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

Percentage Accurate: 60.9% → 99.3%

Time: 5.4s

Alternatives: 13

Speedup: 0.7×

Specification

Math

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

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: 60.9% accurate, 1.0× speedup

Math

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

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: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \left(t + x\right) + y\\ t_3 := \frac{y + x}{t\_2}\\ t_4 := \mathsf{fma}\left(z, t\_3, \frac{a}{t\_2} \cdot \left(t + y\right) - b \cdot \frac{y}{t\_2}\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+284}:\\ \;\;\;\;\mathsf{fma}\left(z, t\_3, \frac{a \cdot \left(t + y\right) - b \cdot y}{t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (+ (+ t x) y))
        (t_3 (/ (+ y x) t_2))
        (t_4 (fma z t_3 (- (* (/ a t_2) (+ t y)) (* b (/ y t_2))))))
   (if (<= t_1 (- INFINITY))
     t_4
     (if (<= t_1 5e+284) (fma z t_3 (/ (- (* a (+ t y)) (* b y)) t_2)) t_4))))

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 t_2 = (t + x) + y;
	double t_3 = (y + x) / t_2;
	double t_4 = fma(z, t_3, (((a / t_2) * (t + y)) - (b * (y / t_2))));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_1 <= 5e+284) {
		tmp = fma(z, t_3, (((a * (t + y)) - (b * y)) / t_2));
	} else {
		tmp = t_4;
	}
	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))
	t_2 = Float64(Float64(t + x) + y)
	t_3 = Float64(Float64(y + x) / t_2)
	t_4 = fma(z, t_3, Float64(Float64(Float64(a / t_2) * Float64(t + y)) - Float64(b * Float64(y / t_2))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_1 <= 5e+284)
		tmp = fma(z, t_3, Float64(Float64(Float64(a * Float64(t + y)) - Float64(b * y)) / t_2));
	else
		tmp = t_4;
	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]}, Block[{t$95$2 = N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y + x), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(z * t$95$3 + N[(N[(N[(a / t$95$2), $MachinePrecision] * N[(t + y), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$4, If[LessEqual[t$95$1, 5e+284], N[(z * t$95$3 + N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

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)) < -inf.0 or 4.9999999999999999e284 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 60.9%

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

      1. lift-/.f64 N/A

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

      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

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

      4. associate--l+ N/A

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

      5. div-add N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 N/A

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

      14. lift-+.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 N/A

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

      17. lower-/.f64 N/A

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

   3. Applied rewrites 73.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. sum-to-mult-rev N/A

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

      13. lift-/.f64 N/A

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

      14. lift-+.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. add-flip N/A

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

      17. sub-negate-rev N/A

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

      18. sub-negate N/A

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

   5. Applied rewrites 83.3%

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

      1. lift-fma.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. distribute-neg-frac2 N/A

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

      8. lift-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lift--.f64 N/A

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

      12. associate--r- N/A

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

      13. lift-neg.f64 N/A

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

      14. add-flip N/A

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

      15. lift-+.f64 N/A

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

      16. lift-+.f64 N/A

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

      17. associate-/l* N/A

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

      18. lower-*.f64 N/A

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

      19. lower-/.f64 94.1

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

   7. Applied rewrites 94.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999999e284

   1. Initial program 60.9%

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

      1. lift-/.f64 N/A

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

      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

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

      4. associate--l+ N/A

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

      5. div-add N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 N/A

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

      14. lift-+.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 N/A

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

      17. lower-/.f64 N/A

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

   3. Applied rewrites 73.1%

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

Alternative 2: 95.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \left(t + x\right) + y\\ t_3 := \frac{y + x}{t\_2}\\ t_4 := \mathsf{fma}\left(z, t\_3, a - b \cdot \frac{y}{t\_2}\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+293}:\\ \;\;\;\;\mathsf{fma}\left(z, t\_3, \frac{a \cdot \left(t + y\right) - b \cdot y}{t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (+ (+ t x) y))
        (t_3 (/ (+ y x) t_2))
        (t_4 (fma z t_3 (- a (* b (/ y t_2))))))
   (if (<= t_1 (- INFINITY))
     t_4
     (if (<= t_1 2e+293) (fma z t_3 (/ (- (* a (+ t y)) (* b y)) t_2)) t_4))))

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 t_2 = (t + x) + y;
	double t_3 = (y + x) / t_2;
	double t_4 = fma(z, t_3, (a - (b * (y / t_2))));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_1 <= 2e+293) {
		tmp = fma(z, t_3, (((a * (t + y)) - (b * y)) / t_2));
	} else {
		tmp = t_4;
	}
	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))
	t_2 = Float64(Float64(t + x) + y)
	t_3 = Float64(Float64(y + x) / t_2)
	t_4 = fma(z, t_3, Float64(a - Float64(b * Float64(y / t_2))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_1 <= 2e+293)
		tmp = fma(z, t_3, Float64(Float64(Float64(a * Float64(t + y)) - Float64(b * y)) / t_2));
	else
		tmp = t_4;
	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]}, Block[{t$95$2 = N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y + x), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(z * t$95$3 + N[(a - N[(b * N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$4, If[LessEqual[t$95$1, 2e+293], N[(z * t$95$3 + N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

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)) < -inf.0 or 1.9999999999999998e293 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 60.9%

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

      1. lift-/.f64 N/A

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

      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

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

      4. associate--l+ N/A

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

      5. div-add N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 N/A

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

      14. lift-+.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 N/A

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

      17. lower-/.f64 N/A

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

   3. Applied rewrites 73.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. sum-to-mult-rev N/A

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

      13. lift-/.f64 N/A

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

      14. lift-+.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. add-flip N/A

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

      17. sub-negate-rev N/A

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

      18. sub-negate N/A

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

   5. Applied rewrites 83.3%

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

      1. lift-fma.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. distribute-neg-frac2 N/A

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

      8. lift-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lift--.f64 N/A

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

      12. associate--r- N/A

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

      13. lift-neg.f64 N/A

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

      14. add-flip N/A

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

      15. lift-+.f64 N/A

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

      16. lift-+.f64 N/A

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

      17. associate-/l* N/A

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

      18. lower-*.f64 N/A

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

      19. lower-/.f64 94.1

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

   7. Applied rewrites 94.1%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 84.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.9999999999999998e293

   1. Initial program 60.9%

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

      1. lift-/.f64 N/A

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

      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

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

      4. associate--l+ N/A

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

      5. div-add N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 N/A

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

      14. lift-+.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 N/A

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

      17. lower-/.f64 N/A

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

   3. Applied rewrites 73.1%

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

Alternative 3: 95.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \left(t + x\right) + y\\ t_4 := \mathsf{fma}\left(z, \frac{y + x}{t\_3}, a - b \cdot \frac{y}{t\_3}\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+215}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+293}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-y, b, \mathsf{fma}\left(a, t + y, z \cdot \left(y + x\right)\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \]

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 (+ (+ t x) y))
        (t_4 (fma z (/ (+ y x) t_3) (- a (* b (/ y t_3))))))
   (if (<= t_2 -2e+215)
     t_4
     (if (<= t_2 2e+293)
       (/ (fma (- y) b (fma a (+ t y) (* z (+ y x)))) t_1)
       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)) / t_1;
	double t_3 = (t + x) + y;
	double t_4 = fma(z, ((y + x) / t_3), (a - (b * (y / t_3))));
	double tmp;
	if (t_2 <= -2e+215) {
		tmp = t_4;
	} else if (t_2 <= 2e+293) {
		tmp = fma(-y, b, fma(a, (t + y), (z * (y + x)))) / t_1;
	} 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(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(t + x) + y)
	t_4 = fma(z, Float64(Float64(y + x) / t_3), Float64(a - Float64(b * Float64(y / t_3))))
	tmp = 0.0
	if (t_2 <= -2e+215)
		tmp = t_4;
	elseif (t_2 <= 2e+293)
		tmp = Float64(fma(Float64(-y), b, fma(a, Float64(t + y), Float64(z * Float64(y + x)))) / t_1);
	else
		tmp = t_4;
	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[(t + x), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(y + x), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(a - N[(b * N[(y / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+215], t$95$4, If[LessEqual[t$95$2, 2e+293], N[(N[((-y) * b + N[(a * N[(t + y), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$4]]]]]]

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)) < -1.99999999999999981e215 or 1.9999999999999998e293 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 60.9%

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

      1. lift-/.f64 N/A

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

      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

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

      4. associate--l+ N/A

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

      5. div-add N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 N/A

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

      14. lift-+.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 N/A

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

      17. lower-/.f64 N/A

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

   3. Applied rewrites 73.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. sum-to-mult-rev N/A

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

      13. lift-/.f64 N/A

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

      14. lift-+.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. add-flip N/A

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

      17. sub-negate-rev N/A

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

      18. sub-negate N/A

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

   5. Applied rewrites 83.3%

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

      1. lift-fma.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. distribute-neg-frac2 N/A

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

      8. lift-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lift--.f64 N/A

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

      12. associate--r- N/A

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

      13. lift-neg.f64 N/A

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

      14. add-flip N/A

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

      15. lift-+.f64 N/A

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

      16. lift-+.f64 N/A

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

      17. associate-/l* N/A

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

      18. lower-*.f64 N/A

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

      19. lower-/.f64 94.1

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

   7. Applied rewrites 94.1%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 84.3%

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

   if -1.99999999999999981e215 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.9999999999999998e293

   1. Initial program 60.9%

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

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-lft-neg-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 61.0

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lower-fma.f64 61.1

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 61.1

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 61.1

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

   3. Applied rewrites 61.1%

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

Alternative 4: 94.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \mathsf{fma}\left(\frac{x + y}{\left(t + x\right) + y}, z, a - \frac{y}{t + y} \cdot b\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+215}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+293}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-y, b, \mathsf{fma}\left(a, t + y, z \cdot \left(y + x\right)\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \]

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 (fma (/ (+ x y) (+ (+ t x) y)) z (- a (* (/ y (+ t y)) b)))))
   (if (<= t_2 -2e+215)
     t_3
     (if (<= t_2 2e+293)
       (/ (fma (- y) b (fma a (+ t y) (* z (+ y x)))) 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 = fma(((x + y) / ((t + x) + y)), z, (a - ((y / (t + y)) * b)));
	double tmp;
	if (t_2 <= -2e+215) {
		tmp = t_3;
	} else if (t_2 <= 2e+293) {
		tmp = fma(-y, b, fma(a, (t + y), (z * (y + x)))) / 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 = fma(Float64(Float64(x + y) / Float64(Float64(t + x) + y)), z, Float64(a - Float64(Float64(y / Float64(t + y)) * b)))
	tmp = 0.0
	if (t_2 <= -2e+215)
		tmp = t_3;
	elseif (t_2 <= 2e+293)
		tmp = Float64(fma(Float64(-y), b, fma(a, Float64(t + y), Float64(z * Float64(y + x)))) / 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[(N[(x + y), $MachinePrecision] / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] * z + N[(a - N[(N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+215], t$95$3, If[LessEqual[t$95$2, 2e+293], N[(N[((-y) * b + N[(a * N[(t + y), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]

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)) < -1.99999999999999981e215 or 1.9999999999999998e293 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 60.9%

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

      1. lift-/.f64 N/A

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

      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

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

      4. associate--l+ N/A

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

      5. div-add N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 N/A

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

      14. lift-+.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 N/A

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

      17. lower-/.f64 N/A

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

   3. Applied rewrites 73.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. sum-to-mult-rev N/A

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

      13. lift-/.f64 N/A

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

      14. lift-+.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. add-flip N/A

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

      17. sub-negate-rev N/A

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

      18. sub-negate N/A

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 68.6

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

   8. Applied rewrites 68.6%

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

      1. lift-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 68.6

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 68.6

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

      7. lift-+.f64 N/A

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

      8. add-flip N/A

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

      9. lower--.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. mul-1-neg N/A

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

   10. Applied rewrites 78.2%

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

   if -1.99999999999999981e215 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.9999999999999998e293

   1. Initial program 60.9%

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

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-lft-neg-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 61.0

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lower-fma.f64 61.1

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 61.1

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 61.1

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

   3. Applied rewrites 61.1%

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

Alternative 5: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := a - \left(b - z\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+293}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-y, b, \mathsf{fma}\left(a, t + y, z \cdot \left(y + x\right)\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \]

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 (- b z))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 2e+293)
       (/ (fma (- y) b (fma a (+ t y) (* z (+ y x)))) 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 - (b - z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= 2e+293) {
		tmp = fma(-y, b, fma(a, (t + y), (z * (y + x)))) / 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(a - Float64(b - z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= 2e+293)
		tmp = Float64(fma(Float64(-y), b, fma(a, Float64(t + y), Float64(z * Float64(y + x)))) / 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[(a - N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, 2e+293], N[(N[((-y) * b + N[(a * N[(t + y), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]

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)) < -inf.0 or 1.9999999999999998e293 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 60.9%

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

   2. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 55.4

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

   4. Applied rewrites 55.4%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. sub-negate-rev N/A

         \[\leadsto a + \left(\mathsf{neg}\left(\left(b - z\right)\right)\right) \]

      5. sub-flip-reverse N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 55.4

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

   6. Applied rewrites 55.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.9999999999999998e293

   1. Initial program 60.9%

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

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-lft-neg-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 61.0

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lower-fma.f64 61.1

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 61.1

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 61.1

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

   3. Applied rewrites 61.1%

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

Alternative 6: 67.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \left(a + \frac{y \cdot z}{t + y}\right) - \frac{b \cdot y}{t + y}\\ t_2 := \frac{x + y}{\left(t + x\right) + y} \cdot z\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-103}:\\ \;\;\;\;\frac{a \cdot \left(t + y\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a (/ (* y z) (+ t y))) (/ (* b y) (+ t y))))
        (t_2 (* (/ (+ x y) (+ (+ t x) y)) z)))
   (if (<= z -5.2e+58)
     t_2
     (if (<= z -1.2e-98)
       t_1
       (if (<= z 3.5e-103)
         (/ (- (* a (+ t y)) (* y b)) (+ (+ x t) y))
         (if (<= z 4.2e+105) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + ((y * z) / (t + y))) - ((b * y) / (t + y));
	double t_2 = ((x + y) / ((t + x) + y)) * z;
	double tmp;
	if (z <= -5.2e+58) {
		tmp = t_2;
	} else if (z <= -1.2e-98) {
		tmp = t_1;
	} else if (z <= 3.5e-103) {
		tmp = ((a * (t + y)) - (y * b)) / ((x + t) + y);
	} else if (z <= 4.2e+105) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: tmp
    t_1 = (a + ((y * z) / (t + y))) - ((b * y) / (t + y))
    t_2 = ((x + y) / ((t + x) + y)) * z
    if (z <= (-5.2d+58)) then
        tmp = t_2
    else if (z <= (-1.2d-98)) then
        tmp = t_1
    else if (z <= 3.5d-103) then
        tmp = ((a * (t + y)) - (y * b)) / ((x + t) + y)
    else if (z <= 4.2d+105) then
        tmp = t_1
    else
        tmp = t_2
    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 = (a + ((y * z) / (t + y))) - ((b * y) / (t + y));
	double t_2 = ((x + y) / ((t + x) + y)) * z;
	double tmp;
	if (z <= -5.2e+58) {
		tmp = t_2;
	} else if (z <= -1.2e-98) {
		tmp = t_1;
	} else if (z <= 3.5e-103) {
		tmp = ((a * (t + y)) - (y * b)) / ((x + t) + y);
	} else if (z <= 4.2e+105) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + ((y * z) / (t + y))) - ((b * y) / (t + y))
	t_2 = ((x + y) / ((t + x) + y)) * z
	tmp = 0
	if z <= -5.2e+58:
		tmp = t_2
	elif z <= -1.2e-98:
		tmp = t_1
	elif z <= 3.5e-103:
		tmp = ((a * (t + y)) - (y * b)) / ((x + t) + y)
	elif z <= 4.2e+105:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + Float64(Float64(y * z) / Float64(t + y))) - Float64(Float64(b * y) / Float64(t + y)))
	t_2 = Float64(Float64(Float64(x + y) / Float64(Float64(t + x) + y)) * z)
	tmp = 0.0
	if (z <= -5.2e+58)
		tmp = t_2;
	elseif (z <= -1.2e-98)
		tmp = t_1;
	elseif (z <= 3.5e-103)
		tmp = Float64(Float64(Float64(a * Float64(t + y)) - Float64(y * b)) / Float64(Float64(x + t) + y));
	elseif (z <= 4.2e+105)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + ((y * z) / (t + y))) - ((b * y) / (t + y));
	t_2 = ((x + y) / ((t + x) + y)) * z;
	tmp = 0.0;
	if (z <= -5.2e+58)
		tmp = t_2;
	elseif (z <= -1.2e-98)
		tmp = t_1;
	elseif (z <= 3.5e-103)
		tmp = ((a * (t + y)) - (y * b)) / ((x + t) + y);
	elseif (z <= 4.2e+105)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + N[(N[(y * z), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * y), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x + y), $MachinePrecision] / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -5.2e+58], t$95$2, If[LessEqual[z, -1.2e-98], t$95$1, If[LessEqual[z, 3.5e-103], N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+105], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.19999999999999976e58 or 4.2000000000000002e105 < z

   1. Initial program 60.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 25.8

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

   4. Applied rewrites 25.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lift-+.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. associate-+l+ N/A

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

      10. lift-+.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. lift-/.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 40.9

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

      15. lift-+.f64 N/A

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

      16. +-commutative N/A

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

      17. lift-+.f64 40.9

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

   6. Applied rewrites 40.9%

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

   if -5.19999999999999976e58 < z < -1.20000000000000002e-98 or 3.50000000000000016e-103 < z < 4.2000000000000002e105

   1. Initial program 60.9%

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

      1. lift-/.f64 N/A

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

      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

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

      4. associate--l+ N/A

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

      5. div-add N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 N/A

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

      14. lift-+.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 N/A

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

      17. lower-/.f64 N/A

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

   3. Applied rewrites 73.1%

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

   4. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 50.0

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

   6. Applied rewrites 50.0%

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

   if -1.20000000000000002e-98 < z < 3.50000000000000016e-103

   1. Initial program 60.9%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 37.4

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

   4. Applied rewrites 37.4%

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

Alternative 7: 66.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := a - \left(b - z\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+247}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, x \cdot z\right)}{t + x}\\ \mathbf{elif}\;t\_2 \leq 10^{+137}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, y \cdot \left(z - b\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \]

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 (- b z))))
   (if (<= t_2 -1e+247)
     t_3
     (if (<= t_2 5000000000.0)
       (/ (fma a t (* x z)) (+ t x))
       (if (<= t_2 1e+137) (/ (fma x z (* y (- z b))) 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 - (b - z);
	double tmp;
	if (t_2 <= -1e+247) {
		tmp = t_3;
	} else if (t_2 <= 5000000000.0) {
		tmp = fma(a, t, (x * z)) / (t + x);
	} else if (t_2 <= 1e+137) {
		tmp = fma(x, z, (y * (z - b))) / 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(a - Float64(b - z))
	tmp = 0.0
	if (t_2 <= -1e+247)
		tmp = t_3;
	elseif (t_2 <= 5000000000.0)
		tmp = Float64(fma(a, t, Float64(x * z)) / Float64(t + x));
	elseif (t_2 <= 1e+137)
		tmp = Float64(fma(x, z, Float64(y * Float64(z - b))) / 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[(a - N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+247], t$95$3, If[LessEqual[t$95$2, 5000000000.0], N[(N[(a * t + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+137], N[(N[(x * z + N[(y * N[(z - b), $MachinePrecision]), $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)) < -9.99999999999999952e246 or 1e137 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 60.9%

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

   2. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 55.4

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

   4. Applied rewrites 55.4%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. sub-negate-rev N/A

         \[\leadsto a + \left(\mathsf{neg}\left(\left(b - z\right)\right)\right) \]

      5. sub-flip-reverse N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 55.4

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

   6. Applied rewrites 55.4%

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

   if -9.99999999999999952e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5e9

   1. Initial program 60.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   3. 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. lower-*.f64 N/A

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

      4. lower-+.f64 41.3

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

   4. Applied rewrites 41.3%

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

   if 5e9 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e137

   1. Initial program 60.9%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 37.8

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

   4. Applied rewrites 37.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 37.9

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

   7. Applied rewrites 37.9%

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

Alternative 8: 65.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := a - \left(b - z\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+247}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-30}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, x \cdot z\right)}{t + x}\\ \mathbf{elif}\;t\_2 \leq 10^{+127}:\\ \;\;\;\;\frac{y \cdot \left(\left(a + z\right) - b\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \]

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 (- b z))))
   (if (<= t_2 -1e+247)
     t_3
     (if (<= t_2 5e-30)
       (/ (fma a t (* x z)) (+ t x))
       (if (<= t_2 1e+127) (/ (* y (- (+ a z) b)) 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 - (b - z);
	double tmp;
	if (t_2 <= -1e+247) {
		tmp = t_3;
	} else if (t_2 <= 5e-30) {
		tmp = fma(a, t, (x * z)) / (t + x);
	} else if (t_2 <= 1e+127) {
		tmp = (y * ((a + z) - b)) / 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(a - Float64(b - z))
	tmp = 0.0
	if (t_2 <= -1e+247)
		tmp = t_3;
	elseif (t_2 <= 5e-30)
		tmp = Float64(fma(a, t, Float64(x * z)) / Float64(t + x));
	elseif (t_2 <= 1e+127)
		tmp = Float64(Float64(y * Float64(Float64(a + z) - b)) / 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[(a - N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+247], t$95$3, If[LessEqual[t$95$2, 5e-30], N[(N[(a * t + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+127], N[(N[(y * N[(N[(a + z), $MachinePrecision] - b), $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)) < -9.99999999999999952e246 or 9.99999999999999955e126 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 60.9%

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

   2. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 55.4

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

   4. Applied rewrites 55.4%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. sub-negate-rev N/A

         \[\leadsto a + \left(\mathsf{neg}\left(\left(b - z\right)\right)\right) \]

      5. sub-flip-reverse N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 55.4

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

   6. Applied rewrites 55.4%

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

   if -9.99999999999999952e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.99999999999999972e-30

   1. Initial program 60.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   3. 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. lower-*.f64 N/A

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

      4. lower-+.f64 41.3

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

   4. Applied rewrites 41.3%

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

   if 4.99999999999999972e-30 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999955e126

   1. Initial program 60.9%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 30.4

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

   4. Applied rewrites 30.4%

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

Alternative 9: 64.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := a - \left(b - z\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+247}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, x \cdot z\right)}{t + x}\\ \mathbf{elif}\;t\_2 \leq 10^{+127}:\\ \;\;\;\;\frac{y \cdot \left(z - b\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \]

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 (- b z))))
   (if (<= t_2 -1e+247)
     t_3
     (if (<= t_2 5000000000.0)
       (/ (fma a t (* x z)) (+ t x))
       (if (<= t_2 1e+127) (/ (* y (- z b)) 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 - (b - z);
	double tmp;
	if (t_2 <= -1e+247) {
		tmp = t_3;
	} else if (t_2 <= 5000000000.0) {
		tmp = fma(a, t, (x * z)) / (t + x);
	} else if (t_2 <= 1e+127) {
		tmp = (y * (z - b)) / 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(a - Float64(b - z))
	tmp = 0.0
	if (t_2 <= -1e+247)
		tmp = t_3;
	elseif (t_2 <= 5000000000.0)
		tmp = Float64(fma(a, t, Float64(x * z)) / Float64(t + x));
	elseif (t_2 <= 1e+127)
		tmp = Float64(Float64(y * Float64(z - b)) / 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[(a - N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+247], t$95$3, If[LessEqual[t$95$2, 5000000000.0], N[(N[(a * t + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+127], N[(N[(y * N[(z - b), $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)) < -9.99999999999999952e246 or 9.99999999999999955e126 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 60.9%

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

   2. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 55.4

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

   4. Applied rewrites 55.4%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. sub-negate-rev N/A

         \[\leadsto a + \left(\mathsf{neg}\left(\left(b - z\right)\right)\right) \]

      5. sub-flip-reverse N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 55.4

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

   6. Applied rewrites 55.4%

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

   if -9.99999999999999952e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5e9

   1. Initial program 60.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   3. 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. lower-*.f64 N/A

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

      4. lower-+.f64 41.3

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

   4. Applied rewrites 41.3%

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

   if 5e9 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999955e126

   1. Initial program 60.9%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 37.8

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

   4. Applied rewrites 37.8%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 22.5

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

   7. Applied rewrites 22.5%

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

Alternative 10: 63.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := a - \left(b - z\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+247}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+137}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, x \cdot z\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (- a (- b z))))
   (if (<= t_1 -1e+247)
     t_2
     (if (<= t_1 1e+137) (/ (fma a t (* x z)) (+ t x)) t_2))))

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 t_2 = a - (b - z);
	double tmp;
	if (t_1 <= -1e+247) {
		tmp = t_2;
	} else if (t_1 <= 1e+137) {
		tmp = fma(a, t, (x * z)) / (t + x);
	} else {
		tmp = t_2;
	}
	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))
	t_2 = Float64(a - Float64(b - z))
	tmp = 0.0
	if (t_1 <= -1e+247)
		tmp = t_2;
	elseif (t_1 <= 1e+137)
		tmp = Float64(fma(a, t, Float64(x * z)) / Float64(t + x));
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(a - N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+247], t$95$2, If[LessEqual[t$95$1, 1e+137], N[(N[(a * t + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

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)) < -9.99999999999999952e246 or 1e137 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 60.9%

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

   2. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 55.4

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

   4. Applied rewrites 55.4%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. sub-negate-rev N/A

         \[\leadsto a + \left(\mathsf{neg}\left(\left(b - z\right)\right)\right) \]

      5. sub-flip-reverse N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 55.4

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

   6. Applied rewrites 55.4%

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

   if -9.99999999999999952e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e137

   1. Initial program 60.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   3. 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. lower-*.f64 N/A

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

      4. lower-+.f64 41.3

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

   4. Applied rewrites 41.3%

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

Alternative 11: 57.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+173}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;a - \left(b - z\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.2e+173) a (- a (- b z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.2e+173) {
		tmp = a;
	} else {
		tmp = a - (b - 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 (t <= (-2.2d+173)) then
        tmp = a
    else
        tmp = a - (b - 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 (t <= -2.2e+173) {
		tmp = a;
	} else {
		tmp = a - (b - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.2e+173:
		tmp = a
	else:
		tmp = a - (b - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.2e+173)
		tmp = a;
	else
		tmp = Float64(a - Float64(b - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.2e+173)
		tmp = a;
	else
		tmp = a - (b - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.2e+173], a, N[(a - N[(b - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2e173

   1. Initial program 60.9%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 32.5%

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

   if -2.2e173 < t

   1. Initial program 60.9%

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

   2. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 55.4

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

   4. Applied rewrites 55.4%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. sub-negate-rev N/A

         \[\leadsto a + \left(\mathsf{neg}\left(\left(b - z\right)\right)\right) \]

      5. sub-flip-reverse N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 55.4

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

   6. Applied rewrites 55.4%

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

Alternative 12: 44.7% accurate, 3.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-29}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+105}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8.5e-29) z (if (<= z 4.2e+105) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.5e-29) {
		tmp = z;
	} else if (z <= 4.2e+105) {
		tmp = a;
	} 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 (z <= (-8.5d-29)) then
        tmp = z
    else if (z <= 4.2d+105) then
        tmp = a
    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 (z <= -8.5e-29) {
		tmp = z;
	} else if (z <= 4.2e+105) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8.5e-29:
		tmp = z
	elif z <= 4.2e+105:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.5e-29)
		tmp = z;
	elseif (z <= 4.2e+105)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8.5e-29)
		tmp = z;
	elseif (z <= 4.2e+105)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8.5e-29], z, If[LessEqual[z, 4.2e+105], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000001e-29 or 4.2000000000000002e105 < z

   1. Initial program 60.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 33.3%

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

   if -8.5000000000000001e-29 < z < 4.2000000000000002e105

   1. Initial program 60.9%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 32.5%

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

Alternative 13: 32.5% accurate, 29.5× speedup

Math

\[a \]

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 60.9%

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

2. Taylor expanded in t around inf

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

4. Applied rewrites 32.5%

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

Reproduce

herbie shell --seed 2025170 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64
  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))