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

Percentage Accurate: 74.6% → 92.4%

Time: 14.0s

Alternatives: 18

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: 74.6% 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: 92.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{t\_1} + \frac{\frac{y}{t}}{t\_1}\right)\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-302}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{y \cdot \frac{z}{t\_1}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0))) (t_2 (/ (+ x (/ (* y z) t)) t_1)))
   (if (<= t_2 (- INFINITY))
     (* z (+ (/ (/ x z) t_1) (/ (/ y t) t_1)))
     (if (<= t_2 -1e-302)
       t_2
       (if (<= t_2 0.0)
         (+ (/ z b) (/ (* t (/ x b)) y))
         (if (<= t_2 2e+306)
           t_2
           (if (<= t_2 INFINITY) (/ (* y (/ z t_1)) t) (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * (((x / z) / t_1) + ((y / t) / t_1));
	} else if (t_2 <= -1e-302) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (z / b) + ((t * (x / b)) / y);
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (y * (z / t_1)) / t;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (((x / z) / t_1) + ((y / t) / t_1));
	} else if (t_2 <= -1e-302) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (z / b) + ((t * (x / b)) / y);
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (y * (z / t_1)) / t;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * b) / t) + (a + 1.0)
	t_2 = (x + ((y * z) / t)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = z * (((x / z) / t_1) + ((y / t) / t_1))
	elif t_2 <= -1e-302:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (z / b) + ((t * (x / b)) / y)
	elif t_2 <= 2e+306:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = (y * (z / t_1)) / t
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(Float64(x / z) / t_1) + Float64(Float64(y / t) / t_1)));
	elseif (t_2 <= -1e-302)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y));
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(y * Float64(z / t_1)) / t);
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * b) / t) + (a + 1.0);
	t_2 = (x + ((y * z) / t)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = z * (((x / z) / t_1) + ((y / t) / t_1));
	elseif (t_2 <= -1e-302)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (z / b) + ((t * (x / b)) / y);
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = (y * (z / t_1)) / t;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z * N[(N[(N[(x / z), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-302], 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, 2e+306], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 14.2%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z \cdot y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(z \cdot \frac{y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\frac{y}{t}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      4. /-lowering-/.f64 52.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   4. Applied egg-rr 52.8%

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

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(z \cdot \frac{1}{\frac{t}{y}}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{\frac{t}{y}}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \left(\frac{t}{y}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      4. /-lowering-/.f64 52.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(t, y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   6. Applied egg-rr 52.5%

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

   7. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{x}{z \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\frac{x}{z \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right), \color{blue}{\left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\frac{\frac{x}{z}}{1 + \left(a + \frac{b \cdot y}{t}\right)}\right), \left(\frac{\color{blue}{y}}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\frac{x}{z}\right), \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)\right), \left(\frac{\color{blue}{y}}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)\right), \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(a + \frac{b \cdot y}{t}\right) + 1\right)\right), \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(\frac{b \cdot y}{t} + a\right) + 1\right)\right), \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\frac{b \cdot y}{t} + \left(a + 1\right)\right)\right), \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\frac{b \cdot y}{t} + \left(1 + a\right)\right)\right), \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(\left(\frac{b \cdot y}{t}\right), \left(1 + a\right)\right)\right), \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(b \cdot y\right), t\right), \left(1 + a\right)\right)\right), \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(y \cdot b\right), t\right), \left(1 + a\right)\right)\right), \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right), \left(1 + a\right)\right)\right), \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right), \mathsf{+.f64}\left(1, a\right)\right)\right), \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      15. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right), \mathsf{+.f64}\left(1, a\right)\right)\right), \left(\frac{\frac{y}{t}}{\color{blue}{1 + \left(a + \frac{b \cdot y}{t}\right)}}\right)\right)\right) \]

      16. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right), \mathsf{+.f64}\left(1, a\right)\right)\right), \mathsf{/.f64}\left(\left(\frac{y}{t}\right), \color{blue}{\left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      17. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right), \mathsf{+.f64}\left(1, a\right)\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, t\right), \left(\color{blue}{1} + \left(a + \frac{b \cdot y}{t}\right)\right)\right)\right)\right) \]

   9. Simplified 91.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -9.9999999999999996e-303 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000003e306

   1. Initial program 99.2%

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

   if -9.9999999999999996e-303 < (/.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 45.5%

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

   3. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. sub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-out-- N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z}{b}\right), \color{blue}{\left(t \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \left(\color{blue}{t} \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{x}{b \cdot y}\right), \color{blue}{\left(\frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right)\right) \]

   5. Simplified 65.3%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \color{blue}{\left(\frac{t \cdot x}{b \cdot y}\right)}\right) \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \left(\frac{\frac{t \cdot x}{b}}{\color{blue}{y}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\left(\frac{t \cdot x}{b}\right), \color{blue}{y}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\left(t \cdot \frac{x}{b}\right), y\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{x}{b}\right)\right), y\right)\right) \]

      5. /-lowering-/.f64 74.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(x, b\right)\right), y\right)\right) \]

   8. Simplified 74.1%

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

   if 2.00000000000000003e306 < (/.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 48.1%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z \cdot y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(z \cdot \frac{y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\frac{y}{t}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      4. /-lowering-/.f64 48.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   4. Applied egg-rr 48.1%

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

   5. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{\left(t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\color{blue}{t} \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \color{blue}{\left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(1, \color{blue}{\left(a + \frac{b \cdot y}{t}\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{b \cdot y}{t}\right)}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(b \cdot y\right), \color{blue}{t}\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(y \cdot b\right), t\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 74.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right)\right)\right) \]

   7. Simplified 74.0%

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

      1. times-frac N/A

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

      2. associate-*l/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{z}{1 + \left(a + \frac{y \cdot b}{t}\right)}\right), \color{blue}{t}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{z}{1 + \left(a + \frac{y \cdot b}{t}\right)}\right)\right), t\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{z}{\left(1 + a\right) + \frac{y \cdot b}{t}}\right)\right), t\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{z}{\left(a + 1\right) + \frac{y \cdot b}{t}}\right)\right), t\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \left(\left(a + 1\right) + \frac{y \cdot b}{t}\right)\right)\right), t\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\left(a + 1\right), \left(\frac{y \cdot b}{t}\right)\right)\right)\right), t\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\left(1 + a\right), \left(\frac{y \cdot b}{t}\right)\right)\right)\right), t\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\mathsf{+.f64}\left(1, a\right), \left(\frac{y \cdot b}{t}\right)\right)\right)\right), t\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\mathsf{+.f64}\left(1, a\right), \mathsf{/.f64}\left(\left(y \cdot b\right), t\right)\right)\right)\right), t\right) \]

      12. *-lowering-*.f64 99.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\mathsf{+.f64}\left(1, a\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right)\right), t\right) \]

   9. Applied egg-rr 99.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 100.0%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{b}\right) \]

   5. Simplified 100.0%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{\frac{y \cdot b}{t} + \left(a + 1\right)} + \frac{\frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -1 \cdot 10^{-302}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{y \cdot \frac{z}{\frac{y \cdot b}{t} + \left(a + 1\right)}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1}\\ t_3 := 1 + \left(a + y \cdot \frac{b}{t}\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{t\_3} + \frac{\frac{y}{t}}{t\_3}\right)\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-302}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{y \cdot \frac{z}{t\_1}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0)))
        (t_2 (/ (+ x (/ (* y z) t)) t_1))
        (t_3 (+ 1.0 (+ a (* y (/ b t))))))
   (if (<= t_2 (- INFINITY))
     (* z (+ (/ (/ x z) t_3) (/ (/ y t) t_3)))
     (if (<= t_2 -1e-302)
       t_2
       (if (<= t_2 0.0)
         (+ (/ z b) (/ (* t (/ x b)) y))
         (if (<= t_2 2e+306)
           t_2
           (if (<= t_2 INFINITY) (/ (* y (/ z t_1)) t) (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double t_3 = 1.0 + (a + (y * (b / t)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * (((x / z) / t_3) + ((y / t) / t_3));
	} else if (t_2 <= -1e-302) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (z / b) + ((t * (x / b)) / y);
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (y * (z / t_1)) / t;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double t_3 = 1.0 + (a + (y * (b / t)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (((x / z) / t_3) + ((y / t) / t_3));
	} else if (t_2 <= -1e-302) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (z / b) + ((t * (x / b)) / y);
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (y * (z / t_1)) / t;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * b) / t) + (a + 1.0)
	t_2 = (x + ((y * z) / t)) / t_1
	t_3 = 1.0 + (a + (y * (b / t)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = z * (((x / z) / t_3) + ((y / t) / t_3))
	elif t_2 <= -1e-302:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (z / b) + ((t * (x / b)) / y)
	elif t_2 <= 2e+306:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = (y * (z / t_1)) / t
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	t_3 = Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(Float64(x / z) / t_3) + Float64(Float64(y / t) / t_3)));
	elseif (t_2 <= -1e-302)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y));
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(y * Float64(z / t_1)) / t);
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * b) / t) + (a + 1.0);
	t_2 = (x + ((y * z) / t)) / t_1;
	t_3 = 1.0 + (a + (y * (b / t)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = z * (((x / z) / t_3) + ((y / t) / t_3));
	elseif (t_2 <= -1e-302)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (z / b) + ((t * (x / b)) / y);
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = (y * (z / t_1)) / t;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z * N[(N[(N[(x / z), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-302], 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, 2e+306], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 14.2%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{x}{z \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\frac{x}{z \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right), \color{blue}{\left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\frac{\frac{x}{z}}{1 + \left(a + \frac{b \cdot y}{t}\right)}\right), \left(\frac{\color{blue}{y}}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\frac{x}{z}\right), \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)\right), \left(\frac{\color{blue}{y}}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)\right), \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(1, \left(a + \frac{b \cdot y}{t}\right)\right)\right), \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \left(\frac{b \cdot y}{t}\right)\right)\right)\right), \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \left(\frac{y \cdot b}{t}\right)\right)\right)\right), \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \left(y \cdot \frac{b}{t}\right)\right)\right)\right), \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \left(\frac{b}{t}\right)\right)\right)\right)\right), \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, t\right)\right)\right)\right)\right), \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      12. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, t\right)\right)\right)\right)\right), \left(\frac{\frac{y}{t}}{\color{blue}{1 + \left(a + \frac{b \cdot y}{t}\right)}}\right)\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, t\right)\right)\right)\right)\right), \mathsf{/.f64}\left(\left(\frac{y}{t}\right), \color{blue}{\left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, t\right)\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, t\right), \left(\color{blue}{1} + \left(a + \frac{b \cdot y}{t}\right)\right)\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, t\right)\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, t\right), \mathsf{+.f64}\left(1, \color{blue}{\left(a + \frac{b \cdot y}{t}\right)}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, t\right)\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, t\right), \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{b \cdot y}{t}\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 91.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -9.9999999999999996e-303 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000003e306

   1. Initial program 99.2%

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

   if -9.9999999999999996e-303 < (/.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 45.5%

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

   3. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. sub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-out-- N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z}{b}\right), \color{blue}{\left(t \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \left(\color{blue}{t} \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{x}{b \cdot y}\right), \color{blue}{\left(\frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right)\right) \]

   5. Simplified 65.3%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \color{blue}{\left(\frac{t \cdot x}{b \cdot y}\right)}\right) \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \left(\frac{\frac{t \cdot x}{b}}{\color{blue}{y}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\left(\frac{t \cdot x}{b}\right), \color{blue}{y}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\left(t \cdot \frac{x}{b}\right), y\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{x}{b}\right)\right), y\right)\right) \]

      5. /-lowering-/.f64 74.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(x, b\right)\right), y\right)\right) \]

   8. Simplified 74.1%

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

   if 2.00000000000000003e306 < (/.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 48.1%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z \cdot y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(z \cdot \frac{y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\frac{y}{t}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      4. /-lowering-/.f64 48.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   4. Applied egg-rr 48.1%

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

   5. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{\left(t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\color{blue}{t} \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \color{blue}{\left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(1, \color{blue}{\left(a + \frac{b \cdot y}{t}\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{b \cdot y}{t}\right)}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(b \cdot y\right), \color{blue}{t}\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(y \cdot b\right), t\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 74.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right)\right)\right) \]

   7. Simplified 74.0%

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

      1. times-frac N/A

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

      2. associate-*l/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{z}{1 + \left(a + \frac{y \cdot b}{t}\right)}\right), \color{blue}{t}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{z}{1 + \left(a + \frac{y \cdot b}{t}\right)}\right)\right), t\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{z}{\left(1 + a\right) + \frac{y \cdot b}{t}}\right)\right), t\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{z}{\left(a + 1\right) + \frac{y \cdot b}{t}}\right)\right), t\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \left(\left(a + 1\right) + \frac{y \cdot b}{t}\right)\right)\right), t\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\left(a + 1\right), \left(\frac{y \cdot b}{t}\right)\right)\right)\right), t\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\left(1 + a\right), \left(\frac{y \cdot b}{t}\right)\right)\right)\right), t\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\mathsf{+.f64}\left(1, a\right), \left(\frac{y \cdot b}{t}\right)\right)\right)\right), t\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\mathsf{+.f64}\left(1, a\right), \mathsf{/.f64}\left(\left(y \cdot b\right), t\right)\right)\right)\right), t\right) \]

      12. *-lowering-*.f64 99.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\mathsf{+.f64}\left(1, a\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right)\right), t\right) \]

   9. Applied egg-rr 99.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 100.0%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{b}\right) \]

   5. Simplified 100.0%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{1 + \left(a + y \cdot \frac{b}{t}\right)} + \frac{\frac{y}{t}}{1 + \left(a + y \cdot \frac{b}{t}\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -1 \cdot 10^{-302}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{y \cdot \frac{z}{\frac{y \cdot b}{t} + \left(a + 1\right)}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-302}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{y \cdot \frac{z}{t\_1}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0))) (t_2 (/ (+ x (/ (* y z) t)) t_1)))
   (if (<= t_2 -1e-302)
     (/ (+ x (* z (/ y t))) t_1)
     (if (<= t_2 0.0)
       (+ (/ z b) (/ (* t (/ x b)) y))
       (if (<= t_2 2e+306)
         t_2
         (if (<= t_2 INFINITY) (/ (* y (/ z t_1)) t) (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -1e-302) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = (z / b) + ((t * (x / b)) / y);
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (y * (z / t_1)) / t;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -1e-302) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = (z / b) + ((t * (x / b)) / y);
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (y * (z / t_1)) / t;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * b) / t) + (a + 1.0)
	t_2 = (x + ((y * z) / t)) / t_1
	tmp = 0
	if t_2 <= -1e-302:
		tmp = (x + (z * (y / t))) / t_1
	elif t_2 <= 0.0:
		tmp = (z / b) + ((t * (x / b)) / y)
	elif t_2 <= 2e+306:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = (y * (z / t_1)) / t
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_2 <= -1e-302)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y));
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(y * Float64(z / t_1)) / t);
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * b) / t) + (a + 1.0);
	t_2 = (x + ((y * z) / t)) / t_1;
	tmp = 0.0;
	if (t_2 <= -1e-302)
		tmp = (x + (z * (y / t))) / t_1;
	elseif (t_2 <= 0.0)
		tmp = (z / b) + ((t * (x / b)) / y);
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = (y * (z / t_1)) / t;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-302], N[(N[(x + N[(z * N[(y / 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, 2e+306], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -9.9999999999999996e-303

   1. Initial program 89.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z \cdot y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(z \cdot \frac{y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\frac{y}{t}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      4. /-lowering-/.f64 92.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   4. Applied egg-rr 92.9%

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

   if -9.9999999999999996e-303 < (/.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 45.5%

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

   3. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. sub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-out-- N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z}{b}\right), \color{blue}{\left(t \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \left(\color{blue}{t} \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{x}{b \cdot y}\right), \color{blue}{\left(\frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right)\right) \]

   5. Simplified 65.3%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \color{blue}{\left(\frac{t \cdot x}{b \cdot y}\right)}\right) \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \left(\frac{\frac{t \cdot x}{b}}{\color{blue}{y}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\left(\frac{t \cdot x}{b}\right), \color{blue}{y}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\left(t \cdot \frac{x}{b}\right), y\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{x}{b}\right)\right), y\right)\right) \]

      5. /-lowering-/.f64 74.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(x, b\right)\right), y\right)\right) \]

   8. Simplified 74.1%

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

   if 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000003e306

   1. Initial program 98.6%

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

   if 2.00000000000000003e306 < (/.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 48.1%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z \cdot y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(z \cdot \frac{y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\frac{y}{t}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      4. /-lowering-/.f64 48.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   4. Applied egg-rr 48.1%

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

   5. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{\left(t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\color{blue}{t} \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \color{blue}{\left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(1, \color{blue}{\left(a + \frac{b \cdot y}{t}\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{b \cdot y}{t}\right)}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(b \cdot y\right), \color{blue}{t}\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(y \cdot b\right), t\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 74.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right)\right)\right) \]

   7. Simplified 74.0%

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

      1. times-frac N/A

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

      2. associate-*l/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{z}{1 + \left(a + \frac{y \cdot b}{t}\right)}\right), \color{blue}{t}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{z}{1 + \left(a + \frac{y \cdot b}{t}\right)}\right)\right), t\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{z}{\left(1 + a\right) + \frac{y \cdot b}{t}}\right)\right), t\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{z}{\left(a + 1\right) + \frac{y \cdot b}{t}}\right)\right), t\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \left(\left(a + 1\right) + \frac{y \cdot b}{t}\right)\right)\right), t\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\left(a + 1\right), \left(\frac{y \cdot b}{t}\right)\right)\right)\right), t\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\left(1 + a\right), \left(\frac{y \cdot b}{t}\right)\right)\right)\right), t\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\mathsf{+.f64}\left(1, a\right), \left(\frac{y \cdot b}{t}\right)\right)\right)\right), t\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\mathsf{+.f64}\left(1, a\right), \mathsf{/.f64}\left(\left(y \cdot b\right), t\right)\right)\right)\right), t\right) \]

      12. *-lowering-*.f64 99.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\mathsf{+.f64}\left(1, a\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right)\right), t\right) \]

   9. Applied egg-rr 99.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 100.0%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{b}\right) \]

   5. Simplified 100.0%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -1 \cdot 10^{-302}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{y \cdot \frac{z}{\frac{y \cdot b}{t} + \left(a + 1\right)}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+175}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;b \leq -4 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;b \leq 1.62 \cdot 10^{+35}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+149}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.5e+175)
   (/ (+ z (* t (/ x y))) b)
   (if (<= b -4e+90)
     (/ x (+ (/ (* y b) t) (+ a 1.0)))
     (if (<= b 1.62e+35)
       (/ (+ x (* z (/ y t))) (+ a 1.0))
       (if (<= b 4.5e+149)
         (/ x (+ 1.0 (+ a (* y (/ b t)))))
         (+ (/ z b) (/ (* t (/ x b)) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e+175) {
		tmp = (z + (t * (x / y))) / b;
	} else if (b <= -4e+90) {
		tmp = x / (((y * b) / t) + (a + 1.0));
	} else if (b <= 1.62e+35) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (b <= 4.5e+149) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else {
		tmp = (z / b) + ((t * (x / b)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9.5d+175)) then
        tmp = (z + (t * (x / y))) / b
    else if (b <= (-4d+90)) then
        tmp = x / (((y * b) / t) + (a + 1.0d0))
    else if (b <= 1.62d+35) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else if (b <= 4.5d+149) then
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    else
        tmp = (z / b) + ((t * (x / b)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e+175) {
		tmp = (z + (t * (x / y))) / b;
	} else if (b <= -4e+90) {
		tmp = x / (((y * b) / t) + (a + 1.0));
	} else if (b <= 1.62e+35) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (b <= 4.5e+149) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else {
		tmp = (z / b) + ((t * (x / b)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.5e+175:
		tmp = (z + (t * (x / y))) / b
	elif b <= -4e+90:
		tmp = x / (((y * b) / t) + (a + 1.0))
	elif b <= 1.62e+35:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	elif b <= 4.5e+149:
		tmp = x / (1.0 + (a + (y * (b / t))))
	else:
		tmp = (z / b) + ((t * (x / b)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.5e+175)
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	elseif (b <= -4e+90)
		tmp = Float64(x / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	elseif (b <= 1.62e+35)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	elseif (b <= 4.5e+149)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.5e+175)
		tmp = (z + (t * (x / y))) / b;
	elseif (b <= -4e+90)
		tmp = x / (((y * b) / t) + (a + 1.0));
	elseif (b <= 1.62e+35)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	elseif (b <= 4.5e+149)
		tmp = x / (1.0 + (a + (y * (b / t))));
	else
		tmp = (z / b) + ((t * (x / b)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.5e+175], N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[b, -4e+90], N[(x / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.62e+35], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+149], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -9.5000000000000006e175

   1. Initial program 48.7%

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

   3. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. sub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-out-- N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z}{b}\right), \color{blue}{\left(t \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \left(\color{blue}{t} \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{x}{b \cdot y}\right), \color{blue}{\left(\frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right)\right) \]

   5. Simplified 68.2%

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

   6. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z + \frac{t \cdot x}{y}\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \left(\frac{t \cdot x}{y}\right)\right), b\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \left(t \cdot \frac{x}{y}\right)\right), b\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(t, \left(\frac{x}{y}\right)\right)\right), b\right) \]

      5. /-lowering-/.f64 80.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(x, y\right)\right)\right), b\right) \]

   8. Simplified 80.9%

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

   if -9.5000000000000006e175 < b < -3.99999999999999987e90

   1. Initial program 89.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 80.1%

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

   if -3.99999999999999987e90 < b < 1.62e35

   1. Initial program 81.6%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z \cdot y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(z \cdot \frac{y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\frac{y}{t}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      4. /-lowering-/.f64 83.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   4. Applied egg-rr 83.9%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, t\right)\right)\right), \color{blue}{\left(1 + a\right)}\right) \]
   6. Step-by-step derivation

      1. +-lowering-+.f64 72.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(1, \color{blue}{a}\right)\right) \]

   7. Simplified 72.0%

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

   if 1.62e35 < b < 4.49999999999999982e149

   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 x around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(a + \frac{b \cdot y}{t}\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{b \cdot y}{t}\right)}\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \left(\frac{y \cdot b}{t}\right)\right)\right)\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \left(y \cdot \color{blue}{\frac{b}{t}}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{b}{t}\right)}\right)\right)\right)\right) \]

      7. /-lowering-/.f64 82.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, \color{blue}{t}\right)\right)\right)\right)\right) \]

   5. Simplified 82.4%

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

   if 4.49999999999999982e149 < b

   1. Initial program 54.5%

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

   3. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. sub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-out-- N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z}{b}\right), \color{blue}{\left(t \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \left(\color{blue}{t} \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{x}{b \cdot y}\right), \color{blue}{\left(\frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right)\right) \]

   5. Simplified 60.5%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \color{blue}{\left(\frac{t \cdot x}{b \cdot y}\right)}\right) \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \left(\frac{\frac{t \cdot x}{b}}{\color{blue}{y}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\left(\frac{t \cdot x}{b}\right), \color{blue}{y}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\left(t \cdot \frac{x}{b}\right), y\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{x}{b}\right)\right), y\right)\right) \]

      5. /-lowering-/.f64 76.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(x, b\right)\right), y\right)\right) \]

   8. Simplified 76.0%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+175}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;b \leq -4 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;b \leq 1.62 \cdot 10^{+35}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+149}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a + 1 \leq 1:\\ \;\;\;\;\frac{t\_1}{a + 1}\\ \mathbf{elif}\;a + 1 \leq 4 \cdot 10^{+15}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{1 + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))))
   (if (<= (+ a 1.0) 1.0)
     (/ t_1 (+ a 1.0))
     (if (<= (+ a 1.0) 4e+15)
       (/ (+ x (/ z (/ t y))) (+ 1.0 (* y (/ b t))))
       (/ t_1 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) <= 1.0) {
		tmp = t_1 / (a + 1.0);
	} else if ((a + 1.0) <= 4e+15) {
		tmp = (x + (z / (t / y))) / (1.0 + (y * (b / t)));
	} else {
		tmp = t_1 / 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) <= 1.0d0) then
        tmp = t_1 / (a + 1.0d0)
    else if ((a + 1.0d0) <= 4d+15) then
        tmp = (x + (z / (t / y))) / (1.0d0 + (y * (b / t)))
    else
        tmp = t_1 / 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) <= 1.0) {
		tmp = t_1 / (a + 1.0);
	} else if ((a + 1.0) <= 4e+15) {
		tmp = (x + (z / (t / y))) / (1.0 + (y * (b / t)));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	tmp = 0
	if (a + 1.0) <= 1.0:
		tmp = t_1 / (a + 1.0)
	elif (a + 1.0) <= 4e+15:
		tmp = (x + (z / (t / y))) / (1.0 + (y * (b / t)))
	else:
		tmp = t_1 / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (Float64(a + 1.0) <= 1.0)
		tmp = Float64(t_1 / Float64(a + 1.0));
	elseif (Float64(a + 1.0) <= 4e+15)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(1.0 + Float64(y * Float64(b / t))));
	else
		tmp = Float64(t_1 / 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) <= 1.0)
		tmp = t_1 / (a + 1.0);
	elseif ((a + 1.0) <= 4e+15)
		tmp = (x + (z / (t / y))) / (1.0 + (y * (b / t)));
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a + 1.0), $MachinePrecision], 1.0], N[(t$95$1 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], 4e+15], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 76.3%

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

   3. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z}{t}\right), \color{blue}{\left(1 + a\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y \cdot z}{t}\right)\right), \left(\color{blue}{1} + a\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), t\right)\right), \left(1 + a\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \left(1 + a\right)\right) \]

      5. +-lowering-+.f64 55.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \color{blue}{a}\right)\right) \]

   5. Simplified 55.0%

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

   if 1 < (+.f64 a #s(literal 1 binary64)) < 4e15

   1. Initial program 99.2%

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

   3. Taylor expanded in a around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z}{t}\right), \color{blue}{\left(1 + \frac{b \cdot y}{t}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y \cdot z}{t}\right)\right), \left(\color{blue}{1} + \frac{b \cdot y}{t}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), t\right)\right), \left(1 + \frac{b \cdot y}{t}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \left(1 + \frac{b \cdot y}{t}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{b \cdot y}{t}\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \left(\frac{y \cdot b}{t}\right)\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \left(y \cdot \color{blue}{\frac{b}{t}}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{b}{t}\right)}\right)\right)\right) \]

      9. /-lowering-/.f64 70.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 70.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z \cdot y}{t}\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, t\right)\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(z \cdot \frac{y}{t}\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, t\right)\right)\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(z \cdot \frac{1}{\frac{t}{y}}\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, t\right)\right)\right)\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{\frac{t}{y}}\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, t\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \left(\frac{t}{y}\right)\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, t\right)\right)\right)\right) \]

      6. /-lowering-/.f64 70.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(t, y\right)\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, t\right)\right)\right)\right) \]

   7. Applied egg-rr 70.9%

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

   if 4e15 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 68.3%

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

   3. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z}{t}\right), \color{blue}{a}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y \cdot z}{t}\right)\right), a\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), t\right)\right), a\right) \]

      4. *-lowering-*.f64 65.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), a\right) \]

   5. Simplified 65.2%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq 1:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;a + 1 \leq 4 \cdot 10^{+15}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{1 + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a + 1 \leq 0.99:\\ \;\;\;\;\frac{t\_1}{a + 1}\\ \mathbf{elif}\;a + 1 \leq 4 \cdot 10^{+15}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))))
   (if (<= (+ a 1.0) 0.99)
     (/ t_1 (+ a 1.0))
     (if (<= (+ a 1.0) 4e+15)
       (/ (+ x (* z (/ y t))) (+ 1.0 (/ (* y b) t)))
       (/ t_1 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) <= 0.99) {
		tmp = t_1 / (a + 1.0);
	} else if ((a + 1.0) <= 4e+15) {
		tmp = (x + (z * (y / t))) / (1.0 + ((y * b) / t));
	} else {
		tmp = t_1 / 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) <= 0.99d0) then
        tmp = t_1 / (a + 1.0d0)
    else if ((a + 1.0d0) <= 4d+15) then
        tmp = (x + (z * (y / t))) / (1.0d0 + ((y * b) / t))
    else
        tmp = t_1 / 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) <= 0.99) {
		tmp = t_1 / (a + 1.0);
	} else if ((a + 1.0) <= 4e+15) {
		tmp = (x + (z * (y / t))) / (1.0 + ((y * b) / t));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	tmp = 0
	if (a + 1.0) <= 0.99:
		tmp = t_1 / (a + 1.0)
	elif (a + 1.0) <= 4e+15:
		tmp = (x + (z * (y / t))) / (1.0 + ((y * b) / t))
	else:
		tmp = t_1 / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (Float64(a + 1.0) <= 0.99)
		tmp = Float64(t_1 / Float64(a + 1.0));
	elseif (Float64(a + 1.0) <= 4e+15)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(1.0 + Float64(Float64(y * b) / t)));
	else
		tmp = Float64(t_1 / 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) <= 0.99)
		tmp = t_1 / (a + 1.0);
	elseif ((a + 1.0) <= 4e+15)
		tmp = (x + (z * (y / t))) / (1.0 + ((y * b) / t));
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a + 1.0), $MachinePrecision], 0.99], N[(t$95$1 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], 4e+15], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 a #s(literal 1 binary64)) < 0.98999999999999999

   1. Initial program 75.6%

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

   3. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z}{t}\right), \color{blue}{\left(1 + a\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y \cdot z}{t}\right)\right), \left(\color{blue}{1} + a\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), t\right)\right), \left(1 + a\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \left(1 + a\right)\right) \]

      5. +-lowering-+.f64 62.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \color{blue}{a}\right)\right) \]

   5. Simplified 62.7%

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

   if 0.98999999999999999 < (+.f64 a #s(literal 1 binary64)) < 4e15

   1. Initial program 77.7%

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

   3. Taylor expanded in a around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z}{t}\right), \color{blue}{\left(1 + \frac{b \cdot y}{t}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y \cdot z}{t}\right)\right), \left(\color{blue}{1} + \frac{b \cdot y}{t}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), t\right)\right), \left(1 + \frac{b \cdot y}{t}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \left(1 + \frac{b \cdot y}{t}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{b \cdot y}{t}\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \left(\frac{y \cdot b}{t}\right)\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \left(y \cdot \color{blue}{\frac{b}{t}}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{b}{t}\right)}\right)\right)\right) \]

      9. /-lowering-/.f64 76.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 76.2%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z}{t}\right), \color{blue}{\left(1 + y \cdot \frac{b}{t}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y \cdot z}{t}\right)\right), \left(\color{blue}{1} + y \cdot \frac{b}{t}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z \cdot y}{t}\right)\right), \left(1 + y \cdot \frac{b}{t}\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(z \cdot \frac{y}{t}\right)\right), \left(1 + y \cdot \frac{b}{t}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\frac{y}{t}\right)\right)\right), \left(1 + y \cdot \frac{b}{t}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, t\right)\right)\right), \left(1 + y \cdot \frac{b}{t}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, t\right)\right)\right), \left(1 + \frac{y \cdot b}{\color{blue}{t}}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{y \cdot b}{t}\right)}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot b\right), \color{blue}{t}\right)\right)\right) \]

      10. *-lowering-*.f64 78.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   7. Applied egg-rr 78.7%

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

   if 4e15 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 68.3%

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

   3. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z}{t}\right), \color{blue}{a}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y \cdot z}{t}\right)\right), a\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), t\right)\right), a\right) \]

      4. *-lowering-*.f64 65.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), a\right) \]

   5. Simplified 65.2%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq 0.99:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;a + 1 \leq 4 \cdot 10^{+15}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+71}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (* t (/ x y))) b)))
   (if (<= y -4.6e+135)
     t_1
     (if (<= y 7.8e+71)
       (/ (+ x (/ z (/ t y))) (+ (/ (* y b) t) (+ a 1.0)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (t * (x / y))) / b;
	double tmp;
	if (y <= -4.6e+135) {
		tmp = t_1;
	} else if (y <= 7.8e+71) {
		tmp = (x + (z / (t / y))) / (((y * b) / t) + (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + (t * (x / y))) / b
    if (y <= (-4.6d+135)) then
        tmp = t_1
    else if (y <= 7.8d+71) then
        tmp = (x + (z / (t / y))) / (((y * b) / t) + (a + 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (t * (x / y))) / b;
	double tmp;
	if (y <= -4.6e+135) {
		tmp = t_1;
	} else if (y <= 7.8e+71) {
		tmp = (x + (z / (t / y))) / (((y * b) / t) + (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + (t * (x / y))) / b
	tmp = 0
	if y <= -4.6e+135:
		tmp = t_1
	elif y <= 7.8e+71:
		tmp = (x + (z / (t / y))) / (((y * b) / t) + (a + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(t * Float64(x / y))) / b)
	tmp = 0.0
	if (y <= -4.6e+135)
		tmp = t_1;
	elseif (y <= 7.8e+71)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + (t * (x / y))) / b;
	tmp = 0.0;
	if (y <= -4.6e+135)
		tmp = t_1;
	elseif (y <= 7.8e+71)
		tmp = (x + (z / (t / y))) / (((y * b) / t) + (a + 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -4.6e+135], t$95$1, If[LessEqual[y, 7.8e+71], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.6000000000000002e135 or 7.8000000000000002e71 < y

   1. Initial program 36.8%

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

   3. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. sub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-out-- N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z}{b}\right), \color{blue}{\left(t \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \left(\color{blue}{t} \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{x}{b \cdot y}\right), \color{blue}{\left(\frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right)\right) \]

   5. Simplified 57.4%

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

   6. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z + \frac{t \cdot x}{y}\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \left(\frac{t \cdot x}{y}\right)\right), b\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \left(t \cdot \frac{x}{y}\right)\right), b\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(t, \left(\frac{x}{y}\right)\right)\right), b\right) \]

      5. /-lowering-/.f64 69.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(x, y\right)\right)\right), b\right) \]

   8. Simplified 69.1%

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

   if -4.6000000000000002e135 < y < 7.8000000000000002e71

   1. Initial program 92.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z \cdot y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(z \cdot \frac{y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\frac{y}{t}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      4. /-lowering-/.f64 92.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   4. Applied egg-rr 92.2%

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

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(z \cdot \frac{1}{\frac{t}{y}}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{\frac{t}{y}}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \left(\frac{t}{y}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      4. /-lowering-/.f64 92.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(t, y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   6. Applied egg-rr 92.7%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+135}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+71}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+71}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (* t (/ x y))) b)))
   (if (<= y -4.9e+139)
     t_1
     (if (<= y 5.2e+71)
       (/ (+ x (* z (/ y t))) (+ (/ (* y b) t) (+ a 1.0)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (t * (x / y))) / b;
	double tmp;
	if (y <= -4.9e+139) {
		tmp = t_1;
	} else if (y <= 5.2e+71) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + (t * (x / y))) / b
    if (y <= (-4.9d+139)) then
        tmp = t_1
    else if (y <= 5.2d+71) then
        tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (t * (x / y))) / b;
	double tmp;
	if (y <= -4.9e+139) {
		tmp = t_1;
	} else if (y <= 5.2e+71) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + (t * (x / y))) / b
	tmp = 0
	if y <= -4.9e+139:
		tmp = t_1
	elif y <= 5.2e+71:
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(t * Float64(x / y))) / b)
	tmp = 0.0
	if (y <= -4.9e+139)
		tmp = t_1;
	elseif (y <= 5.2e+71)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + (t * (x / y))) / b;
	tmp = 0.0;
	if (y <= -4.9e+139)
		tmp = t_1;
	elseif (y <= 5.2e+71)
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -4.9e+139], t$95$1, If[LessEqual[y, 5.2e+71], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.90000000000000023e139 or 5.19999999999999983e71 < y

   1. Initial program 36.8%

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

   3. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. sub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-out-- N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z}{b}\right), \color{blue}{\left(t \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \left(\color{blue}{t} \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{x}{b \cdot y}\right), \color{blue}{\left(\frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right)\right) \]

   5. Simplified 57.4%

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

   6. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z + \frac{t \cdot x}{y}\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \left(\frac{t \cdot x}{y}\right)\right), b\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \left(t \cdot \frac{x}{y}\right)\right), b\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(t, \left(\frac{x}{y}\right)\right)\right), b\right) \]

      5. /-lowering-/.f64 69.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(x, y\right)\right)\right), b\right) \]

   8. Simplified 69.1%

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

   if -4.90000000000000023e139 < y < 5.19999999999999983e71

   1. Initial program 92.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z \cdot y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(z \cdot \frac{y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\frac{y}{t}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      4. /-lowering-/.f64 92.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   4. Applied egg-rr 92.2%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+139}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+71}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (* t (/ x y))) b)))
   (if (<= y -1e+78)
     t_1
     (if (<= y 5.5e+69) (/ x (+ (/ (* y b) t) (+ a 1.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (t * (x / y))) / b;
	double tmp;
	if (y <= -1e+78) {
		tmp = t_1;
	} else if (y <= 5.5e+69) {
		tmp = x / (((y * b) / t) + (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + (t * (x / y))) / b
    if (y <= (-1d+78)) then
        tmp = t_1
    else if (y <= 5.5d+69) then
        tmp = x / (((y * b) / t) + (a + 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (t * (x / y))) / b;
	double tmp;
	if (y <= -1e+78) {
		tmp = t_1;
	} else if (y <= 5.5e+69) {
		tmp = x / (((y * b) / t) + (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + (t * (x / y))) / b
	tmp = 0
	if y <= -1e+78:
		tmp = t_1
	elif y <= 5.5e+69:
		tmp = x / (((y * b) / t) + (a + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(t * Float64(x / y))) / b)
	tmp = 0.0
	if (y <= -1e+78)
		tmp = t_1;
	elseif (y <= 5.5e+69)
		tmp = Float64(x / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + (t * (x / y))) / b;
	tmp = 0.0;
	if (y <= -1e+78)
		tmp = t_1;
	elseif (y <= 5.5e+69)
		tmp = x / (((y * b) / t) + (a + 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -1e+78], t$95$1, If[LessEqual[y, 5.5e+69], N[(x / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.00000000000000001e78 or 5.50000000000000002e69 < y

   1. Initial program 40.0%

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

   3. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. sub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-out-- N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z}{b}\right), \color{blue}{\left(t \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \left(\color{blue}{t} \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{x}{b \cdot y}\right), \color{blue}{\left(\frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right)\right) \]

   5. Simplified 58.2%

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

   6. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z + \frac{t \cdot x}{y}\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \left(\frac{t \cdot x}{y}\right)\right), b\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \left(t \cdot \frac{x}{y}\right)\right), b\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(t, \left(\frac{x}{y}\right)\right)\right), b\right) \]

      5. /-lowering-/.f64 69.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(x, y\right)\right)\right), b\right) \]

   8. Simplified 69.0%

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

   if -1.00000000000000001e78 < y < 5.50000000000000002e69

   1. Initial program 93.1%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 68.9%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+78}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{if}\;t \leq -2 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-87}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (+ a (* y (/ b t)))))))
   (if (<= t -2e-51) t_1 (if (<= t 1.35e-87) (/ (+ z (/ (* x t) y)) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + (y * (b / t))));
	double tmp;
	if (t <= -2e-51) {
		tmp = t_1;
	} else if (t <= 1.35e-87) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 + (a + (y * (b / t))))
    if (t <= (-2d-51)) then
        tmp = t_1
    else if (t <= 1.35d-87) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + (y * (b / t))));
	double tmp;
	if (t <= -2e-51) {
		tmp = t_1;
	} else if (t <= 1.35e-87) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (a + (y * (b / t))))
	tmp = 0
	if t <= -2e-51:
		tmp = t_1
	elif t <= 1.35e-87:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))))
	tmp = 0.0
	if (t <= -2e-51)
		tmp = t_1;
	elseif (t <= 1.35e-87)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + (a + (y * (b / t))));
	tmp = 0.0;
	if (t <= -2e-51)
		tmp = t_1;
	elseif (t <= 1.35e-87)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e-51], t$95$1, If[LessEqual[t, 1.35e-87], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2e-51 or 1.34999999999999992e-87 < t

   1. Initial program 82.8%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(a + \frac{b \cdot y}{t}\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{b \cdot y}{t}\right)}\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \left(\frac{y \cdot b}{t}\right)\right)\right)\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \left(y \cdot \color{blue}{\frac{b}{t}}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{b}{t}\right)}\right)\right)\right)\right) \]

      7. /-lowering-/.f64 70.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, \color{blue}{t}\right)\right)\right)\right)\right) \]

   5. Simplified 70.8%

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

   if -2e-51 < t < 1.34999999999999992e-87

   1. Initial program 63.0%

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

   3. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. sub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-out-- N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z}{b}\right), \color{blue}{\left(t \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \left(\color{blue}{t} \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{x}{b \cdot y}\right), \color{blue}{\left(\frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right)\right) \]

   5. Simplified 50.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \color{blue}{\left(\frac{t \cdot x}{b \cdot y}\right)}\right) \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \left(\frac{\frac{t \cdot x}{b}}{\color{blue}{y}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\left(\frac{t \cdot x}{b}\right), \color{blue}{y}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\left(t \cdot \frac{x}{b}\right), y\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{x}{b}\right)\right), y\right)\right) \]

      5. /-lowering-/.f64 61.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(x, b\right)\right), y\right)\right) \]

   8. Simplified 61.7%

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

   9. Taylor expanded in b around 0

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

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(z + \frac{t \cdot x}{y}\right), \color{blue}{b}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \left(\frac{t \cdot x}{y}\right)\right), b\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\left(t \cdot x\right), y\right)\right), b\right) \]

       4. *-lowering-*.f64 64.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, x\right), y\right)\right), b\right) \]

   11. Simplified 64.9%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-87}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-54}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -4.5e-33)
     t_1
     (if (<= t 2.45e-54) (/ (+ z (/ (* x t) y)) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -4.5e-33) {
		tmp = t_1;
	} else if (t <= 2.45e-54) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-4.5d-33)) then
        tmp = t_1
    else if (t <= 2.45d-54) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -4.5e-33) {
		tmp = t_1;
	} else if (t <= 2.45e-54) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -4.5e-33:
		tmp = t_1
	elif t <= 2.45e-54:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -4.5e-33)
		tmp = t_1;
	elseif (t <= 2.45e-54)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -4.5e-33)
		tmp = t_1;
	elseif (t <= 2.45e-54)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e-33], t$95$1, If[LessEqual[t, 2.45e-54], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.49999999999999991e-33 or 2.4500000000000001e-54 < t

   1. Initial program 82.4%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a\right)}\right) \]

      2. +-lowering-+.f64 61.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{a}\right)\right) \]

   5. Simplified 61.4%

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

   if -4.49999999999999991e-33 < t < 2.4500000000000001e-54

   1. Initial program 65.1%

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

   3. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. sub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-out-- N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z}{b}\right), \color{blue}{\left(t \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \left(\color{blue}{t} \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{x}{b \cdot y}\right), \color{blue}{\left(\frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right)\right) \]

   5. Simplified 51.1%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \color{blue}{\left(\frac{t \cdot x}{b \cdot y}\right)}\right) \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \left(\frac{\frac{t \cdot x}{b}}{\color{blue}{y}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\left(\frac{t \cdot x}{b}\right), \color{blue}{y}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\left(t \cdot \frac{x}{b}\right), y\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{x}{b}\right)\right), y\right)\right) \]

      5. /-lowering-/.f64 62.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(x, b\right)\right), y\right)\right) \]

   8. Simplified 62.0%

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

   9. Taylor expanded in b around 0

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

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(z + \frac{t \cdot x}{y}\right), \color{blue}{b}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \left(\frac{t \cdot x}{y}\right)\right), b\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\left(t \cdot x\right), y\right)\right), b\right) \]

       4. *-lowering-*.f64 65.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, x\right), y\right)\right), b\right) \]

   11. Simplified 65.0%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-54}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (* t (/ x y))) b)))
   (if (<= y -1.55e-82) t_1 (if (<= y 3.3e+70) (/ x (+ a 1.0)) t_1))))

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 <= -1.55e-82) {
		tmp = t_1;
	} else if (y <= 3.3e+70) {
		tmp = x / (a + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + (t * (x / y))) / b
    if (y <= (-1.55d-82)) then
        tmp = t_1
    else if (y <= 3.3d+70) then
        tmp = x / (a + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (t * (x / y))) / b;
	double tmp;
	if (y <= -1.55e-82) {
		tmp = t_1;
	} else if (y <= 3.3e+70) {
		tmp = x / (a + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + (t * (x / y))) / b
	tmp = 0
	if y <= -1.55e-82:
		tmp = t_1
	elif y <= 3.3e+70:
		tmp = x / (a + 1.0)
	else:
		tmp = t_1
	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 <= -1.55e-82)
		tmp = t_1;
	elseif (y <= 3.3e+70)
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + (t * (x / y))) / b;
	tmp = 0.0;
	if (y <= -1.55e-82)
		tmp = t_1;
	elseif (y <= 3.3e+70)
		tmp = x / (a + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -1.55e-82], t$95$1, If[LessEqual[y, 3.3e+70], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55e-82 or 3.30000000000000016e70 < y

   1. Initial program 54.4%

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

   3. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. sub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-out-- N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z}{b}\right), \color{blue}{\left(t \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \left(\color{blue}{t} \cdot \left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{x}{b \cdot y} - \frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{x}{b \cdot y}\right), \color{blue}{\left(\frac{z \cdot \left(1 + a\right)}{{b}^{2} \cdot y}\right)}\right)\right)\right) \]

   5. Simplified 51.8%

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

   6. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z + \frac{t \cdot x}{y}\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \left(\frac{t \cdot x}{y}\right)\right), b\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \left(t \cdot \frac{x}{y}\right)\right), b\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(t, \left(\frac{x}{y}\right)\right)\right), b\right) \]

      5. /-lowering-/.f64 60.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(x, y\right)\right)\right), b\right) \]

   8. Simplified 60.3%

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

   if -1.55e-82 < y < 3.30000000000000016e70

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a\right)}\right) \]

      2. +-lowering-+.f64 63.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{a}\right)\right) \]

   5. Simplified 63.8%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-82}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{if}\;a \leq -27000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 18000000:\\ \;\;\;\;\frac{x}{1 + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) a)))
   (if (<= a -27000.0)
     t_1
     (if (<= a 18000000.0) (/ x (+ 1.0 (* y (/ b t)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / a;
	double tmp;
	if (a <= -27000.0) {
		tmp = t_1;
	} else if (a <= 18000000.0) {
		tmp = x / (1.0 + (y * (b / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / a
    if (a <= (-27000.0d0)) then
        tmp = t_1
    else if (a <= 18000000.0d0) then
        tmp = x / (1.0d0 + (y * (b / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / a;
	double tmp;
	if (a <= -27000.0) {
		tmp = t_1;
	} else if (a <= 18000000.0) {
		tmp = x / (1.0 + (y * (b / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / a
	tmp = 0
	if a <= -27000.0:
		tmp = t_1
	elif a <= 18000000.0:
		tmp = x / (1.0 + (y * (b / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / a)
	tmp = 0.0
	if (a <= -27000.0)
		tmp = t_1;
	elseif (a <= 18000000.0)
		tmp = Float64(x / Float64(1.0 + Float64(y * Float64(b / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / a;
	tmp = 0.0;
	if (a <= -27000.0)
		tmp = t_1;
	elseif (a <= 18000000.0)
		tmp = x / (1.0 + (y * (b / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -27000.0], t$95$1, If[LessEqual[a, 18000000.0], N[(x / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -27000 or 1.8e7 < a

   1. Initial program 73.7%

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

   3. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z}{t}\right), \color{blue}{a}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y \cdot z}{t}\right)\right), a\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), t\right)\right), a\right) \]

      4. *-lowering-*.f64 64.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), a\right) \]

   5. Simplified 64.4%

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

   if -27000 < a < 1.8e7

   1. Initial program 76.1%

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

   3. Taylor expanded in a around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z}{t}\right), \color{blue}{\left(1 + \frac{b \cdot y}{t}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y \cdot z}{t}\right)\right), \left(\color{blue}{1} + \frac{b \cdot y}{t}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), t\right)\right), \left(1 + \frac{b \cdot y}{t}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \left(1 + \frac{b \cdot y}{t}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{b \cdot y}{t}\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \left(\frac{y \cdot b}{t}\right)\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \left(y \cdot \color{blue}{\frac{b}{t}}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{b}{t}\right)}\right)\right)\right) \]

      9. /-lowering-/.f64 74.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 74.8%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, t\right)\right)\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 52.7%

      \[\leadsto \frac{\color{blue}{x}}{1 + y \cdot \frac{b}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 56.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{if}\;a \leq -22500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 13200:\\ \;\;\;\;\frac{x}{1 + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* z (/ y t))) a)))
   (if (<= a -22500.0)
     t_1
     (if (<= a 13200.0) (/ x (+ 1.0 (* y (/ b t)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / a;
	double tmp;
	if (a <= -22500.0) {
		tmp = t_1;
	} else if (a <= 13200.0) {
		tmp = x / (1.0 + (y * (b / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z * (y / t))) / a
    if (a <= (-22500.0d0)) then
        tmp = t_1
    else if (a <= 13200.0d0) then
        tmp = x / (1.0d0 + (y * (b / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / a;
	double tmp;
	if (a <= -22500.0) {
		tmp = t_1;
	} else if (a <= 13200.0) {
		tmp = x / (1.0 + (y * (b / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (z * (y / t))) / a
	tmp = 0
	if a <= -22500.0:
		tmp = t_1
	elif a <= 13200.0:
		tmp = x / (1.0 + (y * (b / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(z * Float64(y / t))) / a)
	tmp = 0.0
	if (a <= -22500.0)
		tmp = t_1;
	elseif (a <= 13200.0)
		tmp = Float64(x / Float64(1.0 + Float64(y * Float64(b / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (z * (y / t))) / a;
	tmp = 0.0;
	if (a <= -22500.0)
		tmp = t_1;
	elseif (a <= 13200.0)
		tmp = x / (1.0 + (y * (b / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -22500.0], t$95$1, If[LessEqual[a, 13200.0], N[(x / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -22500 or 13200 < a

   1. Initial program 73.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z \cdot y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(z \cdot \frac{y}{t}\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\frac{y}{t}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      4. /-lowering-/.f64 71.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   4. Applied egg-rr 71.1%

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

   5. Taylor expanded in a around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, t\right)\right)\right), \color{blue}{a}\right) \]
   6. Step-by-step derivation

   7. Simplified 62.7%

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

   if -22500 < a < 13200

   1. Initial program 76.1%

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

   3. Taylor expanded in a around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z}{t}\right), \color{blue}{\left(1 + \frac{b \cdot y}{t}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y \cdot z}{t}\right)\right), \left(\color{blue}{1} + \frac{b \cdot y}{t}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), t\right)\right), \left(1 + \frac{b \cdot y}{t}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \left(1 + \frac{b \cdot y}{t}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{b \cdot y}{t}\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \left(\frac{y \cdot b}{t}\right)\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \left(y \cdot \color{blue}{\frac{b}{t}}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{b}{t}\right)}\right)\right)\right) \]

      9. /-lowering-/.f64 74.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 74.8%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, t\right)\right)\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 52.7%

      \[\leadsto \frac{\color{blue}{x}}{1 + y \cdot \frac{b}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 40.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-63}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.3e+23)
   (/ x a)
   (if (<= a -6.5e-63) (/ z b) (if (<= a 1.0) x (/ x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.3e+23) {
		tmp = x / a;
	} else if (a <= -6.5e-63) {
		tmp = z / b;
	} else if (a <= 1.0) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.3d+23)) then
        tmp = x / a
    else if (a <= (-6.5d-63)) then
        tmp = z / b
    else if (a <= 1.0d0) then
        tmp = x
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.3e+23) {
		tmp = x / a;
	} else if (a <= -6.5e-63) {
		tmp = z / b;
	} else if (a <= 1.0) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.3e+23:
		tmp = x / a
	elif a <= -6.5e-63:
		tmp = z / b
	elif a <= 1.0:
		tmp = x
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.3e+23)
		tmp = Float64(x / a);
	elseif (a <= -6.5e-63)
		tmp = Float64(z / b);
	elseif (a <= 1.0)
		tmp = x;
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.3e+23)
		tmp = x / a;
	elseif (a <= -6.5e-63)
		tmp = z / b;
	elseif (a <= 1.0)
		tmp = x;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.3e+23], N[(x / a), $MachinePrecision], If[LessEqual[a, -6.5e-63], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.0], x, N[(x / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.29999999999999996e23 or 1 < a

   1. Initial program 74.3%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 54.3%

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

   6. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{x}{a}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 49.0%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{a}\right) \]

   8. Simplified 49.0%

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

   if -1.29999999999999996e23 < a < -6.4999999999999998e-63

   1. Initial program 60.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 40.0%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{b}\right) \]

   5. Simplified 40.0%

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

   if -6.4999999999999998e-63 < a < 1

   1. Initial program 78.1%

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

   3. Taylor expanded in a around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z}{t}\right), \color{blue}{\left(1 + \frac{b \cdot y}{t}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y \cdot z}{t}\right)\right), \left(\color{blue}{1} + \frac{b \cdot y}{t}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), t\right)\right), \left(1 + \frac{b \cdot y}{t}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \left(1 + \frac{b \cdot y}{t}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{b \cdot y}{t}\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \left(\frac{y \cdot b}{t}\right)\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \left(y \cdot \color{blue}{\frac{b}{t}}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{b}{t}\right)}\right)\right)\right) \]

      9. /-lowering-/.f64 78.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 78.1%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   7. Step-by-step derivation

   8. Simplified 41.8%

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

Alternative 16: 56.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-91}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -2.8e-41) t_1 (if (<= t 4.4e-91) (/ z b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -2.8e-41) {
		tmp = t_1;
	} else if (t <= 4.4e-91) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-2.8d-41)) then
        tmp = t_1
    else if (t <= 4.4d-91) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -2.8e-41) {
		tmp = t_1;
	} else if (t <= 4.4e-91) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -2.8e-41:
		tmp = t_1
	elif t <= 4.4e-91:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -2.8e-41)
		tmp = t_1;
	elseif (t <= 4.4e-91)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -2.8e-41)
		tmp = t_1;
	elseif (t <= 4.4e-91)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e-41], t$95$1, If[LessEqual[t, 4.4e-91], N[(z / b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8000000000000002e-41 or 4.4000000000000002e-91 < t

   1. Initial program 83.2%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a\right)}\right) \]

      2. +-lowering-+.f64 59.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{a}\right)\right) \]

   5. Simplified 59.5%

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

   if -2.8000000000000002e-41 < t < 4.4000000000000002e-91

   1. Initial program 62.8%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 52.2%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{b}\right) \]

   5. Simplified 52.2%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-91}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 40.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.6e-6) (/ x a) (if (<= a 1.0) x (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.6e-6) {
		tmp = x / a;
	} else if (a <= 1.0) {
		tmp = x;
	} 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-6)) then
        tmp = x / a
    else if (a <= 1.0d0) then
        tmp = x
    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-6) {
		tmp = x / a;
	} else if (a <= 1.0) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.6e-6:
		tmp = x / a
	elif a <= 1.0:
		tmp = x
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.6e-6)
		tmp = Float64(x / a);
	elseif (a <= 1.0)
		tmp = x;
	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-6)
		tmp = x / a;
	elseif (a <= 1.0)
		tmp = x;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.6e-6], N[(x / a), $MachinePrecision], If[LessEqual[a, 1.0], x, N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.60000000000000009e-6 or 1 < a

   1. Initial program 72.3%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 52.1%

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

   6. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{x}{a}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 45.8%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{a}\right) \]

   8. Simplified 45.8%

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

   if -2.60000000000000009e-6 < a < 1

   1. Initial program 77.6%

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

   3. Taylor expanded in a around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z}{t}\right), \color{blue}{\left(1 + \frac{b \cdot y}{t}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y \cdot z}{t}\right)\right), \left(\color{blue}{1} + \frac{b \cdot y}{t}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), t\right)\right), \left(1 + \frac{b \cdot y}{t}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \left(1 + \frac{b \cdot y}{t}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{b \cdot y}{t}\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \left(\frac{y \cdot b}{t}\right)\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \left(y \cdot \color{blue}{\frac{b}{t}}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{b}{t}\right)}\right)\right)\right) \]

      9. /-lowering-/.f64 77.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 77.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   7. Step-by-step derivation

   8. Simplified 40.2%

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

Alternative 18: 19.5% 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 75.1%

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

3. Taylor expanded in a around 0

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

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z}{t}\right), \color{blue}{\left(1 + \frac{b \cdot y}{t}\right)}\right) \]

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y \cdot z}{t}\right)\right), \left(\color{blue}{1} + \frac{b \cdot y}{t}\right)\right) \]

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), t\right)\right), \left(1 + \frac{b \cdot y}{t}\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \left(1 + \frac{b \cdot y}{t}\right)\right) \]

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{b \cdot y}{t}\right)}\right)\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \left(\frac{y \cdot b}{t}\right)\right)\right) \]

   7. associate-/l* N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \left(y \cdot \color{blue}{\frac{b}{t}}\right)\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{b}{t}\right)}\right)\right)\right) \]

   9. /-lowering-/.f64 47.0%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, \color{blue}{t}\right)\right)\right)\right) \]

5. Simplified 47.0%

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

6. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x} \]
7. Step-by-step derivation

8. Simplified 23.0%

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

Developer Target 1: 78.8% 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 2024138 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1707385670788761/12500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b))))) (if (< t 1518483551868623/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ z b) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b))))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))