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

Percentage Accurate: 74.9% → 89.9%

Time: 12.6s

Alternatives: 21

Speedup: 0.3×

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: 74.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := \frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-290}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+301}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (* (/ y (fma b y (fma a t t))) z)))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -2e-304)
       t_1
       (if (<= t_1 5e-290)
         t_2
         (if (<= t_1 2e+301) 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 t_2 = (y / fma(b, y, fma(a, t, t))) * z;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -2e-304) {
		tmp = t_1;
	} else if (t_1 <= 5e-290) {
		tmp = t_2;
	} else if (t_1 <= 2e+301) {
		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)))
	t_2 = Float64(Float64(y / fma(b, y, fma(a, t, t))) * z)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -2e-304)
		tmp = t_1;
	elseif (t_1 <= 5e-290)
		tmp = t_2;
	elseif (t_1 <= 2e+301)
		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]}, Block[{t$95$2 = N[(N[(y / N[(b * y + N[(a * t + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -2e-304], t$95$1, If[LessEqual[t$95$1, 5e-290], t$95$2, If[LessEqual[t$95$1, 2e+301], 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))) < -inf.0 or -1.99999999999999994e-304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.0000000000000001e-290

   1. Initial program 51.4%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 71.7

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

   5. Applied rewrites 71.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 82.6%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999994e-304 or 5.0000000000000001e-290 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000011e301

   1. Initial program 99.7%

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

   if 2.00000000000000011e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 6.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/l/ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 37.5%

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

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 88.9

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

   7. Applied rewrites 88.9%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-304}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{-290}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+301}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 62.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + a}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_3 := \frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-304}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, y, t \cdot x\right)}{\mathsf{fma}\left(a, t, t\right)}\\ \mathbf{elif}\;t\_2 \leq 10^{-232}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 a)))
        (t_2 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_3 (* (/ y (fma b y (fma a t t))) z)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -1e+30)
       t_1
       (if (<= t_2 -2e-304)
         (/ (fma z y (* t x)) (fma a t t))
         (if (<= t_2 1e-232)
           t_3
           (if (<= t_2 1e+196)
             t_1
             (if (<= t_2 INFINITY) 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 / (1.0 + a);
	double t_2 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_3 = (y / fma(b, y, fma(a, t, t))) * z;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -1e+30) {
		tmp = t_1;
	} else if (t_2 <= -2e-304) {
		tmp = fma(z, y, (t * x)) / fma(a, t, t);
	} else if (t_2 <= 1e-232) {
		tmp = t_3;
	} else if (t_2 <= 1e+196) {
		tmp = t_1;
	} else if (t_2 <= ((double) INFINITY)) {
		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(1.0 + a))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_3 = Float64(Float64(y / fma(b, y, fma(a, t, t))) * z)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -1e+30)
		tmp = t_1;
	elseif (t_2 <= -2e-304)
		tmp = Float64(fma(z, y, Float64(t * x)) / fma(a, t, t));
	elseif (t_2 <= 1e-232)
		tmp = t_3;
	elseif (t_2 <= 1e+196)
		tmp = t_1;
	elseif (t_2 <= Inf)
		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[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, Block[{t$95$3 = N[(N[(y / N[(b * y + N[(a * t + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -1e+30], t$95$1, If[LessEqual[t$95$2, -2e-304], N[(N[(z * y + N[(t * x), $MachinePrecision]), $MachinePrecision] / N[(a * t + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-232], t$95$3, If[LessEqual[t$95$2, 1e+196], t$95$1, If[LessEqual[t$95$2, Infinity], t$95$3, N[(N[(t * N[(x / y), $MachinePrecision] + z), $MachinePrecision] / b), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0 or -1.99999999999999994e-304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.00000000000000002e-232 or 9.9999999999999995e195 < (/.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 51.3%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 70.3

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

   5. Applied rewrites 70.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 81.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1e30 or 1.00000000000000002e-232 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999995e195

   1. Initial program 99.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   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 61.8

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

   5. Applied rewrites 61.8%

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

   if -1e30 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999994e-304

   1. Initial program 99.7%

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

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 83.6%

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

   7. Applied rewrites 54.6%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 74.1%

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

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

   1. Initial program 0.0%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/l/ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 15.7%

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

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 96.3

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

   7. Applied rewrites 96.3%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-304}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, y, t \cdot x\right)}{\mathsf{fma}\left(a, t, t\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{-232}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+196}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_3 := \frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-304}:\\ \;\;\;\;\frac{t\_1}{1 + a}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-290}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{+196}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\frac{y}{t}, b, 1 + a\right)}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{\frac{y}{\mathsf{fma}\left(\frac{b}{t}, y, 1 + a\right)}}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \end{array} \]

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 (* (/ y (fma b y (fma a t t))) z)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -2e-304)
       (/ t_1 (+ 1.0 a))
       (if (<= t_2 5e-290)
         t_3
         (if (<= t_2 1e+196)
           (/ x (fma (/ y t) b (+ 1.0 a)))
           (if (<= t_2 INFINITY)
             (* (/ (/ y (fma (/ b t) y (+ 1.0 a))) t) z)
             (/ (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 = (y / fma(b, y, fma(a, t, t))) * z;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -2e-304) {
		tmp = t_1 / (1.0 + a);
	} else if (t_2 <= 5e-290) {
		tmp = t_3;
	} else if (t_2 <= 1e+196) {
		tmp = x / fma((y / t), b, (1.0 + a));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = ((y / fma((b / t), y, (1.0 + a))) / t) * z;
	} 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(Float64(y / fma(b, y, fma(a, t, t))) * z)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -2e-304)
		tmp = Float64(t_1 / Float64(1.0 + a));
	elseif (t_2 <= 5e-290)
		tmp = t_3;
	elseif (t_2 <= 1e+196)
		tmp = Float64(x / fma(Float64(y / t), b, Float64(1.0 + a)));
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(Float64(y / fma(Float64(b / t), y, Float64(1.0 + a))) / t) * z);
	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[(N[(y / N[(b * y + N[(a * t + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -2e-304], N[(t$95$1 / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e-290], t$95$3, If[LessEqual[t$95$2, 1e+196], N[(x / N[(N[(y / t), $MachinePrecision] * b + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[(N[(y / N[(N[(b / t), $MachinePrecision] * y + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision], N[(N[(t * N[(x / y), $MachinePrecision] + z), $MachinePrecision] / 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 or -1.99999999999999994e-304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.0000000000000001e-290

   1. Initial program 51.4%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 71.7

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

   5. Applied rewrites 71.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 82.6%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999994e-304

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-+.f64 85.2

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

   5. Applied rewrites 85.2%

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

   if 5.0000000000000001e-290 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999995e195

   1. Initial program 99.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   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 71.2

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

   5. Applied rewrites 71.2%

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

   if 9.9999999999999995e195 < (/.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 43.7%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 70.7

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

   5. Applied rewrites 70.7%

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

   7. Applied rewrites 90.1%

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

   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. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/l/ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 15.7%

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

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 96.3

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

   7. Applied rewrites 96.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-304}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{1 + a}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{-290}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+196}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\frac{y}{t}, b, 1 + a\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{\frac{y}{\mathsf{fma}\left(\frac{b}{t}, y, 1 + a\right)}}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := \frac{x}{1 + a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(a, t, t\right)} \cdot z\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-304}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, y, t \cdot x\right)}{\mathsf{fma}\left(a, t, t\right)}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-222} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+154}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (/ x (+ 1.0 a))))
   (if (<= t_1 (- INFINITY))
     (* (/ y (fma a t t)) z)
     (if (<= t_1 -1e+30)
       t_2
       (if (<= t_1 -2e-304)
         (/ (fma z y (* t x)) (fma a t t))
         (if (or (<= t_1 2e-222) (not (<= t_1 2e+154)))
           (/ (fma t (/ x y) z) b)
           t_2))))))

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 t_2 = x / (1.0 + a);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y / fma(a, t, t)) * z;
	} else if (t_1 <= -1e+30) {
		tmp = t_2;
	} else if (t_1 <= -2e-304) {
		tmp = fma(z, y, (t * x)) / fma(a, t, t);
	} else if ((t_1 <= 2e-222) || !(t_1 <= 2e+154)) {
		tmp = fma(t, (x / y), z) / b;
	} else {
		tmp = t_2;
	}
	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)))
	t_2 = Float64(x / Float64(1.0 + a))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y / fma(a, t, t)) * z);
	elseif (t_1 <= -1e+30)
		tmp = t_2;
	elseif (t_1 <= -2e-304)
		tmp = Float64(fma(z, y, Float64(t * x)) / fma(a, t, t));
	elseif ((t_1 <= 2e-222) || !(t_1 <= 2e+154))
		tmp = Float64(fma(t, Float64(x / y), z) / b);
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y / N[(a * t + t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, -1e+30], t$95$2, If[LessEqual[t$95$1, -2e-304], N[(N[(z * y + N[(t * x), $MachinePrecision]), $MachinePrecision] / N[(a * t + t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, 2e-222], N[Not[LessEqual[t$95$1, 2e+154]], $MachinePrecision]], N[(N[(t * N[(x / y), $MachinePrecision] + z), $MachinePrecision] / b), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 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 x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 83.0

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

   5. Applied rewrites 83.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{y}{t + a \cdot t} \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 71.1%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1e30 or 2.0000000000000001e-222 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000007e154

   1. Initial program 99.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   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 62.6

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

   5. Applied rewrites 62.6%

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

   if -1e30 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999994e-304

   1. Initial program 99.7%

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

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 83.6%

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

   7. Applied rewrites 54.6%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 74.1%

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

   if -1.99999999999999994e-304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e-222 or 2.00000000000000007e154 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 45.0%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/l/ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 62.9%

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

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 74.0

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

   7. Applied rewrites 74.0%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(a, t, t\right)} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-304}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, y, t \cdot x\right)}{\mathsf{fma}\left(a, t, t\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{-222} \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+154}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_3 := \frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-304}:\\ \;\;\;\;\frac{t\_1}{1 + a}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-290}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{+196}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\frac{y}{t}, b, 1 + a\right)}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \end{array} \]

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 (* (/ y (fma b y (fma a t t))) z)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -2e-304)
       (/ t_1 (+ 1.0 a))
       (if (<= t_2 5e-290)
         t_3
         (if (<= t_2 1e+196)
           (/ x (fma (/ y t) b (+ 1.0 a)))
           (if (<= t_2 INFINITY) 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 = (y / fma(b, y, fma(a, t, t))) * z;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -2e-304) {
		tmp = t_1 / (1.0 + a);
	} else if (t_2 <= 5e-290) {
		tmp = t_3;
	} else if (t_2 <= 1e+196) {
		tmp = x / fma((y / t), b, (1.0 + a));
	} else if (t_2 <= ((double) INFINITY)) {
		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(Float64(y / fma(b, y, fma(a, t, t))) * z)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -2e-304)
		tmp = Float64(t_1 / Float64(1.0 + a));
	elseif (t_2 <= 5e-290)
		tmp = t_3;
	elseif (t_2 <= 1e+196)
		tmp = Float64(x / fma(Float64(y / t), b, Float64(1.0 + a)));
	elseif (t_2 <= Inf)
		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[(N[(y / N[(b * y + N[(a * t + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -2e-304], N[(t$95$1 / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e-290], t$95$3, If[LessEqual[t$95$2, 1e+196], N[(x / N[(N[(y / t), $MachinePrecision] * b + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$3, N[(N[(t * N[(x / y), $MachinePrecision] + z), $MachinePrecision] / b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0 or -1.99999999999999994e-304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.0000000000000001e-290 or 9.9999999999999995e195 < (/.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 49.5%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 71.5

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

   5. Applied rewrites 71.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 83.3%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999994e-304

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-+.f64 85.2

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

   5. Applied rewrites 85.2%

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

   if 5.0000000000000001e-290 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999995e195

   1. Initial program 99.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   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 71.2

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

   5. Applied rewrites 71.2%

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

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

   1. Initial program 0.0%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/l/ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 15.7%

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

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 96.3

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

   7. Applied rewrites 96.3%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-304}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{1 + a}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{-290}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+196}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\frac{y}{t}, b, 1 + a\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := \frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-304}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{1 + a}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-290}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+196}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\frac{y}{t}, b, 1 + a\right)}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (* (/ y (fma b y (fma a t t))) z)))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -2e-304)
       (/ (fma (/ y t) z x) (+ 1.0 a))
       (if (<= t_1 5e-290)
         t_2
         (if (<= t_1 1e+196)
           (/ x (fma (/ y t) b (+ 1.0 a)))
           (if (<= t_1 INFINITY) t_2 (/ (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 t_2 = (y / fma(b, y, fma(a, t, t))) * z;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -2e-304) {
		tmp = fma((y / t), z, x) / (1.0 + a);
	} else if (t_1 <= 5e-290) {
		tmp = t_2;
	} else if (t_1 <= 1e+196) {
		tmp = x / fma((y / t), b, (1.0 + a));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} 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)))
	t_2 = Float64(Float64(y / fma(b, y, fma(a, t, t))) * z)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -2e-304)
		tmp = Float64(fma(Float64(y / t), z, x) / Float64(1.0 + a));
	elseif (t_1 <= 5e-290)
		tmp = t_2;
	elseif (t_1 <= 1e+196)
		tmp = Float64(x / fma(Float64(y / t), b, Float64(1.0 + a)));
	elseif (t_1 <= Inf)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(y / N[(b * y + N[(a * t + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -2e-304], N[(N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision] / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-290], t$95$2, If[LessEqual[t$95$1, 1e+196], N[(x / N[(N[(y / t), $MachinePrecision] * b + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(N[(t * N[(x / y), $MachinePrecision] + z), $MachinePrecision] / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0 or -1.99999999999999994e-304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.0000000000000001e-290 or 9.9999999999999995e195 < (/.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 49.5%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 71.5

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

   5. Applied rewrites 71.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 83.3%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999994e-304

   1. Initial program 99.7%

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

   3. Taylor expanded in b around 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 84.2

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

   5. Applied rewrites 84.2%

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

   if 5.0000000000000001e-290 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999995e195

   1. Initial program 99.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   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 71.2

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

   5. Applied rewrites 71.2%

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

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

   1. Initial program 0.0%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/l/ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 15.7%

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

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 96.3

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

   7. Applied rewrites 96.3%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-304}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{1 + a}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{-290}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+196}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\frac{y}{t}, b, 1 + a\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(a, t, t\right)} \cdot z\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-304} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-222} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+154}\right)\right):\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 (- INFINITY))
     (* (/ y (fma a t t)) z)
     (if (or (<= t_1 -2e-304) (not (or (<= t_1 2e-222) (not (<= t_1 2e+154)))))
       (/ 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 <= -((double) INFINITY)) {
		tmp = (y / fma(a, t, t)) * z;
	} else if ((t_1 <= -2e-304) || !((t_1 <= 2e-222) || !(t_1 <= 2e+154))) {
		tmp = 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 <= Float64(-Inf))
		tmp = Float64(Float64(y / fma(a, t, t)) * z);
	elseif ((t_1 <= -2e-304) || !((t_1 <= 2e-222) || !(t_1 <= 2e+154)))
		tmp = Float64(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[LessEqual[t$95$1, (-Infinity)], N[(N[(y / N[(a * t + t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e-304], N[Not[Or[LessEqual[t$95$1, 2e-222], N[Not[LessEqual[t$95$1, 2e+154]], $MachinePrecision]]], $MachinePrecision]], N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], 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))) < -inf.0

   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 x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 83.0

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

   5. Applied rewrites 83.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{y}{t + a \cdot t} \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 71.1%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999994e-304 or 2.0000000000000001e-222 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000007e154

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 60.4

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

   5. Applied rewrites 60.4%

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

   if -1.99999999999999994e-304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e-222 or 2.00000000000000007e154 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 45.0%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/l/ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 62.9%

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

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 74.0

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

   7. Applied rewrites 74.0%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(a, t, t\right)} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-304} \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{-222} \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+154}\right)\right):\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{z}{\mathsf{fma}\left(a, t, t\right)}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-304} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-290} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+154}\right)\right):\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 (- INFINITY))
     (* y (/ z (fma a t t)))
     (if (or (<= t_1 -2e-304) (not (or (<= t_1 5e-290) (not (<= t_1 2e+154)))))
       (/ x (+ 1.0 a))
       (/ 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 <= -((double) INFINITY)) {
		tmp = y * (z / fma(a, t, t));
	} else if ((t_1 <= -2e-304) || !((t_1 <= 5e-290) || !(t_1 <= 2e+154))) {
		tmp = x / (1.0 + a);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(z / fma(a, t, t)));
	elseif ((t_1 <= -2e-304) || !((t_1 <= 5e-290) || !(t_1 <= 2e+154)))
		tmp = Float64(x / Float64(1.0 + a));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(z / N[(a * t + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e-304], N[Not[Or[LessEqual[t$95$1, 5e-290], N[Not[LessEqual[t$95$1, 2e+154]], $MachinePrecision]]], $MachinePrecision]], N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   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 x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 83.0

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

   5. Applied rewrites 83.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 70.9%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999994e-304 or 5.0000000000000001e-290 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000007e154

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 59.6

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

   5. Applied rewrites 59.6%

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

   if -1.99999999999999994e-304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.0000000000000001e-290 or 2.00000000000000007e154 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 42.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 71.5

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

   5. Applied rewrites 71.5%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;y \cdot \frac{z}{\mathsf{fma}\left(a, t, t\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-304} \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{-290} \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+154}\right)\right):\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y}{a \cdot t} \cdot z\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-304} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-290} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+154}\right)\right):\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 (- INFINITY))
     (* (/ y (* a t)) z)
     (if (or (<= t_1 -2e-304) (not (or (<= t_1 5e-290) (not (<= t_1 2e+154)))))
       (/ x (+ 1.0 a))
       (/ 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 <= -((double) INFINITY)) {
		tmp = (y / (a * t)) * z;
	} else if ((t_1 <= -2e-304) || !((t_1 <= 5e-290) || !(t_1 <= 2e+154))) {
		tmp = x / (1.0 + a);
	} 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 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / (a * t)) * z;
	} else if ((t_1 <= -2e-304) || !((t_1 <= 5e-290) || !(t_1 <= 2e+154))) {
		tmp = x / (1.0 + a);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (y / (a * t)) * z
	elif (t_1 <= -2e-304) or not ((t_1 <= 5e-290) or not (t_1 <= 2e+154)):
		tmp = x / (1.0 + a)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y / Float64(a * t)) * z);
	elseif ((t_1 <= -2e-304) || !((t_1 <= 5e-290) || !(t_1 <= 2e+154)))
		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)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (y / (a * t)) * z;
	elseif ((t_1 <= -2e-304) || ~(((t_1 <= 5e-290) || ~((t_1 <= 2e+154)))))
		tmp = x / (1.0 + a);
	else
		tmp = z / b;
	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] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y / N[(a * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e-304], N[Not[Or[LessEqual[t$95$1, 5e-290], N[Not[LessEqual[t$95$1, 2e+154]], $MachinePrecision]]], $MachinePrecision]], N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   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 x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 83.0

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

   5. Applied rewrites 83.0%

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

   6. Taylor expanded in a around inf

      \[\leadsto \frac{y}{a \cdot t} \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 51.4%

      \[\leadsto \frac{y}{a \cdot t} \cdot z \]

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999994e-304 or 5.0000000000000001e-290 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000007e154

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 59.6

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

   5. Applied rewrites 59.6%

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

   if -1.99999999999999994e-304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.0000000000000001e-290 or 2.00000000000000007e154 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 42.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 71.5

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

   5. Applied rewrites 71.5%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{a \cdot t} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-304} \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{-290} \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+154}\right)\right):\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := \frac{x}{1 + a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(a, t, t\right)} \cdot z\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-304}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-290}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, t\right)} \cdot z\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (/ x (+ 1.0 a))))
   (if (<= t_1 (- INFINITY))
     (* (/ y (fma a t t)) z)
     (if (<= t_1 -2e-304)
       t_2
       (if (<= t_1 5e-290)
         (* (/ y (fma b y t)) z)
         (if (<= t_1 2e+154) t_2 (/ 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 t_2 = x / (1.0 + a);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y / fma(a, t, t)) * z;
	} else if (t_1 <= -2e-304) {
		tmp = t_2;
	} else if (t_1 <= 5e-290) {
		tmp = (y / fma(b, y, t)) * z;
	} else if (t_1 <= 2e+154) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_2 = Float64(x / Float64(1.0 + a))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y / fma(a, t, t)) * z);
	elseif (t_1 <= -2e-304)
		tmp = t_2;
	elseif (t_1 <= 5e-290)
		tmp = Float64(Float64(y / fma(b, y, t)) * z);
	elseif (t_1 <= 2e+154)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y / N[(a * t + t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, -2e-304], t$95$2, If[LessEqual[t$95$1, 5e-290], N[(N[(y / N[(b * y + t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 2e+154], t$95$2, N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 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 x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 83.0

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

   5. Applied rewrites 83.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{y}{t + a \cdot t} \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 71.1%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999994e-304 or 5.0000000000000001e-290 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000007e154

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 59.6

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

   5. Applied rewrites 59.6%

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

   if -1.99999999999999994e-304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.0000000000000001e-290

   1. Initial program 63.7%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 68.3

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

   5. Applied rewrites 68.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 66.9%

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

   if 2.00000000000000007e154 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 21.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 80.3

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

   5. Applied rewrites 80.3%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(a, t, t\right)} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-304}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{-290}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, t\right)} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := \frac{x}{1 + a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(a, t, t\right)} \cdot z\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-304}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-290}:\\ \;\;\;\;y \cdot \frac{z}{\mathsf{fma}\left(b, y, t\right)}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (/ x (+ 1.0 a))))
   (if (<= t_1 (- INFINITY))
     (* (/ y (fma a t t)) z)
     (if (<= t_1 -2e-304)
       t_2
       (if (<= t_1 5e-290)
         (* y (/ z (fma b y t)))
         (if (<= t_1 2e+154) t_2 (/ 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 t_2 = x / (1.0 + a);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y / fma(a, t, t)) * z;
	} else if (t_1 <= -2e-304) {
		tmp = t_2;
	} else if (t_1 <= 5e-290) {
		tmp = y * (z / fma(b, y, t));
	} else if (t_1 <= 2e+154) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_2 = Float64(x / Float64(1.0 + a))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y / fma(a, t, t)) * z);
	elseif (t_1 <= -2e-304)
		tmp = t_2;
	elseif (t_1 <= 5e-290)
		tmp = Float64(y * Float64(z / fma(b, y, t)));
	elseif (t_1 <= 2e+154)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y / N[(a * t + t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, -2e-304], t$95$2, If[LessEqual[t$95$1, 5e-290], N[(y * N[(z / N[(b * y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+154], t$95$2, N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 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 x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 83.0

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

   5. Applied rewrites 83.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{y}{t + a \cdot t} \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 71.1%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999994e-304 or 5.0000000000000001e-290 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000007e154

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 59.6

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

   5. Applied rewrites 59.6%

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

   if -1.99999999999999994e-304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.0000000000000001e-290

   1. Initial program 63.7%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 68.3

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

   5. Applied rewrites 68.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 64.0%

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

   if 2.00000000000000007e154 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 21.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 80.3

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

   5. Applied rewrites 80.3%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(a, t, t\right)} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-304}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{-290}:\\ \;\;\;\;y \cdot \frac{z}{\mathsf{fma}\left(b, y, t\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := \frac{x}{1 + a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{z}{\mathsf{fma}\left(a, t, t\right)}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-304}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-290}:\\ \;\;\;\;y \cdot \frac{z}{\mathsf{fma}\left(b, y, t\right)}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (/ x (+ 1.0 a))))
   (if (<= t_1 (- INFINITY))
     (* y (/ z (fma a t t)))
     (if (<= t_1 -2e-304)
       t_2
       (if (<= t_1 5e-290)
         (* y (/ z (fma b y t)))
         (if (<= t_1 2e+154) t_2 (/ 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 t_2 = x / (1.0 + a);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * (z / fma(a, t, t));
	} else if (t_1 <= -2e-304) {
		tmp = t_2;
	} else if (t_1 <= 5e-290) {
		tmp = y * (z / fma(b, y, t));
	} else if (t_1 <= 2e+154) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_2 = Float64(x / Float64(1.0 + a))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(z / fma(a, t, t)));
	elseif (t_1 <= -2e-304)
		tmp = t_2;
	elseif (t_1 <= 5e-290)
		tmp = Float64(y * Float64(z / fma(b, y, t)));
	elseif (t_1 <= 2e+154)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(z / N[(a * t + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-304], t$95$2, If[LessEqual[t$95$1, 5e-290], N[(y * N[(z / N[(b * y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+154], t$95$2, N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 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 x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 83.0

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

   5. Applied rewrites 83.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 70.9%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999994e-304 or 5.0000000000000001e-290 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000007e154

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 59.6

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

   5. Applied rewrites 59.6%

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

   if -1.99999999999999994e-304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.0000000000000001e-290

   1. Initial program 63.7%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 68.3

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

   5. Applied rewrites 68.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 64.0%

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

   if 2.00000000000000007e154 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 21.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 80.3

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

   5. Applied rewrites 80.3%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;y \cdot \frac{z}{\mathsf{fma}\left(a, t, t\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-304}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{-290}:\\ \;\;\;\;y \cdot \frac{z}{\mathsf{fma}\left(b, y, t\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := \frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+196}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\frac{y}{t}, b, 1 + a\right)}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (* (/ y (fma b y (fma a t t))) z)))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 1e+196)
       (/ x (fma (/ y t) b (+ 1.0 a)))
       (if (<= t_1 INFINITY) t_2 (/ (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 t_2 = (y / fma(b, y, fma(a, t, t))) * z;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 1e+196) {
		tmp = x / fma((y / t), b, (1.0 + a));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} 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)))
	t_2 = Float64(Float64(y / fma(b, y, fma(a, t, t))) * z)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 1e+196)
		tmp = Float64(x / fma(Float64(y / t), b, Float64(1.0 + a)));
	elseif (t_1 <= Inf)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(y / N[(b * y + N[(a * t + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 1e+196], N[(x / N[(N[(y / t), $MachinePrecision] * b + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, 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))) < -inf.0 or 9.9999999999999995e195 < (/.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 29.8%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 76.0

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

   5. Applied rewrites 76.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 87.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999995e195

   1. Initial program 90.6%

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

   3. 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 68.9

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

   5. Applied rewrites 68.9%

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

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

   1. Initial program 0.0%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/l/ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 15.7%

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

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 96.3

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

   7. Applied rewrites 96.3%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+196}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\frac{y}{t}, b, 1 + a\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y}, z\right)}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 84.6% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (/ (* y b) t))) (t_2 (/ (+ x (/ (* y z) t)) t_1)))
   (if (<= t_2 (- INFINITY))
     (* (/ y (fma b y (fma a t t))) z)
     (if (<= t_2 2e+301) (/ (fma (/ z t) y x) 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 = (a + 1.0) + ((y * b) / t);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (y / fma(b, y, fma(a, t, t))) * z;
	} else if (t_2 <= 2e+301) {
		tmp = fma((z / t), y, x) / 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(a + 1.0) + Float64(Float64(y * b) / t))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(y / fma(b, y, fma(a, t, t))) * z);
	elseif (t_2 <= 2e+301)
		tmp = Float64(fma(Float64(z / t), y, x) / 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[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(y / N[(b * y + N[(a * t + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$2, 2e+301], N[(N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision] / t$95$1), $MachinePrecision], 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))) < -inf.0

   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 x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 83.0

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

   5. Applied rewrites 83.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 89.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000011e301

   1. Initial program 90.9%

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

      1. 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 87.0

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

   4. Applied rewrites 87.0%

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

   if 2.00000000000000011e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 6.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/l/ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 37.5%

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

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 88.9

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

   7. Applied rewrites 88.9%

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

4. Final simplification 87.5%

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

Alternative 15: 84.5% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 (- INFINITY))
     (* (/ y (fma b y (fma a t t))) z)
     (if (<= t_1 2e+301)
       (/ (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 t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y / fma(b, y, fma(a, t, t))) * z;
	} else if (t_1 <= 2e+301) {
		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)
	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 <= Float64(-Inf))
		tmp = Float64(Float64(y / fma(b, y, fma(a, t, t))) * z);
	elseif (t_1 <= 2e+301)
		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_] := 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, (-Infinity)], N[(N[(y / N[(b * y + N[(a * t + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 2e+301], 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 3 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 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 x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 83.0

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

   5. Applied rewrites 83.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 89.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000011e301

   1. Initial program 90.9%

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

      1. 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 87.0

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

      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 85.5

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

      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 85.5

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

   4. Applied rewrites 85.5%

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

   if 2.00000000000000011e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 6.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/l/ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 37.5%

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

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 88.9

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

   7. Applied rewrites 88.9%

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

4. Final simplification 86.3%

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

Alternative 16: 42.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a + 1 \leq -2 \cdot 10^{+65} \lor \neg \left(a + 1 \leq 5 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ a 1.0) -2e+65) (not (<= (+ a 1.0) 5e+59))) (/ x a) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a + 1.0) <= -2e+65) || !((a + 1.0) <= 5e+59)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((a + 1.0d0) <= (-2d+65)) .or. (.not. ((a + 1.0d0) <= 5d+59))) then
        tmp = x / a
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a + 1.0) <= -2e+65) || !((a + 1.0) <= 5e+59)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a + 1.0) <= -2e+65) or not ((a + 1.0) <= 5e+59):
		tmp = x / a
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a + 1.0) <= -2e+65) || !(Float64(a + 1.0) <= 5e+59))
		tmp = Float64(x / a);
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a + 1.0) <= -2e+65) || ~(((a + 1.0) <= 5e+59)))
		tmp = x / a;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a + 1.0), $MachinePrecision], -2e+65], N[Not[LessEqual[N[(a + 1.0), $MachinePrecision], 5e+59]], $MachinePrecision]], N[(x / a), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 a #s(literal 1 binary64)) < -2e65 or 4.9999999999999997e59 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 75.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   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 57.7

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

   5. Applied rewrites 57.7%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 52.5%

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

   if -2e65 < (+.f64 a #s(literal 1 binary64)) < 4.9999999999999997e59

   1. Initial program 69.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 45.2

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

   5. Applied rewrites 45.2%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -2 \cdot 10^{+65} \lor \neg \left(a + 1 \leq 5 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 39.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a + 1 \leq -2 \cdot 10^{+65} \lor \neg \left(a + 1 \leq 1.00000000000005\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(a - 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ a 1.0) -2e+65) (not (<= (+ a 1.0) 1.00000000000005)))
   (/ x a)
   (* (- x) (- a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a + 1.0) <= -2e+65) || !((a + 1.0) <= 1.00000000000005)) {
		tmp = x / a;
	} else {
		tmp = -x * (a - 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((a + 1.0d0) <= (-2d+65)) .or. (.not. ((a + 1.0d0) <= 1.00000000000005d0))) then
        tmp = x / a
    else
        tmp = -x * (a - 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a + 1.0) <= -2e+65) || !((a + 1.0) <= 1.00000000000005)) {
		tmp = x / a;
	} else {
		tmp = -x * (a - 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a + 1.0) <= -2e+65) or not ((a + 1.0) <= 1.00000000000005):
		tmp = x / a
	else:
		tmp = -x * (a - 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a + 1.0) <= -2e+65) || !(Float64(a + 1.0) <= 1.00000000000005))
		tmp = Float64(x / a);
	else
		tmp = Float64(Float64(-x) * Float64(a - 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a + 1.0) <= -2e+65) || ~(((a + 1.0) <= 1.00000000000005)))
		tmp = x / a;
	else
		tmp = -x * (a - 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a + 1.0), $MachinePrecision], -2e+65], N[Not[LessEqual[N[(a + 1.0), $MachinePrecision], 1.00000000000005]], $MachinePrecision]], N[(x / a), $MachinePrecision], N[((-x) * N[(a - 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 a #s(literal 1 binary64)) < -2e65 or 1.00000000000004996 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 75.2%

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

   3. Taylor expanded in 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 56.2

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

   5. Applied rewrites 56.2%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 50.1%

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

   if -2e65 < (+.f64 a #s(literal 1 binary64)) < 1.00000000000004996

   1. Initial program 69.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   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 32.9

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

   5. Applied rewrites 32.9%

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

   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 32.7%

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

   9. Taylor expanded in x around -inf

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

   11. Applied rewrites 32.7%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -2 \cdot 10^{+65} \lor \neg \left(a + 1 \leq 1.00000000000005\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(a - 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 54.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-132} \lor \neg \left(t \leq 7.8 \cdot 10^{-106}\right):\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.5e-132) (not (<= t 7.8e-106))) (/ 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 <= -6.5e-132) || !(t <= 7.8e-106)) {
		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 <= (-6.5d-132)) .or. (.not. (t <= 7.8d-106))) 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 <= -6.5e-132) || !(t <= 7.8e-106)) {
		tmp = x / (1.0 + a);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6.5e-132) or not (t <= 7.8e-106):
		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 <= -6.5e-132) || !(t <= 7.8e-106))
		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 <= -6.5e-132) || ~((t <= 7.8e-106)))
		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, -6.5e-132], N[Not[LessEqual[t, 7.8e-106]], $MachinePrecision]], N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.49999999999999991e-132 or 7.80000000000000019e-106 < t

   1. Initial program 84.5%

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

   3. Taylor expanded in y around 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 56.5

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

   5. Applied rewrites 56.5%

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

   if -6.49999999999999991e-132 < t < 7.80000000000000019e-106

   1. Initial program 47.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 66.0

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

   5. Applied rewrites 66.0%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-132} \lor \neg \left(t \leq 7.8 \cdot 10^{-106}\right):\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 18.8% accurate, 4.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.7%

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

3. Taylor expanded in y around 0

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

   1. lower-/.f64 N/A

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

   2. lower-+.f64 42.5

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

5. Applied rewrites 42.5%

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

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 15.8%

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

9. Taylor expanded in x around -inf

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

11. Applied rewrites 15.8%

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

12. Final simplification 15.8%

    \[\leadsto \left(-x\right) \cdot \left(a - 1\right) \]
13. Add Preprocessing

Alternative 20: 18.8% accurate, 5.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 72.7%

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

3. Taylor expanded in y around 0

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

   1. lower-/.f64 N/A

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

   2. lower-+.f64 42.5

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

5. Applied rewrites 42.5%

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

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 15.8%

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

9. Final simplification 15.8%

   \[\leadsto \mathsf{fma}\left(-x, a, x\right) \]
10. Add Preprocessing

Alternative 21: 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 72.7%

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

3. Taylor expanded in y around 0

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

   1. lower-/.f64 N/A

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

   2. lower-+.f64 42.5

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

5. Applied rewrites 42.5%

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

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 15.8%

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

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 4.1%

    \[\leadsto \left(-a\right) \cdot x \]

12. Final simplification 4.1%

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

Developer Target 1: 79.6% 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 2024337 
(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))))