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

Percentage Accurate: 61.2% → 88.5%

Time: 9.3s

Alternatives: 22

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t + y}\\ t_2 := \left(t + y\right) \cdot \left(t + y\right)\\ t_3 := t\_2 \cdot \left(t + y\right)\\ t_4 := \frac{z}{t\_2}\\ t_5 := \frac{y}{y + x}\\ t_6 := \frac{y}{\left(y + x\right) \cdot \left(y + x\right)}\\ t_7 := t + \left(x + y\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+82}:\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, \frac{z}{t\_3}, \frac{a}{t\_2}\right) - \mathsf{fma}\left(b, \frac{y}{t\_3}, t\_4\right), x, \mathsf{fma}\left(b, \frac{y}{t\_2}, t\_1\right)\right) - \mathsf{fma}\left(y, t\_4, \frac{a}{t + y}\right), x, y \cdot t\_1\right) + a\right) - b \cdot \frac{y}{t + y}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-64}:\\ \;\;\;\;z + \left(\mathsf{fma}\left(\mathsf{fma}\left(b, t\_6, \frac{a}{y + x}\right) - \mathsf{fma}\left(a, t\_6, \frac{z}{y + x}\right), t, a \cdot t\_5\right) - b \cdot t\_5\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t + y}{\left(y + x\right) + t}, a, b \cdot \mathsf{fma}\left(-1, \frac{y}{t\_7}, \frac{z \cdot \left(x + y\right)}{b \cdot t\_7}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ z (+ t y)))
        (t_2 (* (+ t y) (+ t y)))
        (t_3 (* t_2 (+ t y)))
        (t_4 (/ z t_2))
        (t_5 (/ y (+ y x)))
        (t_6 (/ y (* (+ y x) (+ y x))))
        (t_7 (+ t (+ x y))))
   (if (<= t -7.5e+82)
     (-
      (+
       (fma
        (-
         (fma
          (- (fma y (/ z t_3) (/ a t_2)) (fma b (/ y t_3) t_4))
          x
          (fma b (/ y t_2) t_1))
         (fma y t_4 (/ a (+ t y))))
        x
        (* y t_1))
       a)
      (* b (/ y (+ t y))))
     (if (<= t 2.15e-64)
       (+
        z
        (-
         (fma
          (- (fma b t_6 (/ a (+ y x))) (fma a t_6 (/ z (+ y x))))
          t
          (* a t_5))
         (* b t_5)))
       (fma
        (/ (+ t y) (+ (+ y x) t))
        a
        (* b (fma -1.0 (/ y t_7) (/ (* z (+ x y)) (* b t_7)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z / (t + y);
	double t_2 = (t + y) * (t + y);
	double t_3 = t_2 * (t + y);
	double t_4 = z / t_2;
	double t_5 = y / (y + x);
	double t_6 = y / ((y + x) * (y + x));
	double t_7 = t + (x + y);
	double tmp;
	if (t <= -7.5e+82) {
		tmp = (fma((fma((fma(y, (z / t_3), (a / t_2)) - fma(b, (y / t_3), t_4)), x, fma(b, (y / t_2), t_1)) - fma(y, t_4, (a / (t + y)))), x, (y * t_1)) + a) - (b * (y / (t + y)));
	} else if (t <= 2.15e-64) {
		tmp = z + (fma((fma(b, t_6, (a / (y + x))) - fma(a, t_6, (z / (y + x)))), t, (a * t_5)) - (b * t_5));
	} else {
		tmp = fma(((t + y) / ((y + x) + t)), a, (b * fma(-1.0, (y / t_7), ((z * (x + y)) / (b * t_7)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z / Float64(t + y))
	t_2 = Float64(Float64(t + y) * Float64(t + y))
	t_3 = Float64(t_2 * Float64(t + y))
	t_4 = Float64(z / t_2)
	t_5 = Float64(y / Float64(y + x))
	t_6 = Float64(y / Float64(Float64(y + x) * Float64(y + x)))
	t_7 = Float64(t + Float64(x + y))
	tmp = 0.0
	if (t <= -7.5e+82)
		tmp = Float64(Float64(fma(Float64(fma(Float64(fma(y, Float64(z / t_3), Float64(a / t_2)) - fma(b, Float64(y / t_3), t_4)), x, fma(b, Float64(y / t_2), t_1)) - fma(y, t_4, Float64(a / Float64(t + y)))), x, Float64(y * t_1)) + a) - Float64(b * Float64(y / Float64(t + y))));
	elseif (t <= 2.15e-64)
		tmp = Float64(z + Float64(fma(Float64(fma(b, t_6, Float64(a / Float64(y + x))) - fma(a, t_6, Float64(z / Float64(y + x)))), t, Float64(a * t_5)) - Float64(b * t_5)));
	else
		tmp = fma(Float64(Float64(t + y) / Float64(Float64(y + x) + t)), a, Float64(b * fma(-1.0, Float64(y / t_7), Float64(Float64(z * Float64(x + y)) / Float64(b * t_7)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z / N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t + y), $MachinePrecision] * N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y / N[(N[(y + x), $MachinePrecision] * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+82], N[(N[(N[(N[(N[(N[(N[(y * N[(z / t$95$3), $MachinePrecision] + N[(a / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / t$95$3), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision] * x + N[(b * N[(y / t$95$2), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$4 + N[(a / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] - N[(b * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.15e-64], N[(z + N[(N[(N[(N[(b * t$95$6 + N[(a / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * t$95$6 + N[(z / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t + N[(a * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * a + N[(b * N[(-1.0 * N[(y / t$95$7), $MachinePrecision] + N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(b * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.4999999999999999e82

   1. Initial program 49.3%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 82.6%

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

   if -7.4999999999999999e82 < t < 2.14999999999999987e-64

   1. Initial program 68.3%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 82.9%

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

   if 2.14999999999999987e-64 < t

   1. Initial program 56.1%

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

   3. Applied rewrites 73.5%

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

   4. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lift-+.f64 75.1

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

   6. Applied rewrites 75.1%

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

Alternative 2: 85.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot \left(t + y\right)\\ t_2 := \frac{z}{t + y}\\ t_3 := \frac{y}{y + x}\\ t_4 := \frac{y}{\left(y + x\right) \cdot \left(y + x\right)}\\ t_5 := t + \left(x + y\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+82}:\\ \;\;\;\;\left(a + \mathsf{fma}\left(\mathsf{fma}\left(b, \frac{y}{t\_1}, t\_2\right) - \mathsf{fma}\left(y, \frac{z}{t\_1}, \frac{a}{t + y}\right), x, y \cdot t\_2\right)\right) - b \cdot \frac{y}{t + y}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-64}:\\ \;\;\;\;z + \left(\mathsf{fma}\left(\mathsf{fma}\left(b, t\_4, \frac{a}{y + x}\right) - \mathsf{fma}\left(a, t\_4, \frac{z}{y + x}\right), t, a \cdot t\_3\right) - b \cdot t\_3\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t + y}{\left(y + x\right) + t}, a, b \cdot \mathsf{fma}\left(-1, \frac{y}{t\_5}, \frac{z \cdot \left(x + y\right)}{b \cdot t\_5}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t y) (+ t y)))
        (t_2 (/ z (+ t y)))
        (t_3 (/ y (+ y x)))
        (t_4 (/ y (* (+ y x) (+ y x))))
        (t_5 (+ t (+ x y))))
   (if (<= t -7.5e+82)
     (-
      (+
       a
       (fma
        (- (fma b (/ y t_1) t_2) (fma y (/ z t_1) (/ a (+ t y))))
        x
        (* y t_2)))
      (* b (/ y (+ t y))))
     (if (<= t 2.15e-64)
       (+
        z
        (-
         (fma
          (- (fma b t_4 (/ a (+ y x))) (fma a t_4 (/ z (+ y x))))
          t
          (* a t_3))
         (* b t_3)))
       (fma
        (/ (+ t y) (+ (+ y x) t))
        a
        (* b (fma -1.0 (/ y t_5) (/ (* z (+ x y)) (* b t_5)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) * (t + y);
	double t_2 = z / (t + y);
	double t_3 = y / (y + x);
	double t_4 = y / ((y + x) * (y + x));
	double t_5 = t + (x + y);
	double tmp;
	if (t <= -7.5e+82) {
		tmp = (a + fma((fma(b, (y / t_1), t_2) - fma(y, (z / t_1), (a / (t + y)))), x, (y * t_2))) - (b * (y / (t + y)));
	} else if (t <= 2.15e-64) {
		tmp = z + (fma((fma(b, t_4, (a / (y + x))) - fma(a, t_4, (z / (y + x)))), t, (a * t_3)) - (b * t_3));
	} else {
		tmp = fma(((t + y) / ((y + x) + t)), a, (b * fma(-1.0, (y / t_5), ((z * (x + y)) / (b * t_5)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) * Float64(t + y))
	t_2 = Float64(z / Float64(t + y))
	t_3 = Float64(y / Float64(y + x))
	t_4 = Float64(y / Float64(Float64(y + x) * Float64(y + x)))
	t_5 = Float64(t + Float64(x + y))
	tmp = 0.0
	if (t <= -7.5e+82)
		tmp = Float64(Float64(a + fma(Float64(fma(b, Float64(y / t_1), t_2) - fma(y, Float64(z / t_1), Float64(a / Float64(t + y)))), x, Float64(y * t_2))) - Float64(b * Float64(y / Float64(t + y))));
	elseif (t <= 2.15e-64)
		tmp = Float64(z + Float64(fma(Float64(fma(b, t_4, Float64(a / Float64(y + x))) - fma(a, t_4, Float64(z / Float64(y + x)))), t, Float64(a * t_3)) - Float64(b * t_3)));
	else
		tmp = fma(Float64(Float64(t + y) / Float64(Float64(y + x) + t)), a, Float64(b * fma(-1.0, Float64(y / t_5), Float64(Float64(z * Float64(x + y)) / Float64(b * t_5)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] * N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y / N[(N[(y + x), $MachinePrecision] * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+82], N[(N[(a + N[(N[(N[(b * N[(y / t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision] - N[(y * N[(z / t$95$1), $MachinePrecision] + N[(a / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.15e-64], N[(z + N[(N[(N[(N[(b * t$95$4 + N[(a / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * t$95$4 + N[(z / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t + N[(a * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * a + N[(b * N[(-1.0 * N[(y / t$95$5), $MachinePrecision] + N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(b * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.4999999999999999e82

   1. Initial program 49.3%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 82.8%

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

   if -7.4999999999999999e82 < t < 2.14999999999999987e-64

   1. Initial program 68.3%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 82.9%

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

   if 2.14999999999999987e-64 < t

   1. Initial program 56.1%

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

   3. Applied rewrites 73.5%

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

   4. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lift-+.f64 75.1

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

   6. Applied rewrites 75.1%

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

Alternative 3: 83.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \frac{y}{y + x}\\ t_3 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{\left(x + t\right) + y}\\ t_4 := \left(y + x\right) + t\\ t_5 := \frac{y}{\left(y + x\right) \cdot \left(y + x\right)}\\ t_6 := z + \left(\mathsf{fma}\left(\mathsf{fma}\left(b, t\_5, \frac{a}{y + x}\right) - \mathsf{fma}\left(a, t\_5, \frac{z}{y + x}\right), t, a \cdot t\_2\right) - b \cdot t\_2\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_3 \leq 10^{+296}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y + x}{t\_4}, z, \frac{t\_1 - b \cdot y}{t\_4}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t y) a))
        (t_2 (/ y (+ y x)))
        (t_3 (/ (- (+ (* (+ x y) z) t_1) (* y b)) (+ (+ x t) y)))
        (t_4 (+ (+ y x) t))
        (t_5 (/ y (* (+ y x) (+ y x))))
        (t_6
         (+
          z
          (-
           (fma
            (- (fma b t_5 (/ a (+ y x))) (fma a t_5 (/ z (+ y x))))
            t
            (* a t_2))
           (* b t_2)))))
   (if (<= t_3 (- INFINITY))
     t_6
     (if (<= t_3 1e+296)
       (fma (/ (+ y x) t_4) z (/ (- t_1 (* b y)) t_4))
       t_6))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) * a;
	double t_2 = y / (y + x);
	double t_3 = ((((x + y) * z) + t_1) - (y * b)) / ((x + t) + y);
	double t_4 = (y + x) + t;
	double t_5 = y / ((y + x) * (y + x));
	double t_6 = z + (fma((fma(b, t_5, (a / (y + x))) - fma(a, t_5, (z / (y + x)))), t, (a * t_2)) - (b * t_2));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_6;
	} else if (t_3 <= 1e+296) {
		tmp = fma(((y + x) / t_4), z, ((t_1 - (b * y)) / t_4));
	} else {
		tmp = t_6;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) * a)
	t_2 = Float64(y / Float64(y + x))
	t_3 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_4 = Float64(Float64(y + x) + t)
	t_5 = Float64(y / Float64(Float64(y + x) * Float64(y + x)))
	t_6 = Float64(z + Float64(fma(Float64(fma(b, t_5, Float64(a / Float64(y + x))) - fma(a, t_5, Float64(z / Float64(y + x)))), t, Float64(a * t_2)) - Float64(b * t_2)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_6;
	elseif (t_3 <= 1e+296)
		tmp = fma(Float64(Float64(y + x) / t_4), z, Float64(Float64(t_1 - Float64(b * y)) / t_4));
	else
		tmp = t_6;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$5 = N[(y / N[(N[(y + x), $MachinePrecision] * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(z + N[(N[(N[(N[(b * t$95$5 + N[(a / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * t$95$5 + N[(z / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t + N[(a * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$6, If[LessEqual[t$95$3, 1e+296], N[(N[(N[(y + x), $MachinePrecision] / t$95$4), $MachinePrecision] * z + N[(N[(t$95$1 - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision], t$95$6]]]]]]]]

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 9.99999999999999981e295 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.9%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 73.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999981e295

   1. Initial program 99.6%

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

   3. Applied rewrites 99.1%

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

Alternative 4: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := z \cdot \frac{x + y}{t\_1}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+146}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+83}:\\ \;\;\;\;\frac{t + y}{\left(y + x\right) + t} \cdot a + b \cdot \mathsf{fma}\left(-1, \frac{y}{t\_1}, \frac{z \cdot \left(x + y\right)}{b \cdot t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))) (t_2 (* z (/ (+ x y) t_1))))
   (if (<= z -7.5e+146)
     t_2
     (if (<= z 3.7e+83)
       (+
        (* (/ (+ t y) (+ (+ y x) t)) a)
        (* b (fma -1.0 (/ y t_1) (/ (* z (+ x y)) (* b t_1)))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -7.5e+146) {
		tmp = t_2;
	} else if (z <= 3.7e+83) {
		tmp = (((t + y) / ((y + x) + t)) * a) + (b * fma(-1.0, (y / t_1), ((z * (x + y)) / (b * t_1))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (z <= -7.5e+146)
		tmp = t_2;
	elseif (z <= 3.7e+83)
		tmp = Float64(Float64(Float64(Float64(t + y) / Float64(Float64(y + x) + t)) * a) + Float64(b * fma(-1.0, Float64(y / t_1), Float64(Float64(z * Float64(x + y)) / Float64(b * t_1)))));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+146], t$95$2, If[LessEqual[z, 3.7e+83], N[(N[(N[(N[(t + y), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision] + N[(b * N[(-1.0 * N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999983e146 or 3.7000000000000002e83 < z

   1. Initial program 40.7%

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

   3. Applied rewrites 47.5%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. div-add-rev N/A

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

      3. lower-/.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lift-+.f64 70.3

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

   6. Applied rewrites 70.3%

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

   if -7.49999999999999983e146 < z < 3.7000000000000002e83

   1. Initial program 70.4%

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

   3. Applied rewrites 83.9%

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

   4. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lift-+.f64 87.7

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

   6. Applied rewrites 87.7%

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

      1. lift-fma.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lower-+.f64 N/A

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

   8. Applied rewrites 87.7%

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

Alternative 5: 83.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := z \cdot \frac{x + y}{t\_1}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+146}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+83}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t + y}{\left(y + x\right) + t}, a, b \cdot \mathsf{fma}\left(-1, \frac{y}{t\_1}, \frac{z \cdot \left(x + y\right)}{b \cdot t\_1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))) (t_2 (* z (/ (+ x y) t_1))))
   (if (<= z -7.5e+146)
     t_2
     (if (<= z 3.7e+83)
       (fma
        (/ (+ t y) (+ (+ y x) t))
        a
        (* b (fma -1.0 (/ y t_1) (/ (* z (+ x y)) (* b t_1)))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -7.5e+146) {
		tmp = t_2;
	} else if (z <= 3.7e+83) {
		tmp = fma(((t + y) / ((y + x) + t)), a, (b * fma(-1.0, (y / t_1), ((z * (x + y)) / (b * t_1)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (z <= -7.5e+146)
		tmp = t_2;
	elseif (z <= 3.7e+83)
		tmp = fma(Float64(Float64(t + y) / Float64(Float64(y + x) + t)), a, Float64(b * fma(-1.0, Float64(y / t_1), Float64(Float64(z * Float64(x + y)) / Float64(b * t_1)))));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+146], t$95$2, If[LessEqual[z, 3.7e+83], N[(N[(N[(t + y), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * a + N[(b * N[(-1.0 * N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999983e146 or 3.7000000000000002e83 < z

   1. Initial program 40.7%

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

   3. Applied rewrites 47.5%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. div-add-rev N/A

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

      3. lower-/.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lift-+.f64 70.3

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

   6. Applied rewrites 70.3%

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

   if -7.49999999999999983e146 < z < 3.7000000000000002e83

   1. Initial program 70.4%

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

   3. Applied rewrites 83.9%

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

   4. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lift-+.f64 87.7

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

   6. Applied rewrites 87.7%

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

Alternative 6: 83.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{\left(x + t\right) + y}\\ t_3 := \left(y + x\right) + t\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{t + y}{t\_3} \cdot a + b \cdot \left(-1 \cdot \frac{y}{t + \left(x + y\right)}\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+140}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y + x}{t\_3}, z, \frac{t\_1 - b \cdot y}{t\_3}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t y) a))
        (t_2 (/ (- (+ (* (+ x y) z) t_1) (* y b)) (+ (+ x t) y)))
        (t_3 (+ (+ y x) t)))
   (if (<= t_2 (- INFINITY))
     (+ (* (/ (+ t y) t_3) a) (* b (* -1.0 (/ y (+ t (+ x y))))))
     (if (<= t_2 1e+140)
       (fma (/ (+ y x) t_3) z (/ (- t_1 (* b y)) t_3))
       (- (+ a z) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) * a;
	double t_2 = ((((x + y) * z) + t_1) - (y * b)) / ((x + t) + y);
	double t_3 = (y + x) + t;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (((t + y) / t_3) * a) + (b * (-1.0 * (y / (t + (x + y)))));
	} else if (t_2 <= 1e+140) {
		tmp = fma(((y + x) / t_3), z, ((t_1 - (b * y)) / t_3));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) * a)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_3 = Float64(Float64(y + x) + t)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(t + y) / t_3) * a) + Float64(b * Float64(-1.0 * Float64(y / Float64(t + Float64(x + y))))));
	elseif (t_2 <= 1e+140)
		tmp = fma(Float64(Float64(y + x) / t_3), z, Float64(Float64(t_1 - Float64(b * y)) / t_3));
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(N[(t + y), $MachinePrecision] / t$95$3), $MachinePrecision] * a), $MachinePrecision] + N[(b * N[(-1.0 * N[(y / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+140], N[(N[(N[(y + x), $MachinePrecision] / t$95$3), $MachinePrecision] * z + N[(N[(t$95$1 - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]]]]]

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)) < -inf.0

   1. Initial program 6.1%

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

   3. Applied rewrites 39.8%

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

   4. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lift-+.f64 55.3

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

   6. Applied rewrites 55.3%

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

      1. lift-fma.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lower-+.f64 N/A

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

   8. Applied rewrites 55.3%

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

   9. Taylor expanded in z around 0

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

       1. lower-*.f64 N/A

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

       2. lift-+.f64 N/A

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

       3. lift-+.f64 N/A

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

       4. lift-/.f64 59.5

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

   11. Applied rewrites 59.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000006e140

   1. Initial program 99.5%

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

   3. Applied rewrites 99.0%

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

   if 1.00000000000000006e140 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 25.6%

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

   2. 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 70.4

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

   4. Applied rewrites 70.4%

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

Alternative 7: 82.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \left(y + x\right) + t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{t + y}{t\_2} \cdot a + b \cdot \left(-1 \cdot \frac{y}{t + \left(x + y\right)}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+140}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, \left(y + x\right) \cdot z\right)}{t\_2} - b \cdot \frac{y}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (+ (+ y x) t)))
   (if (<= t_1 (- INFINITY))
     (+ (* (/ (+ t y) t_2) a) (* b (* -1.0 (/ y (+ t (+ x y))))))
     (if (<= t_1 1e+140)
       (- (/ (fma (+ t y) a (* (+ y x) z)) t_2) (* b (/ y t_2)))
       (- (+ a z) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = (y + x) + t;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (((t + y) / t_2) * a) + (b * (-1.0 * (y / (t + (x + y)))));
	} else if (t_1 <= 1e+140) {
		tmp = (fma((t + y), a, ((y + x) * z)) / t_2) - (b * (y / t_2));
	} else {
		tmp = (a + z) - b;
	}
	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(y + x) + t)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(t + y) / t_2) * a) + Float64(b * Float64(-1.0 * Float64(y / Float64(t + Float64(x + y))))));
	elseif (t_1 <= 1e+140)
		tmp = Float64(Float64(fma(Float64(t + y), a, Float64(Float64(y + x) * z)) / t_2) - Float64(b * Float64(y / t_2)));
	else
		tmp = Float64(Float64(a + z) - b);
	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[(y + x), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision] * a), $MachinePrecision] + N[(b * N[(-1.0 * N[(y / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+140], N[(N[(N[(N[(t + y), $MachinePrecision] * a + N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision] - N[(b * N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]]]]

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)) < -inf.0

   1. Initial program 6.1%

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

   3. Applied rewrites 39.8%

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

   4. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lift-+.f64 55.3

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

   6. Applied rewrites 55.3%

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

      1. lift-fma.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lower-+.f64 N/A

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

   8. Applied rewrites 55.3%

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

   9. Taylor expanded in z around 0

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

       1. lower-*.f64 N/A

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

       2. lift-+.f64 N/A

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

       3. lift-+.f64 N/A

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

       4. lift-/.f64 59.5

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

   11. Applied rewrites 59.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000006e140

   1. Initial program 99.5%

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

   3. Applied rewrites 98.1%

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

   if 1.00000000000000006e140 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 25.6%

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

   2. 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 70.4

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

   4. Applied rewrites 70.4%

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

Alternative 8: 82.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{t + y}{\left(y + x\right) + t} \cdot a + b \cdot \left(-1 \cdot \frac{y}{t + \left(x + y\right)}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (<= t_1 (- INFINITY))
     (+ (* (/ (+ t y) (+ (+ y x) t)) a) (* b (* -1.0 (/ y (+ t (+ x y))))))
     (if (<= t_1 1e+140) t_1 (- (+ a z) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (((t + y) / ((y + x) + t)) * a) + (b * (-1.0 * (y / (t + (x + y)))));
	} else if (t_1 <= 1e+140) {
		tmp = t_1;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (((t + y) / ((y + x) + t)) * a) + (b * (-1.0 * (y / (t + (x + y)))));
	} else if (t_1 <= 1e+140) {
		tmp = t_1;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (((t + y) / ((y + x) + t)) * a) + (b * (-1.0 * (y / (t + (x + y)))))
	elif t_1 <= 1e+140:
		tmp = t_1
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(t + y) / Float64(Float64(y + x) + t)) * a) + Float64(b * Float64(-1.0 * Float64(y / Float64(t + Float64(x + y))))));
	elseif (t_1 <= 1e+140)
		tmp = t_1;
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (((t + y) / ((y + x) + t)) * a) + (b * (-1.0 * (y / (t + (x + y)))));
	elseif (t_1 <= 1e+140)
		tmp = t_1;
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(N[(t + y), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision] + N[(b * N[(-1.0 * N[(y / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+140], t$95$1, N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]]]

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)) < -inf.0

   1. Initial program 6.1%

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

   3. Applied rewrites 39.8%

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

   4. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lift-+.f64 55.3

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

   6. Applied rewrites 55.3%

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

      1. lift-fma.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lower-+.f64 N/A

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

   8. Applied rewrites 55.3%

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

   9. Taylor expanded in z around 0

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

       1. lower-*.f64 N/A

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

       2. lift-+.f64 N/A

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

       3. lift-+.f64 N/A

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

       4. lift-/.f64 59.5

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

   11. Applied rewrites 59.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000006e140

   1. Initial program 99.5%

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

   if 1.00000000000000006e140 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 25.6%

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

   2. 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 70.4

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

   4. Applied rewrites 70.4%

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

Alternative 9: 80.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{t + y}{\left(y + x\right) + t}, a, b \cdot \left(-1 \cdot \frac{y}{t + \left(x + y\right)}\right)\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (<= t_1 (- INFINITY))
     (fma (/ (+ t y) (+ (+ y x) t)) a (* b (* -1.0 (/ y (+ t (+ x y))))))
     (if (<= t_1 1e+140) t_1 (- (+ a z) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma(((t + y) / ((y + x) + t)), a, (b * (-1.0 * (y / (t + (x + y))))));
	} else if (t_1 <= 1e+140) {
		tmp = t_1;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = fma(Float64(Float64(t + y) / Float64(Float64(y + x) + t)), a, Float64(b * Float64(-1.0 * Float64(y / Float64(t + Float64(x + y))))));
	elseif (t_1 <= 1e+140)
		tmp = t_1;
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(t + y), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * a + N[(b * N[(-1.0 * N[(y / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+140], t$95$1, N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]]]

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)) < -inf.0

   1. Initial program 6.1%

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

   3. Applied rewrites 39.8%

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

   4. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lift-+.f64 55.3

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

   6. Applied rewrites 55.3%

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

   7. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 59.5

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

   9. Applied rewrites 59.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000006e140

   1. Initial program 99.5%

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

   if 1.00000000000000006e140 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 25.6%

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

   2. 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 70.4

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

   4. Applied rewrites 70.4%

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

Alternative 10: 80.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (- (+ a z) b)))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 1e+140) t_1 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 + z) - b;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 1e+140) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = (a + z) - b;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 1e+140) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
	t_2 = (a + z) - b
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 1e+140:
		tmp = t_1
	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(Float64(a + z) - b)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 1e+140)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	t_2 = (a + z) - b;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 1e+140)
		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[(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[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 1e+140], t$95$1, 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)) < -inf.0 or 1.00000000000000006e140 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 18.6%

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

   2. 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 70.0

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

   4. Applied rewrites 70.0%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000006e140

   1. Initial program 99.5%

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

Alternative 11: 72.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \left(a + z\right) - b\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+117}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{+140}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, \left(y + x\right) \cdot z\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_1))
        (t_3 (- (+ a z) b)))
   (if (<= t_2 -2e+117)
     t_3
     (if (<= t_2 1e+140) (/ (fma (+ t y) a (* (+ y x) z)) t_1) t_3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1;
	double t_3 = (a + z) - b;
	double tmp;
	if (t_2 <= -2e+117) {
		tmp = t_3;
	} else if (t_2 <= 1e+140) {
		tmp = fma((t + y), a, ((y + x) * z)) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (t_2 <= -2e+117)
		tmp = t_3;
	elseif (t_2 <= 1e+140)
		tmp = Float64(fma(Float64(t + y), a, Float64(Float64(y + x) * z)) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+117], t$95$3, If[LessEqual[t$95$2, 1e+140], N[(N[(N[(t + y), $MachinePrecision] * a + N[(N[(y + x), $MachinePrecision] * z), $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)) < -2.0000000000000001e117 or 1.00000000000000006e140 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 30.5%

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

   2. 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 69.0

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

   4. Applied rewrites 69.0%

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

   if -2.0000000000000001e117 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000006e140

   1. Initial program 99.5%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 77.7

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

   4. Applied rewrites 77.7%

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

Alternative 12: 69.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+117}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t + y}{\left(y + x\right) + t}, a, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -4.2e+60)
     t_1
     (if (<= y 3.6e+117) (fma (/ (+ t y) (+ (+ y x) t)) a z) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -4.2e+60) {
		tmp = t_1;
	} else if (y <= 3.6e+117) {
		tmp = fma(((t + y) / ((y + x) + t)), a, z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -4.2e+60)
		tmp = t_1;
	elseif (y <= 3.6e+117)
		tmp = fma(Float64(Float64(t + y) / Float64(Float64(y + x) + t)), a, z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -4.2e+60], t$95$1, If[LessEqual[y, 3.6e+117], N[(N[(N[(t + y), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * a + z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2000000000000002e60 or 3.60000000000000013e117 < y

   1. Initial program 34.0%

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

   2. 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 76.4

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

   4. Applied rewrites 76.4%

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

   if -4.2000000000000002e60 < y < 3.60000000000000013e117

   1. Initial program 76.2%

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

   3. Applied rewrites 86.1%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 65.8%

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

Alternative 13: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+110}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+140}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (- (+ a z) b)))
   (if (<= t_1 -5e+110)
     t_2
     (if (<= t_1 1e+140) (/ (fma a t (* z x)) (+ 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 + z) - b;
	double tmp;
	if (t_1 <= -5e+110) {
		tmp = t_2;
	} else if (t_1 <= 1e+140) {
		tmp = fma(a, t, (z * x)) / (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(Float64(a + z) - b)
	tmp = 0.0
	if (t_1 <= -5e+110)
		tmp = t_2;
	elseif (t_1 <= 1e+140)
		tmp = Float64(fma(a, t, Float64(z * x)) / 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[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+110], t$95$2, If[LessEqual[t$95$1, 1e+140], N[(N[(a * t + N[(z * x), $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)) < -4.99999999999999978e110 or 1.00000000000000006e140 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 31.1%

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

   2. 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 68.7

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

   4. Applied rewrites 68.7%

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

   if -4.99999999999999978e110 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000006e140

   1. Initial program 99.5%

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

   2. 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. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 60.7

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

   4. Applied rewrites 60.7%

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

Alternative 14: 59.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+153}:\\ \;\;\;\;a + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+230}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.25e+153)
   (+ a (* x (/ (- z a) t)))
   (if (<= t 5.8e+230) (- (+ a z) b) (* a (/ t (+ t x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.25e+153) {
		tmp = a + (x * ((z - a) / t));
	} else if (t <= 5.8e+230) {
		tmp = (a + z) - b;
	} else {
		tmp = a * (t / (t + x));
	}
	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 <= (-1.25d+153)) then
        tmp = a + (x * ((z - a) / t))
    else if (t <= 5.8d+230) then
        tmp = (a + z) - b
    else
        tmp = a * (t / (t + x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.25e+153) {
		tmp = a + (x * ((z - a) / t));
	} else if (t <= 5.8e+230) {
		tmp = (a + z) - b;
	} else {
		tmp = a * (t / (t + x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.25e+153:
		tmp = a + (x * ((z - a) / t))
	elif t <= 5.8e+230:
		tmp = (a + z) - b
	else:
		tmp = a * (t / (t + x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.25e+153)
		tmp = Float64(a + Float64(x * Float64(Float64(z - a) / t)));
	elseif (t <= 5.8e+230)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(a * Float64(t / Float64(t + x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.25e+153)
		tmp = a + (x * ((z - a) / t));
	elseif (t <= 5.8e+230)
		tmp = (a + z) - b;
	else
		tmp = a * (t / (t + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.25e+153], N[(a + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+230], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25000000000000005e153

   1. Initial program 46.6%

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

   2. 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. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 34.2

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

   4. Applied rewrites 34.2%

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

   5. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 61.6

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

   7. Applied rewrites 61.6%

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

   if -1.25000000000000005e153 < t < 5.7999999999999998e230

   1. Initial program 65.1%

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

   2. 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 58.5

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

   4. Applied rewrites 58.5%

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

   if 5.7999999999999998e230 < t

   1. Initial program 41.0%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 32.3%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. div-add-rev N/A

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

      4. lower-/.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lift-+.f64 37.9

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

   7. Applied rewrites 37.9%

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

   8. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 64.2

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

   10. Applied rewrites 64.2%

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

Alternative 15: 58.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{t}{t + x}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+230}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (/ t (+ t x)))))
   (if (<= t -1.25e+153) t_1 (if (<= t 5.8e+230) (- (+ a z) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t / (t + x));
	double tmp;
	if (t <= -1.25e+153) {
		tmp = t_1;
	} else if (t <= 5.8e+230) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t / (t + x))
    if (t <= (-1.25d+153)) then
        tmp = t_1
    else if (t <= 5.8d+230) then
        tmp = (a + z) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t / (t + x));
	double tmp;
	if (t <= -1.25e+153) {
		tmp = t_1;
	} else if (t <= 5.8e+230) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t / (t + x))
	tmp = 0
	if t <= -1.25e+153:
		tmp = t_1
	elif t <= 5.8e+230:
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t / Float64(t + x)))
	tmp = 0.0
	if (t <= -1.25e+153)
		tmp = t_1;
	elseif (t <= 5.8e+230)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t / (t + x));
	tmp = 0.0;
	if (t <= -1.25e+153)
		tmp = t_1;
	elseif (t <= 5.8e+230)
		tmp = (a + z) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e+153], t$95$1, If[LessEqual[t, 5.8e+230], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.25000000000000005e153 or 5.7999999999999998e230 < t

   1. Initial program 44.8%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 36.5%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. div-add-rev N/A

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

      4. lower-/.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lift-+.f64 38.8

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

   7. Applied rewrites 38.8%

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

   8. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 59.0

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

   10. Applied rewrites 59.0%

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

   if -1.25000000000000005e153 < t < 5.7999999999999998e230

   1. Initial program 65.1%

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

   2. 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 58.5

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

   4. Applied rewrites 58.5%

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

Alternative 16: 58.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{t + x}\\ \mathbf{if}\;x \leq -2.45 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+217}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (/ x (+ t x)))))
   (if (<= x -2.45e+114) t_1 (if (<= x 8e+217) (- (+ a z) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x / (t + x));
	double tmp;
	if (x <= -2.45e+114) {
		tmp = t_1;
	} else if (x <= 8e+217) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x / (t + x))
    if (x <= (-2.45d+114)) then
        tmp = t_1
    else if (x <= 8d+217) then
        tmp = (a + z) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x / (t + x));
	double tmp;
	if (x <= -2.45e+114) {
		tmp = t_1;
	} else if (x <= 8e+217) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (x / (t + x))
	tmp = 0
	if x <= -2.45e+114:
		tmp = t_1
	elif x <= 8e+217:
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(x / Float64(t + x)))
	tmp = 0.0
	if (x <= -2.45e+114)
		tmp = t_1;
	elseif (x <= 8e+217)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (x / (t + x));
	tmp = 0.0;
	if (x <= -2.45e+114)
		tmp = t_1;
	elseif (x <= 8e+217)
		tmp = (a + z) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(x / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.45e+114], t$95$1, If[LessEqual[x, 8e+217], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.45e114 or 7.99999999999999968e217 < x

   1. Initial program 46.6%

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

   3. Applied rewrites 56.3%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. div-add-rev N/A

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

      3. lower-/.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lift-+.f64 57.4

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

   6. Applied rewrites 57.4%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 52.6%

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

   10. Taylor expanded in x around inf

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

   12. Applied rewrites 56.5%

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

   if -2.45e114 < x < 7.99999999999999968e217

   1. Initial program 65.6%

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

   2. 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 58.6

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

   4. Applied rewrites 58.6%

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

Alternative 17: 57.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+153}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+224}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.35e+153) a (if (<= t 6e+224) (- (+ a z) b) (+ a z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.35e+153) {
		tmp = a;
	} else if (t <= 6e+224) {
		tmp = (a + z) - b;
	} else {
		tmp = a + 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 <= (-1.35d+153)) then
        tmp = a
    else if (t <= 6d+224) then
        tmp = (a + z) - b
    else
        tmp = a + 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 <= -1.35e+153) {
		tmp = a;
	} else if (t <= 6e+224) {
		tmp = (a + z) - b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.35e+153:
		tmp = a
	elif t <= 6e+224:
		tmp = (a + z) - b
	else:
		tmp = a + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.35e+153)
		tmp = a;
	elseif (t <= 6e+224)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(a + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.35e+153)
		tmp = a;
	elseif (t <= 6e+224)
		tmp = (a + z) - b;
	else
		tmp = a + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.35e+153], a, If[LessEqual[t, 6e+224], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(a + z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35e153

   1. Initial program 46.6%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 53.4%

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

   if -1.35e153 < t < 6.0000000000000002e224

   1. Initial program 65.3%

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

   2. 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 58.5

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

   4. Applied rewrites 58.5%

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

   if 6.0000000000000002e224 < t

   1. Initial program 40.9%

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

   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 35.4

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

   4. Applied rewrites 35.4%

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

   5. Taylor expanded in b around 0

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

      1. lift-+.f64 47.1

         \[\leadsto a + z \]

   7. Applied rewrites 47.1%

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

Alternative 18: 51.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+198}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+90}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5e+198) (- a b) (if (<= b 1.8e+90) (+ a z) (- z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e+198) {
		tmp = a - b;
	} else if (b <= 1.8e+90) {
		tmp = a + z;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5d+198)) then
        tmp = a - b
    else if (b <= 1.8d+90) then
        tmp = a + z
    else
        tmp = z - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e+198) {
		tmp = a - b;
	} else if (b <= 1.8e+90) {
		tmp = a + z;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5e+198:
		tmp = a - b
	elif b <= 1.8e+90:
		tmp = a + z
	else:
		tmp = z - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5e+198)
		tmp = Float64(a - b);
	elseif (b <= 1.8e+90)
		tmp = Float64(a + z);
	else
		tmp = Float64(z - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5e+198)
		tmp = a - b;
	elseif (b <= 1.8e+90)
		tmp = a + z;
	else
		tmp = z - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5e+198], N[(a - b), $MachinePrecision], If[LessEqual[b, 1.8e+90], N[(a + z), $MachinePrecision], N[(z - b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.00000000000000049e198

   1. Initial program 46.8%

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

   2. 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 40.3

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

   4. Applied rewrites 40.3%

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

   5. Taylor expanded in z around 0

      \[\leadsto a - b \]
   6. Step-by-step derivation

   7. Applied rewrites 35.8%

      \[\leadsto a - b \]

   if -5.00000000000000049e198 < b < 1.8e90

   1. Initial program 64.6%

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

   2. 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 59.4

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

   4. Applied rewrites 59.4%

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

   5. Taylor expanded in b around 0

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

      1. lift-+.f64 57.8

         \[\leadsto a + z \]

   7. Applied rewrites 57.8%

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

   if 1.8e90 < b

   1. Initial program 54.5%

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

   2. 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 40.8

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

   4. Applied rewrites 40.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto z - b \]
   6. Step-by-step derivation

   7. Applied rewrites 30.8%

      \[\leadsto z - b \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 47.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+30}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 3700000000:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.8e+30) a (if (<= a 3700000000.0) (- z b) (- a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.8e+30) {
		tmp = a;
	} else if (a <= 3700000000.0) {
		tmp = z - b;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-3.8d+30)) then
        tmp = a
    else if (a <= 3700000000.0d0) then
        tmp = z - b
    else
        tmp = a - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.8e+30) {
		tmp = a;
	} else if (a <= 3700000000.0) {
		tmp = z - b;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.8e+30:
		tmp = a
	elif a <= 3700000000.0:
		tmp = z - b
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.8e+30)
		tmp = a;
	elseif (a <= 3700000000.0)
		tmp = Float64(z - b);
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3.8e+30)
		tmp = a;
	elseif (a <= 3700000000.0)
		tmp = z - b;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.8e+30], a, If[LessEqual[a, 3700000000.0], N[(z - b), $MachinePrecision], N[(a - b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.8000000000000001e30

   1. Initial program 46.9%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 49.1%

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

   if -3.8000000000000001e30 < a < 3.7e9

   1. Initial program 73.2%

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

   2. 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 50.8

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

   4. Applied rewrites 50.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto z - b \]
   6. Step-by-step derivation

   7. Applied rewrites 46.1%

      \[\leadsto z - b \]

   if 3.7e9 < a

   1. Initial program 49.1%

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

   2. 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 59.0

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto a - b \]
   6. Step-by-step derivation

   7. Applied rewrites 50.4%

      \[\leadsto a - b \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 46.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-19}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+170}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -7.2e-19) z (if (<= x 3.7e+170) (- a b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.2e-19) {
		tmp = z;
	} else if (x <= 3.7e+170) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-7.2d-19)) then
        tmp = z
    else if (x <= 3.7d+170) then
        tmp = a - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.2e-19) {
		tmp = z;
	} else if (x <= 3.7e+170) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -7.2e-19:
		tmp = z
	elif x <= 3.7e+170:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -7.2e-19)
		tmp = z;
	elseif (x <= 3.7e+170)
		tmp = Float64(a - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -7.2e-19)
		tmp = z;
	elseif (x <= 3.7e+170)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -7.2e-19], z, If[LessEqual[x, 3.7e+170], N[(a - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -7.2000000000000002e-19 or 3.69999999999999987e170 < x

   1. Initial program 52.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 46.5%

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

   if -7.2000000000000002e-19 < x < 3.69999999999999987e170

   1. Initial program 66.5%

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

   2. 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 60.5

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

   4. Applied rewrites 60.5%

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

   5. Taylor expanded in z around 0

      \[\leadsto a - b \]
   6. Step-by-step derivation

   7. Applied rewrites 46.2%

      \[\leadsto a - b \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 44.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-50}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2100:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.1e-50) a (if (<= a 2100.0) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.1e-50) {
		tmp = a;
	} else if (a <= 2100.0) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.1d-50)) then
        tmp = a
    else if (a <= 2100.0d0) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.1e-50) {
		tmp = a;
	} else if (a <= 2100.0) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.1e-50:
		tmp = a
	elif a <= 2100.0:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.1e-50)
		tmp = a;
	elseif (a <= 2100.0)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.1e-50)
		tmp = a;
	elseif (a <= 2100.0)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.1e-50], a, If[LessEqual[a, 2100.0], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -1.0999999999999999e-50 or 2100 < a

   1. Initial program 51.1%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 46.4%

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

   if -1.0999999999999999e-50 < a < 2100

   1. Initial program 73.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 41.8%

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

Alternative 22: 32.6% accurate, 29.5× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.2%

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

2. Taylor expanded in t around inf

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

4. Applied rewrites 32.6%

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

Reproduce

herbie shell --seed 2025117 
(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)))