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

Percentage Accurate: 74.7% → 85.4%

Time: 5.3s

Alternatives: 14

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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: 74.7% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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: 85.4% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma b (/ y t) (+ 1.0 a))))
   (if (<= (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))) 2e+304)
     (fma (/ y t) (/ z t_1) (/ x t_1))
     (+ (/ z b) (/ (* t x) (* b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(b, (y / t), (1.0 + a));
	double tmp;
	if (((x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))) <= 2e+304) {
		tmp = fma((y / t), (z / t_1), (x / t_1));
	} else {
		tmp = (z / b) + ((t * x) / (b * y));
	}
	return tmp;
}

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.9999999999999999e304

   1. Initial program 86.4%

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

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

      4. lift-/.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. div-add N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. associate-+r+ N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. associate-+r+ N/A

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

   3. Applied rewrites 86.5%

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

   if 1.9999999999999999e304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.6%

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

   2. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/r* N/A

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

      5. associate-/r* N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

   4. Applied rewrites 50.1%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-*.f64 79.2

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

   7. Applied rewrites 79.2%

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

Alternative 2: 85.3% accurate, 0.5× speedup

Math

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

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 2e+304) t_1 (+ (/ z b) (/ (* t x) (* b y))))))

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 <= 2e+304) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((t * x) / (b * y));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
    if (t_1 <= 2d+304) then
        tmp = t_1
    else
        tmp = (z / b) + ((t * x) / (b * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= 2e+304) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((t * x) / (b * y));
	}
	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 <= 2e+304:
		tmp = t_1
	else:
		tmp = (z / b) + ((t * x) / (b * y))
	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 <= 2e+304)
		tmp = t_1;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t * x) / Float64(b * y)));
	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 <= 2e+304)
		tmp = t_1;
	else
		tmp = (z / b) + ((t * x) / (b * y));
	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, 2e+304], t$95$1, N[(N[(z / b), $MachinePrecision] + N[(N[(t * x), $MachinePrecision] / N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.9999999999999999e304

   1. Initial program 86.4%

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

   if 1.9999999999999999e304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.6%

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

   2. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/r* N/A

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

      5. associate-/r* N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

   4. Applied rewrites 50.1%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-*.f64 79.2

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

   7. Applied rewrites 79.2%

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

Alternative 3: 73.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t\_2}{1 + a}\\ t_4 := \frac{t\_2}{\left(a + 1\right) + t\_1}\\ t_5 := \mathsf{fma}\left(b, \frac{y}{t}, 1 + a\right)\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;\frac{z}{t\_5} \cdot \frac{y}{t}\\ \mathbf{elif}\;t\_4 \leq -2 \cdot 10^{-249}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{t\_5}\\ \mathbf{elif}\;t\_4 \leq 5000000000:\\ \;\;\;\;\frac{t\_2}{a + t\_1}\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{b \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (/ t_2 (+ 1.0 a)))
        (t_4 (/ t_2 (+ (+ a 1.0) t_1)))
        (t_5 (fma b (/ y t) (+ 1.0 a))))
   (if (<= t_4 (- INFINITY))
     (* (/ z t_5) (/ y t))
     (if (<= t_4 -2e-249)
       t_3
       (if (<= t_4 2e-157)
         (/ x t_5)
         (if (<= t_4 5000000000.0)
           (/ t_2 (+ a t_1))
           (if (<= t_4 2e+304) t_3 (+ (/ z b) (/ (* t x) (* b y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / (1.0 + a);
	double t_4 = t_2 / ((a + 1.0) + t_1);
	double t_5 = fma(b, (y / t), (1.0 + a));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = (z / t_5) * (y / t);
	} else if (t_4 <= -2e-249) {
		tmp = t_3;
	} else if (t_4 <= 2e-157) {
		tmp = x / t_5;
	} else if (t_4 <= 5000000000.0) {
		tmp = t_2 / (a + t_1);
	} else if (t_4 <= 2e+304) {
		tmp = t_3;
	} else {
		tmp = (z / b) + ((t * x) / (b * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	t_3 = Float64(t_2 / Float64(1.0 + a))
	t_4 = Float64(t_2 / Float64(Float64(a + 1.0) + t_1))
	t_5 = fma(b, Float64(y / t), Float64(1.0 + a))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(Float64(z / t_5) * Float64(y / t));
	elseif (t_4 <= -2e-249)
		tmp = t_3;
	elseif (t_4 <= 2e-157)
		tmp = Float64(x / t_5);
	elseif (t_4 <= 5000000000.0)
		tmp = Float64(t_2 / Float64(a + t_1));
	elseif (t_4 <= 2e+304)
		tmp = t_3;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t * x) / Float64(b * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(b * N[(y / t), $MachinePrecision] + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(N[(z / t$95$5), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, -2e-249], t$95$3, If[LessEqual[t$95$4, 2e-157], N[(x / t$95$5), $MachinePrecision], If[LessEqual[t$95$4, 5000000000.0], N[(t$95$2 / N[(a + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+304], t$95$3, N[(N[(z / b), $MachinePrecision] + N[(N[(t * x), $MachinePrecision] / N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 34.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. associate-+r+ N/A

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

      7. *-commutative N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 36.9

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

   4. Applied rewrites 36.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-fma.f64 N/A

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

      7. times-frac N/A

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

      8. lower-*.f64 N/A

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

      9. lift-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. lift-/.f64 N/A

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

      13. lift-/.f64 70.4

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

   6. Applied rewrites 70.4%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -2.00000000000000011e-249 or 5e9 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.9999999999999999e304

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 76.7

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

   4. Applied rewrites 76.7%

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

   if -2.00000000000000011e-249 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.99999999999999989e-157

   1. Initial program 68.0%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 63.9

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

   4. Applied rewrites 63.9%

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

   if 1.99999999999999989e-157 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5e9

   1. Initial program 99.7%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 72.7%

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

   if 1.9999999999999999e304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.6%

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

   2. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/r* N/A

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

      5. associate-/r* N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

   4. Applied rewrites 50.1%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-*.f64 79.2

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

   7. Applied rewrites 79.2%

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

Alternative 4: 73.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{1 + a}\\ t_3 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_4 := \mathsf{fma}\left(b, \frac{y}{t}, 1 + a\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\frac{z}{t\_4} \cdot \frac{y}{t}\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-249}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 10^{-132}:\\ \;\;\;\;\frac{x}{t\_4}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{b \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t)))
        (t_2 (/ t_1 (+ 1.0 a)))
        (t_3 (/ t_1 (+ (+ a 1.0) (/ (* y b) t))))
        (t_4 (fma b (/ y t) (+ 1.0 a))))
   (if (<= t_3 (- INFINITY))
     (* (/ z t_4) (/ y t))
     (if (<= t_3 -2e-249)
       t_2
       (if (<= t_3 1e-132)
         (/ x t_4)
         (if (<= t_3 2e+304) t_2 (+ (/ z b) (/ (* t x) (* b y)))))))))

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 / (1.0 + a);
	double t_3 = t_1 / ((a + 1.0) + ((y * b) / t));
	double t_4 = fma(b, (y / t), (1.0 + a));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (z / t_4) * (y / t);
	} else if (t_3 <= -2e-249) {
		tmp = t_2;
	} else if (t_3 <= 1e-132) {
		tmp = x / t_4;
	} else if (t_3 <= 2e+304) {
		tmp = t_2;
	} else {
		tmp = (z / b) + ((t * x) / (b * y));
	}
	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(1.0 + a))
	t_3 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_4 = fma(b, Float64(y / t), Float64(1.0 + a))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(z / t_4) * Float64(y / t));
	elseif (t_3 <= -2e-249)
		tmp = t_2;
	elseif (t_3 <= 1e-132)
		tmp = Float64(x / t_4);
	elseif (t_3 <= 2e+304)
		tmp = t_2;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t * x) / Float64(b * y)));
	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[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(y / t), $MachinePrecision] + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(z / t$95$4), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -2e-249], t$95$2, If[LessEqual[t$95$3, 1e-132], N[(x / t$95$4), $MachinePrecision], If[LessEqual[t$95$3, 2e+304], t$95$2, N[(N[(z / b), $MachinePrecision] + N[(N[(t * x), $MachinePrecision] / N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 34.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. associate-+r+ N/A

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

      7. *-commutative N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 36.9

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

   4. Applied rewrites 36.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-fma.f64 N/A

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

      7. times-frac N/A

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

      8. lower-*.f64 N/A

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

      9. lift-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. lift-/.f64 N/A

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

      13. lift-/.f64 70.4

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

   6. Applied rewrites 70.4%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -2.00000000000000011e-249 or 9.9999999999999999e-133 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.9999999999999999e304

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 76.3

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

   4. Applied rewrites 76.3%

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

   if -2.00000000000000011e-249 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999999e-133

   1. Initial program 69.9%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 63.5

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

   4. Applied rewrites 63.5%

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

   if 1.9999999999999999e304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.6%

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

   2. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/r* N/A

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

      5. associate-/r* N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

   4. Applied rewrites 50.1%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-*.f64 79.2

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

   7. Applied rewrites 79.2%

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

Alternative 5: 72.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{1 + a}\\ t_3 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\frac{z \cdot y}{\mathsf{fma}\left(b, y, t \cdot \left(1 + a\right)\right)}\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-249}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 10^{-132}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(b, \frac{y}{t}, 1 + a\right)}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{b \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t)))
        (t_2 (/ t_1 (+ 1.0 a)))
        (t_3 (/ t_1 (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_3 (- INFINITY))
     (/ (* z y) (fma b y (* t (+ 1.0 a))))
     (if (<= t_3 -2e-249)
       t_2
       (if (<= t_3 1e-132)
         (/ x (fma b (/ y t) (+ 1.0 a)))
         (if (<= t_3 2e+304) t_2 (+ (/ z b) (/ (* t x) (* b y)))))))))

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 / (1.0 + a);
	double t_3 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (z * y) / fma(b, y, (t * (1.0 + a)));
	} else if (t_3 <= -2e-249) {
		tmp = t_2;
	} else if (t_3 <= 1e-132) {
		tmp = x / fma(b, (y / t), (1.0 + a));
	} else if (t_3 <= 2e+304) {
		tmp = t_2;
	} else {
		tmp = (z / b) + ((t * x) / (b * y));
	}
	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(1.0 + a))
	t_3 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(z * y) / fma(b, y, Float64(t * Float64(1.0 + a))));
	elseif (t_3 <= -2e-249)
		tmp = t_2;
	elseif (t_3 <= 1e-132)
		tmp = Float64(x / fma(b, Float64(y / t), Float64(1.0 + a)));
	elseif (t_3 <= 2e+304)
		tmp = t_2;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t * x) / Float64(b * y)));
	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[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(z * y), $MachinePrecision] / N[(b * y + N[(t * N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -2e-249], t$95$2, If[LessEqual[t$95$3, 1e-132], N[(x / N[(b * N[(y / t), $MachinePrecision] + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+304], t$95$2, N[(N[(z / b), $MachinePrecision] + N[(N[(t * x), $MachinePrecision] / N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 34.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. associate-+r+ N/A

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

      7. *-commutative N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 36.9

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

   4. Applied rewrites 36.9%

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

   5. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift-+.f64 58.9

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

   7. Applied rewrites 58.9%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -2.00000000000000011e-249 or 9.9999999999999999e-133 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.9999999999999999e304

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 76.3

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

   4. Applied rewrites 76.3%

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

   if -2.00000000000000011e-249 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999999e-133

   1. Initial program 69.9%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 63.5

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

   4. Applied rewrites 63.5%

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

   if 1.9999999999999999e304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.6%

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

   2. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/r* N/A

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

      5. associate-/r* N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

   4. Applied rewrites 50.1%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-*.f64 79.2

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

   7. Applied rewrites 79.2%

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

Alternative 6: 71.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_3 := \frac{t\_1}{1 + a}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-249}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{-132}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(b, \frac{y}{t}, 1 + a\right)}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t)))
        (t_2 (/ t_1 (+ (+ a 1.0) (/ (* y b) t))))
        (t_3 (/ t_1 (+ 1.0 a))))
   (if (<= t_2 -2e-249)
     t_3
     (if (<= t_2 1e-132)
       (/ x (fma b (/ y t) (+ 1.0 a)))
       (if (<= t_2 2e+304) t_3 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double t_3 = t_1 / (1.0 + a);
	double tmp;
	if (t_2 <= -2e-249) {
		tmp = t_3;
	} else if (t_2 <= 1e-132) {
		tmp = x / fma(b, (y / t), (1.0 + a));
	} else if (t_2 <= 2e+304) {
		tmp = t_3;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_3 = Float64(t_1 / Float64(1.0 + a))
	tmp = 0.0
	if (t_2 <= -2e-249)
		tmp = t_3;
	elseif (t_2 <= 1e-132)
		tmp = Float64(x / fma(b, Float64(y / t), Float64(1.0 + a)));
	elseif (t_2 <= 2e+304)
		tmp = t_3;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-249], t$95$3, If[LessEqual[t$95$2, 1e-132], N[(x / N[(b * N[(y / t), $MachinePrecision] + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+304], t$95$3, 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))) < -2.00000000000000011e-249 or 9.9999999999999999e-133 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.9999999999999999e304

   1. Initial program 94.0%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 71.8

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

   4. Applied rewrites 71.8%

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

   if -2.00000000000000011e-249 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999999e-133

   1. Initial program 69.9%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 63.5

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

   4. Applied rewrites 63.5%

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

   if 1.9999999999999999e304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.6%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 81.4

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

   4. Applied rewrites 81.4%

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

Alternative 7: 70.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_3 := \frac{t\_1}{1 + a}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-249}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{-132}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(b, \frac{y}{t}, 1 + a\right)}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{b \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t)))
        (t_2 (/ t_1 (+ (+ a 1.0) (/ (* y b) t))))
        (t_3 (/ t_1 (+ 1.0 a))))
   (if (<= t_2 -2e-249)
     t_3
     (if (<= t_2 1e-132)
       (/ x (fma b (/ y t) (+ 1.0 a)))
       (if (<= t_2 2e+304) t_3 (+ (/ z b) (/ (* t x) (* b y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double t_3 = t_1 / (1.0 + a);
	double tmp;
	if (t_2 <= -2e-249) {
		tmp = t_3;
	} else if (t_2 <= 1e-132) {
		tmp = x / fma(b, (y / t), (1.0 + a));
	} else if (t_2 <= 2e+304) {
		tmp = t_3;
	} else {
		tmp = (z / b) + ((t * x) / (b * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_3 = Float64(t_1 / Float64(1.0 + a))
	tmp = 0.0
	if (t_2 <= -2e-249)
		tmp = t_3;
	elseif (t_2 <= 1e-132)
		tmp = Float64(x / fma(b, Float64(y / t), Float64(1.0 + a)));
	elseif (t_2 <= 2e+304)
		tmp = t_3;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t * x) / Float64(b * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-249], t$95$3, If[LessEqual[t$95$2, 1e-132], N[(x / N[(b * N[(y / t), $MachinePrecision] + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+304], t$95$3, N[(N[(z / b), $MachinePrecision] + N[(N[(t * x), $MachinePrecision] / N[(b * y), $MachinePrecision]), $MachinePrecision]), $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))) < -2.00000000000000011e-249 or 9.9999999999999999e-133 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.9999999999999999e304

   1. Initial program 94.0%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 71.8

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

   4. Applied rewrites 71.8%

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

   if -2.00000000000000011e-249 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999999e-133

   1. Initial program 69.9%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 63.5

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

   4. Applied rewrites 63.5%

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

   if 1.9999999999999999e304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.6%

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

   2. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/r* N/A

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

      5. associate-/r* N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

   4. Applied rewrites 50.1%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-*.f64 79.2

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

   7. Applied rewrites 79.2%

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

Alternative 8: 69.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := \frac{\mathsf{fma}\left(y, \frac{z}{t}, x\right)}{1 + a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-249}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-132}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(b, \frac{y}{t}, 1 + a\right)}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 (/ (fma y (/ z t) x) (+ 1.0 a))))
   (if (<= t_1 -2e-249)
     t_2
     (if (<= t_1 1e-132)
       (/ x (fma b (/ y t) (+ 1.0 a)))
       (if (<= t_1 2e+304) 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 = fma(y, (z / t), x) / (1.0 + a);
	double tmp;
	if (t_1 <= -2e-249) {
		tmp = t_2;
	} else if (t_1 <= 1e-132) {
		tmp = x / fma(b, (y / t), (1.0 + a));
	} else if (t_1 <= 2e+304) {
		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(fma(y, Float64(z / t), x) / Float64(1.0 + a))
	tmp = 0.0
	if (t_1 <= -2e-249)
		tmp = t_2;
	elseif (t_1 <= 1e-132)
		tmp = Float64(x / fma(b, Float64(y / t), Float64(1.0 + a)));
	elseif (t_1 <= 2e+304)
		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[(N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision] / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-249], t$95$2, If[LessEqual[t$95$1, 1e-132], N[(x / N[(b * N[(y / t), $MachinePrecision] + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+304], t$95$2, 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))) < -2.00000000000000011e-249 or 9.9999999999999999e-133 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.9999999999999999e304

   1. Initial program 94.0%

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

   2. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 69.0

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

   4. Applied rewrites 69.0%

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

   if -2.00000000000000011e-249 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999999e-133

   1. Initial program 69.9%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 63.5

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

   4. Applied rewrites 63.5%

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

   if 1.9999999999999999e304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.6%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 81.4

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

   4. Applied rewrites 81.4%

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

Alternative 9: 65.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{t \cdot x}{y}}{b}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(b, \frac{y}{t}, 1 + a\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ (* t x) y)) b)))
   (if (<= y -1.05e+16)
     t_1
     (if (<= y 4.8e+45) (/ x (fma b (/ y t) (+ 1.0 a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((t * x) / y)) / b;
	double tmp;
	if (y <= -1.05e+16) {
		tmp = t_1;
	} else if (y <= 4.8e+45) {
		tmp = x / fma(b, (y / t), (1.0 + a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(Float64(t * x) / y)) / b)
	tmp = 0.0
	if (y <= -1.05e+16)
		tmp = t_1;
	elseif (y <= 4.8e+45)
		tmp = Float64(x / fma(b, Float64(y / t), Float64(1.0 + a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(N[(t * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -1.05e+16], t$95$1, If[LessEqual[y, 4.8e+45], N[(x / N[(b * N[(y / t), $MachinePrecision] + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e16 or 4.79999999999999979e45 < y

   1. Initial program 52.3%

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

   2. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/r* N/A

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

      5. associate-/r* N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

   4. Applied rewrites 45.0%

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

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift-*.f64 60.6

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

   7. Applied rewrites 60.6%

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

   if -1.05e16 < y < 4.79999999999999979e45

   1. Initial program 93.5%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 69.0

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

   4. Applied rewrites 69.0%

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

Alternative 10: 59.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{t \cdot x}{y}}{b}\\ \mathbf{if}\;y \leq -16500000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-71}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ (* t x) y)) b)))
   (if (<= y -16500000000.0) t_1 (if (<= y 6e-71) (/ x (+ 1.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((t * x) / y)) / b;
	double tmp;
	if (y <= -16500000000.0) {
		tmp = t_1;
	} else if (y <= 6e-71) {
		tmp = x / (1.0 + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + ((t * x) / y)) / b
    if (y <= (-16500000000.0d0)) then
        tmp = t_1
    else if (y <= 6d-71) then
        tmp = x / (1.0d0 + a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((t * x) / y)) / b;
	double tmp;
	if (y <= -16500000000.0) {
		tmp = t_1;
	} else if (y <= 6e-71) {
		tmp = x / (1.0 + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + ((t * x) / y)) / b
	tmp = 0
	if y <= -16500000000.0:
		tmp = t_1
	elif y <= 6e-71:
		tmp = x / (1.0 + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(Float64(t * x) / y)) / b)
	tmp = 0.0
	if (y <= -16500000000.0)
		tmp = t_1;
	elseif (y <= 6e-71)
		tmp = Float64(x / Float64(1.0 + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + ((t * x) / y)) / b;
	tmp = 0.0;
	if (y <= -16500000000.0)
		tmp = t_1;
	elseif (y <= 6e-71)
		tmp = x / (1.0 + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(N[(t * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -16500000000.0], t$95$1, If[LessEqual[y, 6e-71], N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e10 or 6.0000000000000003e-71 < y

   1. Initial program 58.3%

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

   2. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/r* N/A

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

      5. associate-/r* N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

   4. Applied rewrites 42.7%

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

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift-*.f64 56.5

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

   7. Applied rewrites 56.5%

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

   if -1.65e10 < y < 6.0000000000000003e-71

   1. Initial program 95.1%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 62.6

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

   4. Applied rewrites 62.6%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 55.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + a}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 a))))
   (if (<= t -2.8e+27) t_1 (if (<= t 7.6e-18) (/ z b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + a);
	double tmp;
	if (t <= -2.8e+27) {
		tmp = t_1;
	} else if (t <= 7.6e-18) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 + a)
    if (t <= (-2.8d+27)) then
        tmp = t_1
    else if (t <= 7.6d-18) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + a);
	double tmp;
	if (t <= -2.8e+27) {
		tmp = t_1;
	} else if (t <= 7.6e-18) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + a)
	tmp = 0
	if t <= -2.8e+27:
		tmp = t_1
	elif t <= 7.6e-18:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + a))
	tmp = 0.0
	if (t <= -2.8e+27)
		tmp = t_1;
	elseif (t <= 7.6e-18)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + a);
	tmp = 0.0;
	if (t <= -2.8e+27)
		tmp = t_1;
	elseif (t <= 7.6e-18)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+27], t$95$1, If[LessEqual[t, 7.6e-18], N[(z / b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7999999999999999e27 or 7.5999999999999996e-18 < t

   1. Initial program 81.6%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 61.5

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

   4. Applied rewrites 61.5%

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

   if -2.7999999999999999e27 < t < 7.5999999999999996e-18

   1. Initial program 68.2%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 50.3

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

   4. Applied rewrites 50.3%

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

Alternative 12: 41.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+196}:\\ \;\;\;\;\frac{x}{1}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+71}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.4e+196)
   (/ x 1.0)
   (if (<= t -1.2e+68) (/ x a) (if (<= t 8.2e+71) (/ z b) (/ x 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.4e+196) {
		tmp = x / 1.0;
	} else if (t <= -1.2e+68) {
		tmp = x / a;
	} else if (t <= 8.2e+71) {
		tmp = z / b;
	} else {
		tmp = x / 1.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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 <= (-3.4d+196)) then
        tmp = x / 1.0d0
    else if (t <= (-1.2d+68)) then
        tmp = x / a
    else if (t <= 8.2d+71) then
        tmp = z / b
    else
        tmp = x / 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.4e+196) {
		tmp = x / 1.0;
	} else if (t <= -1.2e+68) {
		tmp = x / a;
	} else if (t <= 8.2e+71) {
		tmp = z / b;
	} else {
		tmp = x / 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.4e+196:
		tmp = x / 1.0
	elif t <= -1.2e+68:
		tmp = x / a
	elif t <= 8.2e+71:
		tmp = z / b
	else:
		tmp = x / 1.0
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.4e+196)
		tmp = Float64(x / 1.0);
	elseif (t <= -1.2e+68)
		tmp = Float64(x / a);
	elseif (t <= 8.2e+71)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.4e+196)
		tmp = x / 1.0;
	elseif (t <= -1.2e+68)
		tmp = x / a;
	elseif (t <= 8.2e+71)
		tmp = z / b;
	else
		tmp = x / 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.4e+196], N[(x / 1.0), $MachinePrecision], If[LessEqual[t, -1.2e+68], N[(x / a), $MachinePrecision], If[LessEqual[t, 8.2e+71], N[(z / b), $MachinePrecision], N[(x / 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.4e196 or 8.2000000000000004e71 < t

   1. Initial program 81.3%

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

   2. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 82.9

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

   4. Applied rewrites 82.9%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 68.9%

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

   8. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 68.8

         \[\leadsto \frac{x}{a \cdot \left(1 + \frac{1}{a}\right)} \]

   10. Applied rewrites 68.8%

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

   11. Taylor expanded in a around 0

       \[\leadsto \frac{x}{1} \]
   12. Step-by-step derivation

   13. Applied rewrites 32.7%

       \[\leadsto \frac{x}{1} \]

   if -3.4e196 < t < -1.20000000000000004e68

   1. Initial program 81.0%

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

   2. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 76.0

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

   4. Applied rewrites 76.0%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 59.0%

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

   8. Taylor expanded in a around inf

      \[\leadsto \frac{x}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 34.1%

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

   if -1.20000000000000004e68 < t < 8.2000000000000004e71

   1. Initial program 70.6%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 46.7

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

   4. Applied rewrites 46.7%

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

Alternative 13: 41.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{+183}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+78}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.85e+183) (/ x a) (if (<= a 1.75e+78) (/ z b) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.85e+183) {
		tmp = x / a;
	} else if (a <= 1.75e+78) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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 <= (-1.85d+183)) then
        tmp = x / a
    else if (a <= 1.75d+78) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.85e+183) {
		tmp = x / a;
	} else if (a <= 1.75e+78) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.85e+183:
		tmp = x / a
	elif a <= 1.75e+78:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.85e+183)
		tmp = Float64(x / a);
	elseif (a <= 1.75e+78)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.85e+183)
		tmp = x / a;
	elseif (a <= 1.75e+78)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.85e+183], N[(x / a), $MachinePrecision], If[LessEqual[a, 1.75e+78], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8500000000000001e183 or 1.7500000000000001e78 < a

   1. Initial program 74.0%

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

   2. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 66.8

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

   4. Applied rewrites 66.8%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 52.8%

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

   8. Taylor expanded in a around inf

      \[\leadsto \frac{x}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 52.8%

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

   if -1.8500000000000001e183 < a < 1.7500000000000001e78

   1. Initial program 75.0%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 37.3

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

   4. Applied rewrites 37.3%

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

Alternative 14: 34.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \frac{z}{b} \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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 = z / b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.7%

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

2. Taylor expanded in y around inf

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

   1. lower-/.f64 34.2

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

4. Applied rewrites 34.2%

   \[\leadsto \color{blue}{\frac{z}{b}} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025101 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64
  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))