AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1

Percentage Accurate: 60.7% → 97.5%

Time: 7.5s

Alternatives: 17

Speedup: 0.4×

Specification

Math

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

FPCore

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

C

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

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 + y) * a)) - (y * b)) / ((x + t) + y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + y) * a)) - (y * b)) / ((x + t) + y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := \frac{y + x}{t\_1}\\ t_3 := t + \left(x + y\right)\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+74} \lor \neg \left(a \leq 30000000000\right):\\ \;\;\;\;\left(\left(\frac{t + y}{t\_1} + \frac{z}{a} \cdot t\_2\right) - \frac{b}{a} \cdot \frac{y}{t\_1}\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, z, b \cdot \mathsf{fma}\left(-1, \frac{y}{t\_3}, \frac{a}{b} \cdot \frac{t + y}{t\_3}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t)) (t_2 (/ (+ y x) t_1)) (t_3 (+ t (+ x y))))
   (if (or (<= a -1.25e+74) (not (<= a 30000000000.0)))
     (* (- (+ (/ (+ t y) t_1) (* (/ z a) t_2)) (* (/ b a) (/ y t_1))) a)
     (fma t_2 z (* b (fma -1.0 (/ y t_3) (* (/ a b) (/ (+ t y) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) + t;
	double t_2 = (y + x) / t_1;
	double t_3 = t + (x + y);
	double tmp;
	if ((a <= -1.25e+74) || !(a <= 30000000000.0)) {
		tmp = ((((t + y) / t_1) + ((z / a) * t_2)) - ((b / a) * (y / t_1))) * a;
	} else {
		tmp = fma(t_2, z, (b * fma(-1.0, (y / t_3), ((a / b) * ((t + y) / t_3)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) + t)
	t_2 = Float64(Float64(y + x) / t_1)
	t_3 = Float64(t + Float64(x + y))
	tmp = 0.0
	if ((a <= -1.25e+74) || !(a <= 30000000000.0))
		tmp = Float64(Float64(Float64(Float64(Float64(t + y) / t_1) + Float64(Float64(z / a) * t_2)) - Float64(Float64(b / a) * Float64(y / t_1))) * a);
	else
		tmp = fma(t_2, z, Float64(b * fma(-1.0, Float64(y / t_3), Float64(Float64(a / b) * Float64(Float64(t + y) / t_3)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -1.25e+74], N[Not[LessEqual[a, 30000000000.0]], $MachinePrecision]], N[(N[(N[(N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(N[(b / a), $MachinePrecision] * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], N[(t$95$2 * z + N[(b * N[(-1.0 * N[(y / t$95$3), $MachinePrecision] + N[(N[(a / b), $MachinePrecision] * N[(N[(t + y), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.24999999999999991e74 or 3e10 < a

   1. Initial program 43.6%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 99.0%

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

   if -1.24999999999999991e74 < a < 3e10

   1. Initial program 76.4%

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

   4. Applied rewrites 91.0%

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

   5. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. times-frac N/A

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

      7. div-add-rev N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. div-add-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lift-+.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. lower-+.f64 96.6

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

   7. Applied rewrites 96.6%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+74} \lor \neg \left(a \leq 30000000000\right):\\ \;\;\;\;\left(\left(\frac{t + y}{\left(y + x\right) + t} + \frac{z}{a} \cdot \frac{y + x}{\left(y + x\right) + t}\right) - \frac{b}{a} \cdot \frac{y}{\left(y + x\right) + t}\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y + x}{\left(y + x\right) + t}, z, b \cdot \mathsf{fma}\left(-1, \frac{y}{t + \left(x + y\right)}, \frac{a}{b} \cdot \frac{t + y}{t + \left(x + y\right)}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-b\right) \cdot y\\ t_2 := \left(x + t\right) + y\\ t_3 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_2}\\ t_4 := \left(a + z\right) - b\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+194}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{+42}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, t\_1\right)}{t\_2}\\ \mathbf{elif}\;t\_3 \leq 10^{-7}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, \left(y + x\right) \cdot z\right)}{t\_2}\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{+246}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, t\_1\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b) y))
        (t_2 (+ (+ x t) y))
        (t_3 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_2))
        (t_4 (- (+ a z) b)))
   (if (<= t_3 -5e+194)
     t_4
     (if (<= t_3 -2e+42)
       (/ (fma (+ y x) z t_1) t_2)
       (if (<= t_3 1e-7)
         (/ (fma (+ t y) a (* (+ y x) z)) t_2)
         (if (<= t_3 4e+246) (/ (fma (+ t y) a t_1) t_2) t_4))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -b * y;
	double t_2 = (x + t) + y;
	double t_3 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_2;
	double t_4 = (a + z) - b;
	double tmp;
	if (t_3 <= -5e+194) {
		tmp = t_4;
	} else if (t_3 <= -2e+42) {
		tmp = fma((y + x), z, t_1) / t_2;
	} else if (t_3 <= 1e-7) {
		tmp = fma((t + y), a, ((y + x) * z)) / t_2;
	} else if (t_3 <= 4e+246) {
		tmp = fma((t + y), a, t_1) / t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-b) * y)
	t_2 = Float64(Float64(x + t) + y)
	t_3 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_2)
	t_4 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (t_3 <= -5e+194)
		tmp = t_4;
	elseif (t_3 <= -2e+42)
		tmp = Float64(fma(Float64(y + x), z, t_1) / t_2);
	elseif (t_3 <= 1e-7)
		tmp = Float64(fma(Float64(t + y), a, Float64(Float64(y + x) * z)) / t_2);
	elseif (t_3 <= 4e+246)
		tmp = Float64(fma(Float64(t + y), a, t_1) / t_2);
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-b) * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+194], t$95$4, If[LessEqual[t$95$3, -2e+42], N[(N[(N[(y + x), $MachinePrecision] * z + t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$3, 1e-7], N[(N[(N[(t + y), $MachinePrecision] * a + N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$3, 4e+246], N[(N[(N[(t + y), $MachinePrecision] * a + t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$4]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -4.99999999999999989e194 or 4.00000000000000027e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 16.8%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \left(a + z\right) - \color{blue}{b} \]

      2. lower-+.f64 82.0

         \[\leadsto \left(a + z\right) - b \]

   5. Applied rewrites 82.0%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -4.99999999999999989e194 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -2.00000000000000009e42

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. *-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. mul-1-neg N/A

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

      10. associate-*r* N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lower-neg.f64 87.4

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

   5. Applied rewrites 87.4%

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

   if -2.00000000000000009e42 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.9999999999999995e-8

   1. Initial program 99.6%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 88.5

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

   5. Applied rewrites 88.5%

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

   if 9.9999999999999995e-8 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.00000000000000027e246

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. *-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 78.4

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

   5. Applied rewrites 78.4%

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

Alternative 3: 68.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-b\right) \cdot y\\ t_2 := \left(x + t\right) + y\\ t_3 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_2}\\ t_4 := \left(a + z\right) - b\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+194}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{+42}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, t\_1\right)}{t\_2}\\ \mathbf{elif}\;t\_3 \leq 10^{-7}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, a \cdot t\right)}{t\_2}\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{+246}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, t\_1\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b) y))
        (t_2 (+ (+ x t) y))
        (t_3 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_2))
        (t_4 (- (+ a z) b)))
   (if (<= t_3 -5e+194)
     t_4
     (if (<= t_3 -2e+42)
       (/ (fma (+ y x) z t_1) t_2)
       (if (<= t_3 1e-7)
         (/ (fma (+ y x) z (* a t)) t_2)
         (if (<= t_3 4e+246) (/ (fma (+ t y) a t_1) t_2) t_4))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -b * y;
	double t_2 = (x + t) + y;
	double t_3 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_2;
	double t_4 = (a + z) - b;
	double tmp;
	if (t_3 <= -5e+194) {
		tmp = t_4;
	} else if (t_3 <= -2e+42) {
		tmp = fma((y + x), z, t_1) / t_2;
	} else if (t_3 <= 1e-7) {
		tmp = fma((y + x), z, (a * t)) / t_2;
	} else if (t_3 <= 4e+246) {
		tmp = fma((t + y), a, t_1) / t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-b) * y)
	t_2 = Float64(Float64(x + t) + y)
	t_3 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_2)
	t_4 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (t_3 <= -5e+194)
		tmp = t_4;
	elseif (t_3 <= -2e+42)
		tmp = Float64(fma(Float64(y + x), z, t_1) / t_2);
	elseif (t_3 <= 1e-7)
		tmp = Float64(fma(Float64(y + x), z, Float64(a * t)) / t_2);
	elseif (t_3 <= 4e+246)
		tmp = Float64(fma(Float64(t + y), a, t_1) / t_2);
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-b) * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+194], t$95$4, If[LessEqual[t$95$3, -2e+42], N[(N[(N[(y + x), $MachinePrecision] * z + t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$3, 1e-7], N[(N[(N[(y + x), $MachinePrecision] * z + N[(a * t), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$3, 4e+246], N[(N[(N[(t + y), $MachinePrecision] * a + t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$4]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -4.99999999999999989e194 or 4.00000000000000027e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 16.8%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \left(a + z\right) - \color{blue}{b} \]

      2. lower-+.f64 82.0

         \[\leadsto \left(a + z\right) - b \]

   5. Applied rewrites 82.0%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -4.99999999999999989e194 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -2.00000000000000009e42

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. *-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. mul-1-neg N/A

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

      10. associate-*r* N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lower-neg.f64 87.4

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

   5. Applied rewrites 87.4%

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

   if -2.00000000000000009e42 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.9999999999999995e-8

   1. Initial program 99.6%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate--l+ N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. *-commutative N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. mul-1-neg N/A

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

      19. lower-fma.f64 N/A

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

      20. lift-+.f64 N/A

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

      21. mul-1-neg N/A

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

      22. associate-*r* N/A

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

      23. lower-*.f64 N/A

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

      24. mul-1-neg N/A

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

      25. lower-neg.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 81.7

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

   7. Applied rewrites 81.7%

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

   if 9.9999999999999995e-8 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.00000000000000027e246

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. *-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 78.4

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

   5. Applied rewrites 78.4%

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

Alternative 4: 68.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \left(a + z\right) - b\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+166}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{-7}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, a \cdot t\right)}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+246}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, \left(-b\right) \cdot y\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_1))
        (t_3 (- (+ a z) b)))
   (if (<= t_2 -5e+166)
     t_3
     (if (<= t_2 1e-7)
       (/ (fma (+ y x) z (* a t)) t_1)
       (if (<= t_2 4e+246) (/ (fma (+ t y) a (* (- b) y)) t_1) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1;
	double t_3 = (a + z) - b;
	double tmp;
	if (t_2 <= -5e+166) {
		tmp = t_3;
	} else if (t_2 <= 1e-7) {
		tmp = fma((y + x), z, (a * t)) / t_1;
	} else if (t_2 <= 4e+246) {
		tmp = fma((t + y), a, (-b * y)) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (t_2 <= -5e+166)
		tmp = t_3;
	elseif (t_2 <= 1e-7)
		tmp = Float64(fma(Float64(y + x), z, Float64(a * t)) / t_1);
	elseif (t_2 <= 4e+246)
		tmp = Float64(fma(Float64(t + y), a, Float64(Float64(-b) * y)) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+166], t$95$3, If[LessEqual[t$95$2, 1e-7], N[(N[(N[(y + x), $MachinePrecision] * z + N[(a * t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 4e+246], N[(N[(N[(t + y), $MachinePrecision] * a + N[((-b) * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -5.0000000000000002e166 or 4.00000000000000027e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 20.8%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \left(a + z\right) - \color{blue}{b} \]

      2. lower-+.f64 81.0

         \[\leadsto \left(a + z\right) - b \]

   5. Applied rewrites 81.0%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -5.0000000000000002e166 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.9999999999999995e-8

   1. Initial program 99.6%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate--l+ N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. *-commutative N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. mul-1-neg N/A

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

      19. lower-fma.f64 N/A

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

      20. lift-+.f64 N/A

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

      21. mul-1-neg N/A

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

      22. associate-*r* N/A

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

      23. lower-*.f64 N/A

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

      24. mul-1-neg N/A

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

      25. lower-neg.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 76.4

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

   7. Applied rewrites 76.4%

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

   if 9.9999999999999995e-8 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.00000000000000027e246

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. *-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 78.4

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

   5. Applied rewrites 78.4%

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

Alternative 5: 65.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \left(a + z\right) - b\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+194}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+112}:\\ \;\;\;\;\frac{t\_3 \cdot y}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 10^{+93}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_1))
        (t_3 (- (+ a z) b)))
   (if (<= t_2 -1e+194)
     t_3
     (if (<= t_2 -5e+112)
       (/ (* t_3 y) t_1)
       (if (<= t_2 1e+93) (/ (fma a t (* z x)) (+ t x)) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1;
	double t_3 = (a + z) - b;
	double tmp;
	if (t_2 <= -1e+194) {
		tmp = t_3;
	} else if (t_2 <= -5e+112) {
		tmp = (t_3 * y) / t_1;
	} else if (t_2 <= 1e+93) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (t_2 <= -1e+194)
		tmp = t_3;
	elseif (t_2 <= -5e+112)
		tmp = Float64(Float64(t_3 * y) / t_1);
	elseif (t_2 <= 1e+93)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+194], t$95$3, If[LessEqual[t$95$2, -5e+112], N[(N[(t$95$3 * y), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 1e+93], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.99999999999999945e193 or 1.00000000000000004e93 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 29.7%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \left(a + z\right) - \color{blue}{b} \]

      2. lower-+.f64 79.9

         \[\leadsto \left(a + z\right) - b \]

   5. Applied rewrites 79.9%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -9.99999999999999945e193 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -5e112

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 79.4

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

   5. Applied rewrites 79.4%

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

   if -5e112 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000004e93

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 70.2

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

   5. Applied rewrites 70.2%

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

Alternative 6: 87.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+283} \lor \neg \left(t\_2 \leq 4 \cdot 10^{+246}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t + y}{t\_1}, a, \frac{\mathsf{fma}\left(y + x, z, \left(-b\right) \cdot y\right)}{t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_2 -1e+283) (not (<= t_2 4e+246)))
     (- (+ a z) b)
     (fma (/ (+ t y) t_1) a (/ (fma (+ y x) z (* (- b) y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) + t;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_2 <= -1e+283) || !(t_2 <= 4e+246)) {
		tmp = (a + z) - b;
	} else {
		tmp = fma(((t + y) / t_1), a, (fma((y + x), z, (-b * y)) / t_1));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) + t)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_2 <= -1e+283) || !(t_2 <= 4e+246))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = fma(Float64(Float64(t + y) / t_1), a, Float64(fma(Float64(y + x), z, Float64(Float64(-b) * y)) / t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -1e+283], N[Not[LessEqual[t$95$2, 4e+246]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision] * a + N[(N[(N[(y + x), $MachinePrecision] * z + N[((-b) * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.99999999999999955e282 or 4.00000000000000027e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 9.2%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \left(a + z\right) - \color{blue}{b} \]

      2. lower-+.f64 82.7

         \[\leadsto \left(a + z\right) - b \]

   5. Applied rewrites 82.7%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -9.99999999999999955e282 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.00000000000000027e246

   1. Initial program 99.6%

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

   4. Applied rewrites 99.7%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -1 \cdot 10^{+283} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 4 \cdot 10^{+246}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t + y}{\left(y + x\right) + t}, a, \frac{\mathsf{fma}\left(y + x, z, \left(-b\right) \cdot y\right)}{\left(y + x\right) + t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+283} \lor \neg \left(t\_2 \leq 4 \cdot 10^{+246}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, \mathsf{fma}\left(t + y, a, \left(-b\right) \cdot y\right)\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_1)))
   (if (or (<= t_2 -1e+283) (not (<= t_2 4e+246)))
     (- (+ a z) b)
     (/ (fma (+ y x) z (fma (+ t y) a (* (- b) y))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -1e+283) || !(t_2 <= 4e+246)) {
		tmp = (a + z) - b;
	} else {
		tmp = fma((y + x), z, fma((t + y), a, (-b * y))) / t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= -1e+283) || !(t_2 <= 4e+246))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(fma(Float64(y + x), z, fma(Float64(t + y), a, Float64(Float64(-b) * y))) / t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -1e+283], N[Not[LessEqual[t$95$2, 4e+246]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(y + x), $MachinePrecision] * z + N[(N[(t + y), $MachinePrecision] * a + N[((-b) * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.99999999999999955e282 or 4.00000000000000027e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 9.2%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \left(a + z\right) - \color{blue}{b} \]

      2. lower-+.f64 82.7

         \[\leadsto \left(a + z\right) - b \]

   5. Applied rewrites 82.7%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -9.99999999999999955e282 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.00000000000000027e246

   1. Initial program 99.6%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate--l+ N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. *-commutative N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. mul-1-neg N/A

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

      19. lower-fma.f64 N/A

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

      20. lift-+.f64 N/A

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

      21. mul-1-neg N/A

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

      22. associate-*r* N/A

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

      23. lower-*.f64 N/A

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

      24. mul-1-neg N/A

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

      25. lower-neg.f64 99.7

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

   4. Applied rewrites 99.7%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -1 \cdot 10^{+283} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 4 \cdot 10^{+246}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, \mathsf{fma}\left(t + y, a, \left(-b\right) \cdot y\right)\right)}{\left(x + t\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+166} \lor \neg \left(t\_2 \leq 10^{+93}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, a \cdot t\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_1)))
   (if (or (<= t_2 -5e+166) (not (<= t_2 1e+93)))
     (- (+ a z) b)
     (/ (fma (+ y x) z (* a t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -5e+166) || !(t_2 <= 1e+93)) {
		tmp = (a + z) - b;
	} else {
		tmp = fma((y + x), z, (a * t)) / t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= -5e+166) || !(t_2 <= 1e+93))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(fma(Float64(y + x), z, Float64(a * t)) / t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -5e+166], N[Not[LessEqual[t$95$2, 1e+93]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(y + x), $MachinePrecision] * z + N[(a * t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -5.0000000000000002e166 or 1.00000000000000004e93 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 32.1%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \left(a + z\right) - \color{blue}{b} \]

      2. lower-+.f64 79.0

         \[\leadsto \left(a + z\right) - b \]

   5. Applied rewrites 79.0%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -5.0000000000000002e166 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000004e93

   1. Initial program 99.6%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate--l+ N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. *-commutative N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. mul-1-neg N/A

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

      19. lower-fma.f64 N/A

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

      20. lift-+.f64 N/A

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

      21. mul-1-neg N/A

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

      22. associate-*r* N/A

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

      23. lower-*.f64 N/A

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

      24. mul-1-neg N/A

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

      25. lower-neg.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 73.7

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

   7. Applied rewrites 73.7%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{+166} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10^{+93}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, a \cdot t\right)}{\left(x + t\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+112} \lor \neg \left(t\_1 \leq 10^{+93}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_1 -5e+112) (not (<= t_1 1e+93)))
     (- (+ a z) b)
     (/ (fma a t (* z x)) (+ t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -5e+112) || !(t_1 <= 1e+93)) {
		tmp = (a + z) - b;
	} else {
		tmp = fma(a, t, (z * x)) / (t + x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_1 <= -5e+112) || !(t_1 <= 1e+93))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+112], N[Not[LessEqual[t$95$1, 1e+93]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -5e112 or 1.00000000000000004e93 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 36.0%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \left(a + z\right) - \color{blue}{b} \]

      2. lower-+.f64 77.1

         \[\leadsto \left(a + z\right) - b \]

   5. Applied rewrites 77.1%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -5e112 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000004e93

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 70.2

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

   5. Applied rewrites 70.2%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{+112} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10^{+93}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+166} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+50}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_1 -5e+166) (not (<= t_1 2e+50)))
     (- (+ a z) b)
     (* z (/ (+ x y) (+ t (+ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -5e+166) || !(t_1 <= 2e+50)) {
		tmp = (a + z) - b;
	} else {
		tmp = z * ((x + y) / (t + (x + 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 + y) * a)) - (y * b)) / ((x + t) + y)
    if ((t_1 <= (-5d+166)) .or. (.not. (t_1 <= 2d+50))) then
        tmp = (a + z) - b
    else
        tmp = z * ((x + y) / (t + (x + 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 + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -5e+166) || !(t_1 <= 2e+50)) {
		tmp = (a + z) - b;
	} else {
		tmp = z * ((x + y) / (t + (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
	tmp = 0
	if (t_1 <= -5e+166) or not (t_1 <= 2e+50):
		tmp = (a + z) - b
	else:
		tmp = z * ((x + y) / (t + (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_1 <= -5e+166) || !(t_1 <= 2e+50))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(t + Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	tmp = 0.0;
	if ((t_1 <= -5e+166) || ~((t_1 <= 2e+50)))
		tmp = (a + z) - b;
	else
		tmp = z * ((x + y) / (t + (x + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+166], N[Not[LessEqual[t$95$1, 2e+50]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(z * N[(N[(x + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -5.0000000000000002e166 or 2.0000000000000002e50 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 36.5%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \left(a + z\right) - \color{blue}{b} \]

      2. lower-+.f64 76.0

         \[\leadsto \left(a + z\right) - b \]

   5. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -5.0000000000000002e166 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000002e50

   1. Initial program 99.6%

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

   4. Applied rewrites 99.1%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. div-add-rev N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-+.f64 46.7

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

   7. Applied rewrites 46.7%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{+166} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 2 \cdot 10^{+50}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 92.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := t + \left(x + y\right)\\ t_3 := \frac{y + x}{t\_1}\\ \mathbf{if}\;b \leq -7 \cdot 10^{-6} \lor \neg \left(b \leq 8.2 \cdot 10^{-96}\right):\\ \;\;\;\;\mathsf{fma}\left(t\_3, z, b \cdot \mathsf{fma}\left(-1, \frac{y}{t\_2}, \frac{a}{b} \cdot \frac{t + y}{t\_2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{t + y}{t\_1} + \frac{z}{a} \cdot t\_3\right) - \frac{b \cdot y}{a \cdot t\_1}\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t)) (t_2 (+ t (+ x y))) (t_3 (/ (+ y x) t_1)))
   (if (or (<= b -7e-6) (not (<= b 8.2e-96)))
     (fma t_3 z (* b (fma -1.0 (/ y t_2) (* (/ a b) (/ (+ t y) t_2)))))
     (* (- (+ (/ (+ t y) t_1) (* (/ z a) t_3)) (/ (* b y) (* a t_1))) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) + t;
	double t_2 = t + (x + y);
	double t_3 = (y + x) / t_1;
	double tmp;
	if ((b <= -7e-6) || !(b <= 8.2e-96)) {
		tmp = fma(t_3, z, (b * fma(-1.0, (y / t_2), ((a / b) * ((t + y) / t_2)))));
	} else {
		tmp = ((((t + y) / t_1) + ((z / a) * t_3)) - ((b * y) / (a * t_1))) * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) + t)
	t_2 = Float64(t + Float64(x + y))
	t_3 = Float64(Float64(y + x) / t_1)
	tmp = 0.0
	if ((b <= -7e-6) || !(b <= 8.2e-96))
		tmp = fma(t_3, z, Float64(b * fma(-1.0, Float64(y / t_2), Float64(Float64(a / b) * Float64(Float64(t + y) / t_2)))));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(t + y) / t_1) + Float64(Float64(z / a) * t_3)) - Float64(Float64(b * y) / Float64(a * t_1))) * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[b, -7e-6], N[Not[LessEqual[b, 8.2e-96]], $MachinePrecision]], N[(t$95$3 * z + N[(b * N[(-1.0 * N[(y / t$95$2), $MachinePrecision] + N[(N[(a / b), $MachinePrecision] * N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(N[(b * y), $MachinePrecision] / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.99999999999999989e-6 or 8.20000000000000048e-96 < b

   1. Initial program 63.6%

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

   4. Applied rewrites 71.8%

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

   5. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. times-frac N/A

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

      7. div-add-rev N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. div-add-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lift-+.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. lower-+.f64 96.2

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

   7. Applied rewrites 96.2%

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

   if -6.99999999999999989e-6 < b < 8.20000000000000048e-96

   1. Initial program 57.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 89.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. frac-times N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. lift-+.f64 89.6

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

   7. Applied rewrites 89.6%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{-6} \lor \neg \left(b \leq 8.2 \cdot 10^{-96}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y + x}{\left(y + x\right) + t}, z, b \cdot \mathsf{fma}\left(-1, \frac{y}{t + \left(x + y\right)}, \frac{a}{b} \cdot \frac{t + y}{t + \left(x + y\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{t + y}{\left(y + x\right) + t} + \frac{z}{a} \cdot \frac{y + x}{\left(y + x\right) + t}\right) - \frac{b \cdot y}{a \cdot \left(\left(y + x\right) + t\right)}\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 89.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \frac{y + x}{\left(y + x\right) + t}\\ \mathbf{if}\;b \leq -2 \cdot 10^{-30} \lor \neg \left(b \leq 6.3 \cdot 10^{-96}\right):\\ \;\;\;\;\mathsf{fma}\left(t\_2, z, b \cdot \mathsf{fma}\left(-1, \frac{y}{t\_1}, \frac{a}{b} \cdot \frac{t + y}{t\_1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, z, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))) (t_2 (/ (+ y x) (+ (+ y x) t))))
   (if (or (<= b -2e-30) (not (<= b 6.3e-96)))
     (fma t_2 z (* b (fma -1.0 (/ y t_1) (* (/ a b) (/ (+ t y) t_1)))))
     (fma t_2 z a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = (y + x) / ((y + x) + t);
	double tmp;
	if ((b <= -2e-30) || !(b <= 6.3e-96)) {
		tmp = fma(t_2, z, (b * fma(-1.0, (y / t_1), ((a / b) * ((t + y) / t_1)))));
	} else {
		tmp = fma(t_2, z, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(Float64(y + x) / Float64(Float64(y + x) + t))
	tmp = 0.0
	if ((b <= -2e-30) || !(b <= 6.3e-96))
		tmp = fma(t_2, z, Float64(b * fma(-1.0, Float64(y / t_1), Float64(Float64(a / b) * Float64(Float64(t + y) / t_1)))));
	else
		tmp = fma(t_2, z, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + x), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -2e-30], N[Not[LessEqual[b, 6.3e-96]], $MachinePrecision]], N[(t$95$2 * z + N[(b * N[(-1.0 * N[(y / t$95$1), $MachinePrecision] + N[(N[(a / b), $MachinePrecision] * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 * z + a), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if b < -2e-30 or 6.2999999999999996e-96 < b

   1. Initial program 63.3%

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

   4. Applied rewrites 71.3%

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

   5. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. times-frac N/A

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

      7. div-add-rev N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. div-add-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lift-+.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. lower-+.f64 96.3

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

   7. Applied rewrites 96.3%

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

   if -2e-30 < b < 6.2999999999999996e-96

   1. Initial program 58.0%

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

   4. Applied rewrites 71.4%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 87.2%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-30} \lor \neg \left(b \leq 6.3 \cdot 10^{-96}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y + x}{\left(y + x\right) + t}, z, b \cdot \mathsf{fma}\left(-1, \frac{y}{t + \left(x + y\right)}, \frac{a}{b} \cdot \frac{t + y}{t + \left(x + y\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y + x}{\left(y + x\right) + t}, z, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+134} \lor \neg \left(t \leq 4.3 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{t + y}{t + \left(x + y\right)} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.7e+134) (not (<= t 4.3e+39)))
   (* (/ (+ t y) (+ t (+ x y))) a)
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.7e+134) || !(t <= 4.3e+39)) {
		tmp = ((t + y) / (t + (x + y))) * a;
	} else {
		tmp = (a + z) - b;
	}
	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 <= (-2.7d+134)) .or. (.not. (t <= 4.3d+39))) then
        tmp = ((t + y) / (t + (x + y))) * a
    else
        tmp = (a + z) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.7e+134) || !(t <= 4.3e+39)) {
		tmp = ((t + y) / (t + (x + y))) * a;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.7e+134) or not (t <= 4.3e+39):
		tmp = ((t + y) / (t + (x + y))) * a
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.7e+134) || !(t <= 4.3e+39))
		tmp = Float64(Float64(Float64(t + y) / Float64(t + Float64(x + y))) * a);
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.7e+134) || ~((t <= 4.3e+39)))
		tmp = ((t + y) / (t + (x + y))) * a;
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.7e+134], N[Not[LessEqual[t, 4.3e+39]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7e134 or 4.3e39 < t

   1. Initial program 50.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 77.6%

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

   6. Taylor expanded in a around inf

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

      1. div-add-rev N/A

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

      2. lower-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 67.5

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

   8. Applied rewrites 67.5%

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

   if -2.7e134 < t < 4.3e39

   1. Initial program 66.1%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \left(a + z\right) - \color{blue}{b} \]

      2. lower-+.f64 64.2

         \[\leadsto \left(a + z\right) - b \]

   5. Applied rewrites 64.2%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+134} \lor \neg \left(t \leq 4.3 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{t + y}{t + \left(x + y\right)} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+55}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+31}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.15e+55) a (if (<= t 5.2e+31) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.15e+55) {
		tmp = a;
	} else if (t <= 5.2e+31) {
		tmp = z;
	} else {
		tmp = 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 (t <= (-2.15d+55)) then
        tmp = a
    else if (t <= 5.2d+31) then
        tmp = z
    else
        tmp = 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 (t <= -2.15e+55) {
		tmp = a;
	} else if (t <= 5.2e+31) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.15e+55:
		tmp = a
	elif t <= 5.2e+31:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.15e+55)
		tmp = a;
	elseif (t <= 5.2e+31)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.15e+55)
		tmp = a;
	elseif (t <= 5.2e+31)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.15e+55], a, If[LessEqual[t, 5.2e+31], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1499999999999999e55 or 5.2e31 < t

   1. Initial program 52.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 59.0%

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

   if -2.1499999999999999e55 < t < 5.2e31

   1. Initial program 66.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 47.4%

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

Alternative 15: 56.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.8 \cdot 10^{+125}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x 3.8e+125) (- (+ a z) b) z))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 3.8e+125) {
		tmp = (a + z) - b;
	} else {
		tmp = z;
	}
	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 (x <= 3.8d+125) then
        tmp = (a + z) - b
    else
        tmp = z
    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 (x <= 3.8e+125) {
		tmp = (a + z) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 3.8e+125:
		tmp = (a + z) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 3.8e+125)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 3.8e+125)
		tmp = (a + z) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 3.8e+125], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < 3.80000000000000002e125

   1. Initial program 60.6%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \left(a + z\right) - \color{blue}{b} \]

      2. lower-+.f64 60.8

         \[\leadsto \left(a + z\right) - b \]

   5. Applied rewrites 60.8%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if 3.80000000000000002e125 < x

   1. Initial program 64.3%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 70.4%

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

Alternative 16: 51.9% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.12 \cdot 10^{+211}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x 1.12e+211) (+ a z) z))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.12e+211) {
		tmp = a + z;
	} else {
		tmp = z;
	}
	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 (x <= 1.12d+211) then
        tmp = a + z
    else
        tmp = z
    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 (x <= 1.12e+211) {
		tmp = a + z;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1.12e+211:
		tmp = a + z
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1.12e+211)
		tmp = Float64(a + z);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 1.12e+211)
		tmp = a + z;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1.12e+211], N[(a + z), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < 1.1200000000000001e211

   1. Initial program 61.2%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \left(a + z\right) - \color{blue}{b} \]

      2. lower-+.f64 60.1

         \[\leadsto \left(a + z\right) - b \]

   5. Applied rewrites 60.1%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   6. Taylor expanded in b around 0

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

      1. lift-+.f64 55.8

         \[\leadsto a + z \]

   8. Applied rewrites 55.8%

      \[\leadsto a + \color{blue}{z} \]

   if 1.1200000000000001e211 < x

   1. Initial program 60.6%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 71.4%

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

Alternative 17: 32.2% accurate, 45.0× speedup

Math

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

FPCore

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

C

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

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 = a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.1%

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

3. Taylor expanded in t around inf

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

5. Applied rewrites 35.3%

   \[\leadsto \color{blue}{a} \]
6. Add Preprocessing

Developer Target 1: 82.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\\ t_3 := \frac{t\_2}{t\_1}\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;t\_3 < -3.5813117084150564 \cdot 10^{+153}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 < 1.2285964308315609 \cdot 10^{+82}:\\ \;\;\;\;\frac{1}{\frac{t\_1}{t\_2}}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
        (t_3 (/ t_2 t_1))
        (t_4 (- (+ z a) b)))
   (if (< t_3 -3.5813117084150564e+153)
     t_4
     (if (< t_3 1.2285964308315609e+82) (/ 1.0 (/ t_1 t_2)) t_4))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x + t) + y
    t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
    t_3 = t_2 / t_1
    t_4 = (z + a) - b
    if (t_3 < (-3.5813117084150564d+153)) then
        tmp = t_4
    else if (t_3 < 1.2285964308315609d+82) then
        tmp = 1.0d0 / (t_1 / t_2)
    else
        tmp = t_4
    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 + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
	t_3 = t_2 / t_1
	t_4 = (z + a) - b
	tmp = 0
	if t_3 < -3.5813117084150564e+153:
		tmp = t_4
	elif t_3 < 1.2285964308315609e+82:
		tmp = 1.0 / (t_1 / t_2)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b))
	t_3 = Float64(t_2 / t_1)
	t_4 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = Float64(1.0 / Float64(t_1 / t_2));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	t_3 = t_2 / t_1;
	t_4 = (z + a) - b;
	tmp = 0.0;
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = 1.0 / (t_1 / t_2);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Less[t$95$3, -3.5813117084150564e+153], t$95$4, If[Less[t$95$3, 1.2285964308315609e+82], N[(1.0 / N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

Reproduce

herbie shell --seed 2025051 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3581311708415056400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 12285964308315609000000000000000000000000000000000000000000000000000000000000000000) (/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b))))

  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))