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

Percentage Accurate: 75.1% → 88.2%

Time: 9.2s

Alternatives: 14

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{t \cdot \left(\frac{x}{y} + \frac{z}{t}\right)}{b}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+292}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 -1e-303)
     t_1
     (if (<= t_1 0.0)
       (/ (* t (+ (/ x y) (/ z t))) b)
       (if (<= t_1 5e+292) t_1 (/ (fma t (/ x y) z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -1e-303) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t * ((x / y) + (z / t))) / b;
	} else if (t_1 <= 5e+292) {
		tmp = t_1;
	} else {
		tmp = fma(t, (x / y), z) / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= -1e-303)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(t * Float64(Float64(x / y) + Float64(z / t))) / b);
	elseif (t_1 <= 5e+292)
		tmp = t_1;
	else
		tmp = Float64(fma(t, Float64(x / y), z) / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-303], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(t * N[(N[(x / y), $MachinePrecision] + N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$1, 5e+292], t$95$1, N[(N[(t * N[(x / y), $MachinePrecision] + z), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -9.99999999999999931e-304 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 4.9999999999999996e292

   1. Initial program 97.2%

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

   if -9.99999999999999931e-304 < (/.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 49.0%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 36.8%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 75.6%

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

   if 4.9999999999999996e292 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.2%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 3.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 70.5%

      \[\leadsto \frac{\mathsf{fma}\left(\frac{x - \frac{\mathsf{fma}\left(a, z, z\right)}{b}}{y}, t, z\right)}{b} \]

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 85.5%

       \[\leadsto \frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 85.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1}\\ t_3 := \frac{\mathsf{fma}\left(\frac{z}{t}, y, x\right)}{t\_1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-303}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{t \cdot \left(\frac{x}{y} + \frac{z}{t}\right)}{b}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+292}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (/ (* y b) t)))
        (t_2 (/ (+ x (/ (* y z) t)) t_1))
        (t_3 (/ (fma (/ z t) y x) t_1)))
   (if (<= t_2 -1e-303)
     t_3
     (if (<= t_2 0.0)
       (/ (* t (+ (/ x y) (/ z t))) b)
       (if (<= t_2 5e+292) t_3 (/ (fma t (/ x y) z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + ((y * b) / t);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double t_3 = fma((z / t), y, x) / t_1;
	double tmp;
	if (t_2 <= -1e-303) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = (t * ((x / y) + (z / t))) / b;
	} else if (t_2 <= 5e+292) {
		tmp = t_3;
	} else {
		tmp = fma(t, (x / y), z) / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	t_3 = Float64(fma(Float64(z / t), y, x) / t_1)
	tmp = 0.0
	if (t_2 <= -1e-303)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(t * Float64(Float64(x / y) + Float64(z / t))) / b);
	elseif (t_2 <= 5e+292)
		tmp = t_3;
	else
		tmp = Float64(fma(t, Float64(x / y), z) / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-303], t$95$3, If[LessEqual[t$95$2, 0.0], N[(N[(t * N[(N[(x / y), $MachinePrecision] + N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$2, 5e+292], t$95$3, N[(N[(t * N[(x / y), $MachinePrecision] + z), $MachinePrecision] / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -9.99999999999999931e-304 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 4.9999999999999996e292

   1. Initial program 97.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 90.9

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

   4. Applied rewrites 90.9%

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

   if -9.99999999999999931e-304 < (/.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 49.0%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 36.8%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 75.6%

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

   if 4.9999999999999996e292 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.2%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 3.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 70.5%

      \[\leadsto \frac{\mathsf{fma}\left(\frac{x - \frac{\mathsf{fma}\left(a, z, z\right)}{b}}{y}, t, z\right)}{b} \]

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 85.5%

       \[\leadsto \frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 73.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-303} \lor \neg \left(t\_2 \leq 0 \lor \neg \left(t\_2 \leq 5 \cdot 10^{+292}\right)\right):\\ \;\;\;\;\frac{t\_1}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))) (t_2 (/ t_1 (+ (+ a 1.0) (/ (* y b) t)))))
   (if (or (<= t_2 -1e-303) (not (or (<= t_2 0.0) (not (<= t_2 5e+292)))))
     (/ t_1 (+ 1.0 a))
     (/ (fma t (/ x y) z) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if ((t_2 <= -1e-303) || !((t_2 <= 0.0) || !(t_2 <= 5e+292))) {
		tmp = t_1 / (1.0 + a);
	} else {
		tmp = fma(t, (x / y), z) / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if ((t_2 <= -1e-303) || !((t_2 <= 0.0) || !(t_2 <= 5e+292)))
		tmp = Float64(t_1 / Float64(1.0 + a));
	else
		tmp = Float64(fma(t, Float64(x / y), z) / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -1e-303], N[Not[Or[LessEqual[t$95$2, 0.0], N[Not[LessEqual[t$95$2, 5e+292]], $MachinePrecision]]], $MachinePrecision]], N[(t$95$1 / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(x / y), $MachinePrecision] + z), $MachinePrecision] / b), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -9.99999999999999931e-304 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 4.9999999999999996e292

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-+.f64 79.6

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

   5. Applied rewrites 79.6%

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

   if -9.99999999999999931e-304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -0.0 or 4.9999999999999996e292 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 33.7%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 23.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 70.8%

      \[\leadsto \frac{\mathsf{fma}\left(\frac{x - \frac{\mathsf{fma}\left(a, z, z\right)}{b}}{y}, t, z\right)}{b} \]

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 77.1%

       \[\leadsto \frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-303} \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0 \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+292}\right)\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_3 := \frac{t\_1}{1 + a}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-303}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{t \cdot \left(\frac{x}{y} + \frac{z}{t}\right)}{b}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+292}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t)))
        (t_2 (/ t_1 (+ (+ a 1.0) (/ (* y b) t))))
        (t_3 (/ t_1 (+ 1.0 a))))
   (if (<= t_2 -1e-303)
     t_3
     (if (<= t_2 0.0)
       (/ (* t (+ (/ x y) (/ z t))) b)
       (if (<= t_2 5e+292) t_3 (/ (fma t (/ x y) z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double t_3 = t_1 / (1.0 + a);
	double tmp;
	if (t_2 <= -1e-303) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = (t * ((x / y) + (z / t))) / b;
	} else if (t_2 <= 5e+292) {
		tmp = t_3;
	} else {
		tmp = fma(t, (x / y), z) / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_3 = Float64(t_1 / Float64(1.0 + a))
	tmp = 0.0
	if (t_2 <= -1e-303)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(t * Float64(Float64(x / y) + Float64(z / t))) / b);
	elseif (t_2 <= 5e+292)
		tmp = t_3;
	else
		tmp = Float64(fma(t, Float64(x / y), z) / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-303], t$95$3, If[LessEqual[t$95$2, 0.0], N[(N[(t * N[(N[(x / y), $MachinePrecision] + N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$2, 5e+292], t$95$3, N[(N[(t * N[(x / y), $MachinePrecision] + z), $MachinePrecision] / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -9.99999999999999931e-304 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 4.9999999999999996e292

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-+.f64 79.6

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

   5. Applied rewrites 79.6%

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

   if -9.99999999999999931e-304 < (/.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 49.0%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 36.8%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 75.6%

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

   if 4.9999999999999996e292 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.2%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 3.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 70.5%

      \[\leadsto \frac{\mathsf{fma}\left(\frac{x - \frac{\mathsf{fma}\left(a, z, z\right)}{b}}{y}, t, z\right)}{b} \]

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 85.5%

       \[\leadsto \frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 74.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-303} \lor \neg \left(t\_1 \leq 0 \lor \neg \left(t\_1 \leq 5 \cdot 10^{+292}\right)\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (or (<= t_1 -1e-303) (not (or (<= t_1 0.0) (not (<= t_1 5e+292)))))
     (/ (fma (/ y t) z x) (+ 1.0 a))
     (/ (fma t (/ x y) z) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if ((t_1 <= -1e-303) || !((t_1 <= 0.0) || !(t_1 <= 5e+292))) {
		tmp = fma((y / t), z, x) / (1.0 + a);
	} else {
		tmp = fma(t, (x / y), z) / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if ((t_1 <= -1e-303) || !((t_1 <= 0.0) || !(t_1 <= 5e+292)))
		tmp = Float64(fma(Float64(y / t), z, x) / Float64(1.0 + a));
	else
		tmp = Float64(fma(t, Float64(x / y), z) / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-303], N[Not[Or[LessEqual[t$95$1, 0.0], N[Not[LessEqual[t$95$1, 5e+292]], $MachinePrecision]]], $MachinePrecision]], N[(N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision] / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(x / y), $MachinePrecision] + z), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -9.99999999999999931e-304 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 4.9999999999999996e292

   1. Initial program 97.2%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   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. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*l/ N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 77.5

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

   5. Applied rewrites 77.5%

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

   if -9.99999999999999931e-304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -0.0 or 4.9999999999999996e292 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 33.7%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 23.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 70.8%

      \[\leadsto \frac{\mathsf{fma}\left(\frac{x - \frac{\mathsf{fma}\left(a, z, z\right)}{b}}{y}, t, z\right)}{b} \]

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 77.1%

       \[\leadsto \frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-303} \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0 \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+292}\right)\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{1 + a}{x}\right)}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.95e+33)
   (/ x (+ 1.0 a))
   (if (<= t 2.8e-72) (/ (fma t (/ x y) z) b) (pow (/ (+ 1.0 a) x) -1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.95e+33) {
		tmp = x / (1.0 + a);
	} else if (t <= 2.8e-72) {
		tmp = fma(t, (x / y), z) / b;
	} else {
		tmp = pow(((1.0 + a) / x), -1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.95e+33)
		tmp = Float64(x / Float64(1.0 + a));
	elseif (t <= 2.8e-72)
		tmp = Float64(fma(t, Float64(x / y), z) / b);
	else
		tmp = Float64(Float64(1.0 + a) / x) ^ -1.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.95e+33], N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-72], N[(N[(t * N[(x / y), $MachinePrecision] + z), $MachinePrecision] / b), $MachinePrecision], N[Power[N[(N[(1.0 + a), $MachinePrecision] / x), $MachinePrecision], -1.0], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9500000000000001e33

   1. Initial program 92.1%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 76.3

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

   5. Applied rewrites 76.3%

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

   if -1.9500000000000001e33 < t < 2.7999999999999998e-72

   1. Initial program 66.6%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 16.1%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 55.8%

      \[\leadsto \frac{\mathsf{fma}\left(\frac{x - \frac{\mathsf{fma}\left(a, z, z\right)}{b}}{y}, t, z\right)}{b} \]

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 63.7%

       \[\leadsto \frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b} \]

   if 2.7999999999999998e-72 < t

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 63.8

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

   5. Applied rewrites 63.8%

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

   7. Applied rewrites 64.1%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{1 + a}{x}\right)}^{-1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.15 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-78}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{1 + a}{x}\right)}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.15e-54)
   (/ x (+ 1.0 a))
   (if (<= t 2.65e-78) (/ z b) (pow (/ (+ 1.0 a) x) -1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.15e-54) {
		tmp = x / (1.0 + a);
	} else if (t <= 2.65e-78) {
		tmp = z / b;
	} else {
		tmp = pow(((1.0 + a) / x), -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.15d-54)) then
        tmp = x / (1.0d0 + a)
    else if (t <= 2.65d-78) then
        tmp = z / b
    else
        tmp = ((1.0d0 + a) / x) ** (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.15e-54) {
		tmp = x / (1.0 + a);
	} else if (t <= 2.65e-78) {
		tmp = z / b;
	} else {
		tmp = Math.pow(((1.0 + a) / x), -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.15e-54:
		tmp = x / (1.0 + a)
	elif t <= 2.65e-78:
		tmp = z / b
	else:
		tmp = math.pow(((1.0 + a) / x), -1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.15e-54)
		tmp = Float64(x / Float64(1.0 + a));
	elseif (t <= 2.65e-78)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(1.0 + a) / x) ^ -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.15e-54)
		tmp = x / (1.0 + a);
	elseif (t <= 2.65e-78)
		tmp = z / b;
	else
		tmp = ((1.0 + a) / x) ^ -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.15e-54], N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.65e-78], N[(z / b), $MachinePrecision], N[Power[N[(N[(1.0 + a), $MachinePrecision] / x), $MachinePrecision], -1.0], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.15e-54

   1. Initial program 91.3%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 67.8

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

   5. Applied rewrites 67.8%

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

   if -4.15e-54 < t < 2.64999999999999979e-78

   1. Initial program 62.3%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 59.3

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

   5. Applied rewrites 59.3%

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

   if 2.64999999999999979e-78 < t

   1. Initial program 88.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 63.5

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

   5. Applied rewrites 63.5%

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

   7. Applied rewrites 63.8%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.15 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-78}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{1 + a}{x}\right)}^{-1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{z}{t}, y, x\right)}{\mathsf{fma}\left(\frac{b}{t}, y, 1 + a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))) 5e+292)
   (/ (fma (/ z t) y x) (fma (/ b t) y (+ 1.0 a)))
   (/ (fma t (/ x y) z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))) <= 5e+292) {
		tmp = fma((z / t), y, x) / fma((b / t), y, (1.0 + a));
	} else {
		tmp = fma(t, (x / y), z) / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t))) <= 5e+292)
		tmp = Float64(fma(Float64(z / t), y, x) / fma(Float64(b / t), y, Float64(1.0 + a)));
	else
		tmp = Float64(fma(t, Float64(x / y), z) / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[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], 5e+292], N[(N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision] / N[(N[(b / t), $MachinePrecision] * y + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(x / y), $MachinePrecision] + z), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 4.9999999999999996e292

   1. Initial program 87.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 82.8

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lift-/.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-/l* N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lower-/.f64 82.7

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

      17. lift-+.f64 N/A

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

      18. +-commutative N/A

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

      19. lower-+.f64 82.7

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

   4. Applied rewrites 82.7%

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

   if 4.9999999999999996e292 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.2%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 3.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 70.5%

      \[\leadsto \frac{\mathsf{fma}\left(\frac{x - \frac{\mathsf{fma}\left(a, z, z\right)}{b}}{y}, t, z\right)}{b} \]

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 85.5%

       \[\leadsto \frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 65.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-54} \lor \neg \left(t \leq 2.8 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\frac{y}{t}, b, 1 + a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.6e-54) (not (<= t 2.8e-72)))
   (/ x (fma (/ y t) b (+ 1.0 a)))
   (/ (fma t (/ x y) z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.6e-54) || !(t <= 2.8e-72)) {
		tmp = x / fma((y / t), b, (1.0 + a));
	} else {
		tmp = fma(t, (x / y), z) / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.6e-54) || !(t <= 2.8e-72))
		tmp = Float64(x / fma(Float64(y / t), b, Float64(1.0 + a)));
	else
		tmp = Float64(fma(t, Float64(x / y), z) / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.6e-54], N[Not[LessEqual[t, 2.8e-72]], $MachinePrecision]], N[(x / N[(N[(y / t), $MachinePrecision] * b + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(x / y), $MachinePrecision] + z), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.60000000000000002e-54 or 2.7999999999999998e-72 < t

   1. Initial program 89.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   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. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-+.f64 73.4

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

   5. Applied rewrites 73.4%

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

   if -2.60000000000000002e-54 < t < 2.7999999999999998e-72

   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 b around inf

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 12.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 58.0%

      \[\leadsto \frac{\mathsf{fma}\left(\frac{x - \frac{\mathsf{fma}\left(a, z, z\right)}{b}}{y}, t, z\right)}{b} \]

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 66.1%

       \[\leadsto \frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-54} \lor \neg \left(t \leq 2.8 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\frac{y}{t}, b, 1 + a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a + 1 \leq -5000000000000 \lor \neg \left(a + 1 \leq 400000000000\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(1 - a\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ a 1.0) -5000000000000.0) (not (<= (+ a 1.0) 400000000000.0)))
   (/ x a)
   (* (- 1.0 a) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a + 1.0) <= -5000000000000.0) || !((a + 1.0) <= 400000000000.0)) {
		tmp = x / a;
	} else {
		tmp = (1.0 - a) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((a + 1.0d0) <= (-5000000000000.0d0)) .or. (.not. ((a + 1.0d0) <= 400000000000.0d0))) then
        tmp = x / a
    else
        tmp = (1.0d0 - a) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a + 1.0) <= -5000000000000.0) || !((a + 1.0) <= 400000000000.0)) {
		tmp = x / a;
	} else {
		tmp = (1.0 - a) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a + 1.0) <= -5000000000000.0) or not ((a + 1.0) <= 400000000000.0):
		tmp = x / a
	else:
		tmp = (1.0 - a) * x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a + 1.0) <= -5000000000000.0) || !(Float64(a + 1.0) <= 400000000000.0))
		tmp = Float64(x / a);
	else
		tmp = Float64(Float64(1.0 - a) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a + 1.0) <= -5000000000000.0) || ~(((a + 1.0) <= 400000000000.0)))
		tmp = x / a;
	else
		tmp = (1.0 - a) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a + 1.0), $MachinePrecision], -5000000000000.0], N[Not[LessEqual[N[(a + 1.0), $MachinePrecision], 400000000000.0]], $MachinePrecision]], N[(x / a), $MachinePrecision], N[(N[(1.0 - a), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 a #s(literal 1 binary64)) < -5e12 or 4e11 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 77.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 51.2

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

   5. Applied rewrites 51.2%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 51.1%

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

   if -5e12 < (+.f64 a #s(literal 1 binary64)) < 4e11

   1. Initial program 80.0%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 42.3

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

   5. Applied rewrites 42.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 40.5%

      \[\leadsto \mathsf{fma}\left(-a, \color{blue}{x}, x\right) \]

   9. Taylor expanded in a around 0

      \[\leadsto x + \color{blue}{-1 \cdot \left(a \cdot x\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 40.5%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -5000000000000 \lor \neg \left(a + 1 \leq 400000000000\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(1 - a\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.15 \cdot 10^{-54} \lor \neg \left(t \leq 2.65 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.15e-54) (not (<= t 2.65e-78))) (/ x (+ 1.0 a)) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.15e-54) || !(t <= 2.65e-78)) {
		tmp = x / (1.0 + a);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4.15d-54)) .or. (.not. (t <= 2.65d-78))) then
        tmp = x / (1.0d0 + a)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.15e-54) || !(t <= 2.65e-78)) {
		tmp = x / (1.0 + a);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.15e-54) or not (t <= 2.65e-78):
		tmp = x / (1.0 + a)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.15e-54) || !(t <= 2.65e-78))
		tmp = Float64(x / Float64(1.0 + a));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.15e-54) || ~((t <= 2.65e-78)))
		tmp = x / (1.0 + a);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.15e-54], N[Not[LessEqual[t, 2.65e-78]], $MachinePrecision]], N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.15e-54 or 2.64999999999999979e-78 < t

   1. Initial program 89.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 65.6

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

   5. Applied rewrites 65.6%

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

   if -4.15e-54 < t < 2.64999999999999979e-78

   1. Initial program 62.3%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 59.3

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

   5. Applied rewrites 59.3%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.15 \cdot 10^{-54} \lor \neg \left(t \leq 2.65 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+33} \lor \neg \left(t \leq 2.65 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.7e+33) (not (<= t 2.65e-78))) (/ x a) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.7e+33) || !(t <= 2.65e-78)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4.7d+33)) .or. (.not. (t <= 2.65d-78))) then
        tmp = x / a
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.7e+33) || !(t <= 2.65e-78)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.7e+33) or not (t <= 2.65e-78):
		tmp = x / a
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.7e+33) || !(t <= 2.65e-78))
		tmp = Float64(x / a);
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.7e+33) || ~((t <= 2.65e-78)))
		tmp = x / a;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.7e+33], N[Not[LessEqual[t, 2.65e-78]], $MachinePrecision]], N[(x / a), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.6999999999999998e33 or 2.64999999999999979e-78 < t

   1. Initial program 90.1%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 69.1

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

   5. Applied rewrites 69.1%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 42.7%

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

   if -4.6999999999999998e33 < t < 2.64999999999999979e-78

   1. Initial program 66.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 54.7

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

   5. Applied rewrites 54.7%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+33} \lor \neg \left(t \leq 2.65 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 20.1% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \left(1 - a\right) \cdot x \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (1.0 - a) * 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 = (1.0d0 - a) * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(1.0 - a), $MachinePrecision] * x), $MachinePrecision]

Derivation

1. Initial program 78.8%

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

3. Taylor expanded in y around 0

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

   1. lower-/.f64 N/A

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

   2. lower-+.f64 47.0

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

5. Applied rewrites 47.0%

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

6. Taylor expanded in a around 0

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

8. Applied rewrites 20.6%

   \[\leadsto \mathsf{fma}\left(-a, \color{blue}{x}, x\right) \]

9. Taylor expanded in a around 0

   \[\leadsto x + \color{blue}{-1 \cdot \left(a \cdot x\right)} \]
10. Step-by-step derivation

11. Applied rewrites 20.6%

    \[\leadsto \left(1 - a\right) \cdot \color{blue}{x} \]
12. Add Preprocessing

Alternative 14: 4.1% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \left(-a\right) \cdot x \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return -a * 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 = -a * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.8%

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

3. Taylor expanded in y around 0

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

   1. lower-/.f64 N/A

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

   2. lower-+.f64 47.0

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

5. Applied rewrites 47.0%

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

6. Taylor expanded in a around 0

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

8. Applied rewrites 20.6%

   \[\leadsto \mathsf{fma}\left(-a, \color{blue}{x}, x\right) \]

9. Taylor expanded in a around inf

   \[\leadsto -1 \cdot \left(a \cdot \color{blue}{x}\right) \]
10. Step-by-step derivation

11. Applied rewrites 3.7%

    \[\leadsto \left(-a\right) \cdot x \]
12. Add Preprocessing

Developer Target 1: 78.7% accurate, 0.7× 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 2024313 
(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))))