. Initial program 61.0%

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

   3. Taylor expanded in y around -inf 55.4%

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

      1. +-commutative 55.4%

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

      2. mul-1-neg 55.4%

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

      3. unsub-neg 55.4%

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

      4. sub-neg 55.4%

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

      5. mul-1-neg 55.4%

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

      6. associate-/l* 55.3%

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

      7. distribute-rgt-neg-in 55.3%

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

      8. mul-1-neg 55.3%

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

      9. remove-double-neg 55.3%

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

      10. associate-/l* 55.4%

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

   5. Simplified 55.4%

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

   6. Taylor expanded in x around inf 68.2%

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

      1. mul-1-neg 68.2%

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

      2. associate-*r/ 63.4%

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

      3. *-commutative 63.4%

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

      4. distribute-rgt-neg-in 63.4%

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

   8. Simplified 63.4%

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

   9. Taylor expanded in b around 0 68.4%

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

       1. sub-neg 68.4%

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

       2. mul-1-neg 68.4%

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

       3. remove-double-neg 68.4%

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

       4. associate-/l* 73.5%

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

   11. Simplified 73.5%

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

   if -3.2000000000000001e109 < y < 3.9999999999999997e175

   1. Initial program 90.2%

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

   3. Taylor expanded in y around 0 90.2%

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

      1. associate-*r/ 90.7%

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

   5. Simplified 90.7%

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

   if 3.9999999999999997e175 < y

   1. Initial program 24.2%

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

   3. Taylor expanded in y around -inf 63.5%

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

      1. +-commutative 63.5%

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

      2. mul-1-neg 63.5%

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

      3. unsub-neg 63.5%

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

      4. sub-neg 63.5%

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

      5. mul-1-neg 63.5%

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

      6. associate-/l* 63.5%

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

      7. distribute-rgt-neg-in 63.5%

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

      8. mul-1-neg 63.5%

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

      9. remove-double-neg 63.5%

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

      10. associate-/l* 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in x around inf 75.1%

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

      1. mul-1-neg 75.1%

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

      2. times-frac 86.6%

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

      3. distribute-lft-neg-in 86.6%

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

      4. mul-1-neg 86.6%

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

      5. associate-*r/ 86.6%

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

      6. neg-mul-1 86.6%

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

   8. Simplified 86.6%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+109}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+175}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x}{y} \cdot \frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 81.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+172}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x}{y} \cdot \frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.2e+93)
   (/ (+ z (* t (/ x y))) b)
   (if (<= y 1.16e+172)
     (/ (+ x (* z (/ y t))) (+ (+ a 1.0) (/ (* y b) t)))
     (+ (/ z b) (* (/ x y) (/ t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.2e+93) {
		tmp = (z + (t * (x / y))) / b;
	} else if (y <= 1.16e+172) {
		tmp = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t));
	} else {
		tmp = (z / b) + ((x / y) * (t / b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.2d+93)) then
        tmp = (z + (t * (x / y))) / b
    else if (y <= 1.16d+172) then
        tmp = (x + (z * (y / t))) / ((a + 1.0d0) + ((y * b) / t))
    else
        tmp = (z / b) + ((x / y) * (t / b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.2e+93) {
		tmp = (z + (t * (x / y))) / b;
	} else if (y <= 1.16e+172) {
		tmp = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t));
	} else {
		tmp = (z / b) + ((x / y) * (t / b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.2e+93:
		tmp = (z + (t * (x / y))) / b
	elif y <= 1.16e+172:
		tmp = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t))
	else:
		tmp = (z / b) + ((x / y) * (t / b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.2e+93)
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	elseif (y <= 1.16e+172)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x / y) * Float64(t / b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.2e+93)
		tmp = (z + (t * (x / y))) / b;
	elseif (y <= 1.16e+172)
		tmp = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t));
	else
		tmp = (z / b) + ((x / y) * (t / b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.2e+93], N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 1.16e+172], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] * N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2000000000000001e93

   1. Initial program 62.4%

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

   3. Taylor expanded in y around -inf 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

      4. sub-neg 52.9%

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

      5. mul-1-neg 52.9%

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

      6. associate-/l* 55.0%

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

      7. distribute-rgt-neg-in 55.0%

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

      8. mul-1-neg 55.0%

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

      9. remove-double-neg 55.0%

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

      10. associate-/l* 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in x around inf 64.6%

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

      1. mul-1-neg 64.6%

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

      2. associate-*r/ 62.4%

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

      3. *-commutative 62.4%

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

      4. distribute-rgt-neg-in 62.4%

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

   8. Simplified 62.4%

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

   9. Taylor expanded in b around 0 64.8%

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

       1. sub-neg 64.8%

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

       2. mul-1-neg 64.8%

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

       3. remove-double-neg 64.8%

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

       4. associate-/l* 71.7%

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

   11. Simplified 71.7%

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

   if -3.2000000000000001e93 < y < 1.15999999999999994e172

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-/l* 91.0%

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

   4. Applied egg-rr 91.0%

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

   if 1.15999999999999994e172 < y

   1. Initial program 24.2%

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

   3. Taylor expanded in y around -inf 63.5%

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

      1. +-commutative 63.5%

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

      2. mul-1-neg 63.5%

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

      3. unsub-neg 63.5%

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

      4. sub-neg 63.5%

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

      5. mul-1-neg 63.5%

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

      6. associate-/l* 63.5%

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

      7. distribute-rgt-neg-in 63.5%

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

      8. mul-1-neg 63.5%

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

      9. remove-double-neg 63.5%

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

      10. associate-/l* 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in x around inf 75.1%

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

      1. mul-1-neg 75.1%

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

      2. times-frac 86.6%

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

      3. distribute-lft-neg-in 86.6%

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

      4. mul-1-neg 86.6%

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

      5. associate-*r/ 86.6%

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

      6. neg-mul-1 86.6%

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

   8. Simplified 86.6%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+172}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x}{y} \cdot \frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-117} \lor \neg \left(t \leq 18000\right):\\ \;\;\;\;\frac{x}{\left(a + \frac{b}{\frac{t}{y}}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.7e-117) (not (<= t 18000.0)))
   (/ x (+ (+ a (/ b (/ t y))) 1.0))
   (/ (+ z (* t (/ x y))) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.7e-117) || !(t <= 18000.0)) {
		tmp = x / ((a + (b / (t / y))) + 1.0);
	} else {
		tmp = (z + (t * (x / y))) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.7d-117)) .or. (.not. (t <= 18000.0d0))) then
        tmp = x / ((a + (b / (t / y))) + 1.0d0)
    else
        tmp = (z + (t * (x / y))) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.7e-117) || !(t <= 18000.0)) {
		tmp = x / ((a + (b / (t / y))) + 1.0);
	} else {
		tmp = (z + (t * (x / y))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.7e-117) or not (t <= 18000.0):
		tmp = x / ((a + (b / (t / y))) + 1.0)
	else:
		tmp = (z + (t * (x / y))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.7e-117) || !(t <= 18000.0))
		tmp = Float64(x / Float64(Float64(a + Float64(b / Float64(t / y))) + 1.0));
	else
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.7e-117) || ~((t <= 18000.0)))
		tmp = x / ((a + (b / (t / y))) + 1.0);
	else
		tmp = (z + (t * (x / y))) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.7e-117], N[Not[LessEqual[t, 18000.0]], $MachinePrecision]], N[(x / N[(N[(a + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.70000000000000017e-117 or 18000 < t

   1. Initial program 86.5%

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

   3. Taylor expanded in x around inf 68.7%

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

      1. associate-/l* 73.3%

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

      2. clear-num 73.3%

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

      3. un-div-inv 73.3%

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

   5. Applied egg-rr 73.3%

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

   if -1.70000000000000017e-117 < t < 18000

   1. Initial program 68.6%

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

   3. Taylor expanded in y around -inf 55.3%

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

      1. +-commutative 55.3%

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

      2. mul-1-neg 55.3%

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

      3. unsub-neg 55.3%

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

      4. sub-neg 55.3%

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

      5. mul-1-neg 55.3%

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

      6. associate-/l* 54.4%

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

      7. distribute-rgt-neg-in 54.4%

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

      8. mul-1-neg 54.4%

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

      9. remove-double-neg 54.4%

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

      10. associate-/l* 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in x around inf 65.0%

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

      1. mul-1-neg 65.0%

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

      2. associate-*r/ 62.1%

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

      3. *-commutative 62.1%

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

      4. distribute-rgt-neg-in 62.1%

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

   8. Simplified 62.1%

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

   9. Taylor expanded in b around 0 65.6%

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

       1. sub-neg 65.6%

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

       2. mul-1-neg 65.6%

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

       3. remove-double-neg 65.6%

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

       4. associate-/l* 63.9%

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

   11. Simplified 63.9%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-117} \lor \neg \left(t \leq 18000\right):\\ \;\;\;\;\frac{x}{\left(a + \frac{b}{\frac{t}{y}}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-51} \lor \neg \left(t \leq 480000\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5e-51) (not (<= t 480000.0))) (/ 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 <= -5e-51) || !(t <= 480000.0)) {
		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 <= (-5d-51)) .or. (.not. (t <= 480000.0d0))) 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 <= -5e-51) || !(t <= 480000.0)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5e-51) or not (t <= 480000.0):
		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 <= -5e-51) || !(t <= 480000.0))
		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 <= -5e-51) || ~((t <= 480000.0)))
		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, -5e-51], N[Not[LessEqual[t, 480000.0]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.00000000000000004e-51 or 4.8e5 < t

   1. Initial program 87.2%

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

   3. Taylor expanded in y around 0 65.1%

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

   if -5.00000000000000004e-51 < t < 4.8e5

   1. Initial program 70.1%

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

   3. Taylor expanded in y around inf 52.5%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-51} \lor \neg \left(t \leq 480000\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \lor \neg \left(a \leq 0.00052\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.5) (not (<= a 0.00052))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.5) || !(a <= 0.00052)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.5d0)) .or. (.not. (a <= 0.00052d0))) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.5) || !(a <= 0.00052)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.5) or not (a <= 0.00052):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.5) || !(a <= 0.00052))
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.5) || ~((a <= 0.00052)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.5], N[Not[LessEqual[a, 0.00052]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.5 or 5.19999999999999954e-4 < a

   1. Initial program 79.4%

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

   3. Taylor expanded in y around 0 54.1%

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

   4. Taylor expanded in a around inf 53.4%

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

   if -1.5 < a < 5.19999999999999954e-4

   1. Initial program 78.0%

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

   3. Taylor expanded in y around 0 35.0%

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

   4. Taylor expanded in a around 0 34.7%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \lor \neg \left(a \leq 0.00052\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 19.8% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.7%

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

3. Taylor expanded in y around 0 44.4%

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

4. Taylor expanded in a around 0 19.3%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Developer target: 79.0% 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 2024096 
(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))))