Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A

Percentage Accurate: 90.1% → 91.0%

Time: 12.9s

Alternatives: 21

Speedup: 0.6×

• 47.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    code = 2.0d0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 90.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    code = 2.0d0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 91.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(a + b \cdot c\right) \cdot c \leq 10^{+267}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(i, \left(\left(-b\right) \cdot c\right) \cdot c - c \cdot a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \left(\left(c \cdot \left(\frac{a}{b} + c\right)\right) \cdot i\right)\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* (+ a (* b c)) c) 1e+267)
   (* 2.0 (fma i (- (* (* (- b) c) c) (* c a)) (fma t z (* y x))))
   (* (* -2.0 (* (* c (+ (/ a b) c)) i)) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a + (b * c)) * c) <= 1e+267) {
		tmp = 2.0 * fma(i, (((-b * c) * c) - (c * a)), fma(t, z, (y * x)));
	} else {
		tmp = (-2.0 * ((c * ((a / b) + c)) * i)) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(a + Float64(b * c)) * c) <= 1e+267)
		tmp = Float64(2.0 * fma(i, Float64(Float64(Float64(Float64(-b) * c) * c) - Float64(c * a)), fma(t, z, Float64(y * x))));
	else
		tmp = Float64(Float64(-2.0 * Float64(Float64(c * Float64(Float64(a / b) + c)) * i)) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], 1e+267], N[(2.0 * N[(i * N[(N[(N[((-b) * c), $MachinePrecision] * c), $MachinePrecision] - N[(c * a), $MachinePrecision]), $MachinePrecision] + N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-2.0 * N[(N[(c * N[(N[(a / b), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 a (*.f64 b c)) c) < 9.9999999999999997e266

   1. Initial program 93.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   3. Applied rewrites 91.8%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(i, \left(\left(-b\right) \cdot c\right) \cdot c - c \cdot a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)} \]

   if 9.9999999999999997e266 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 75.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   3. Applied rewrites 66.1%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(i, \left(\left(-b\right) \cdot c\right) \cdot c - c \cdot a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)} \]

   4. Taylor expanded in b around 0

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

   6. Applied rewrites 40.5%

      \[\leadsto 2 \cdot \color{blue}{\left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot c\right) \cdot i\right)} \]

   7. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{-2} \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{-2} \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto -2 \cdot \left(\left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      4. associate-*l* N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot \color{blue}{c} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      6. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      7. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      8. lower-*.f64 N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot \color{blue}{c} \]

   9. Applied rewrites 87.0%

      \[\leadsto \color{blue}{\left(\left(i \cdot \mathsf{fma}\left(c, b, a\right)\right) \cdot -2\right) \cdot c} \]

   10. Taylor expanded in b around inf

       \[\leadsto b \cdot \color{blue}{\left(-2 \cdot \left({c}^{2} \cdot i\right) + -2 \cdot \frac{a \cdot \left(c \cdot i\right)}{b}\right)} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left(-2 \cdot \left({c}^{2} \cdot i\right) + -2 \cdot \frac{a \cdot \left(c \cdot i\right)}{b}\right) \cdot b \]

       2. lower-*.f64 N/A

          \[\leadsto \left(-2 \cdot \left({c}^{2} \cdot i\right) + -2 \cdot \frac{a \cdot \left(c \cdot i\right)}{b}\right) \cdot b \]

   12. Applied rewrites 81.0%

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

Alternative 2: 90.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + b \cdot c\right) \cdot c\\ \mathbf{if}\;t\_1 \leq 10^{+267}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - t\_1 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \left(\left(c \cdot \left(\frac{a}{b} + c\right)\right) \cdot i\right)\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ a (* b c)) c)))
   (if (<= t_1 1e+267)
     (* 2.0 (- (+ (* x y) (* z t)) (* t_1 i)))
     (* (* -2.0 (* (* c (+ (/ a b) c)) i)) b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a + (b * c)) * c;
	double tmp;
	if (t_1 <= 1e+267) {
		tmp = 2.0 * (((x * y) + (z * t)) - (t_1 * i));
	} else {
		tmp = (-2.0 * ((c * ((a / b) + c)) * i)) * 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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + (b * c)) * c
    if (t_1 <= 1d+267) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (t_1 * i))
    else
        tmp = ((-2.0d0) * ((c * ((a / b) + c)) * i)) * 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 c, double i) {
	double t_1 = (a + (b * c)) * c;
	double tmp;
	if (t_1 <= 1e+267) {
		tmp = 2.0 * (((x * y) + (z * t)) - (t_1 * i));
	} else {
		tmp = (-2.0 * ((c * ((a / b) + c)) * i)) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a + (b * c)) * c
	tmp = 0
	if t_1 <= 1e+267:
		tmp = 2.0 * (((x * y) + (z * t)) - (t_1 * i))
	else:
		tmp = (-2.0 * ((c * ((a / b) + c)) * i)) * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a + Float64(b * c)) * c)
	tmp = 0.0
	if (t_1 <= 1e+267)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(t_1 * i)));
	else
		tmp = Float64(Float64(-2.0 * Float64(Float64(c * Float64(Float64(a / b) + c)) * i)) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a + (b * c)) * c;
	tmp = 0.0;
	if (t_1 <= 1e+267)
		tmp = 2.0 * (((x * y) + (z * t)) - (t_1 * i));
	else
		tmp = (-2.0 * ((c * ((a / b) + c)) * i)) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+267], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-2.0 * N[(N[(c * N[(N[(a / b), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 a (*.f64 b c)) c) < 9.9999999999999997e266

   1. Initial program 93.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   if 9.9999999999999997e266 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 75.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   3. Applied rewrites 66.1%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(i, \left(\left(-b\right) \cdot c\right) \cdot c - c \cdot a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)} \]

   4. Taylor expanded in b around 0

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

   6. Applied rewrites 40.5%

      \[\leadsto 2 \cdot \color{blue}{\left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot c\right) \cdot i\right)} \]

   7. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{-2} \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{-2} \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto -2 \cdot \left(\left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      4. associate-*l* N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot \color{blue}{c} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      6. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      7. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      8. lower-*.f64 N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot \color{blue}{c} \]

   9. Applied rewrites 87.0%

      \[\leadsto \color{blue}{\left(\left(i \cdot \mathsf{fma}\left(c, b, a\right)\right) \cdot -2\right) \cdot c} \]

   10. Taylor expanded in b around inf

       \[\leadsto b \cdot \color{blue}{\left(-2 \cdot \left({c}^{2} \cdot i\right) + -2 \cdot \frac{a \cdot \left(c \cdot i\right)}{b}\right)} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left(-2 \cdot \left({c}^{2} \cdot i\right) + -2 \cdot \frac{a \cdot \left(c \cdot i\right)}{b}\right) \cdot b \]

       2. lower-*.f64 N/A

          \[\leadsto \left(-2 \cdot \left({c}^{2} \cdot i\right) + -2 \cdot \frac{a \cdot \left(c \cdot i\right)}{b}\right) \cdot b \]

   12. Applied rewrites 81.0%

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

Alternative 3: 88.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, a\right) \cdot i\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+229}:\\ \;\;\;\;\left(-2 \cdot t\_1\right) \cdot c\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+243}:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot c\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x - t\_1 \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (fma c b a) i)) (t_2 (* (* (+ a (* b c)) c) i)))
   (if (<= t_2 -5e+229)
     (* (* -2.0 t_1) c)
     (if (<= t_2 2e+243)
       (* 2.0 (- (fma x y (* z t)) (* (* a c) i)))
       (* 2.0 (- (* y x) (* t_1 c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(c, b, a) * i;
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -5e+229) {
		tmp = (-2.0 * t_1) * c;
	} else if (t_2 <= 2e+243) {
		tmp = 2.0 * (fma(x, y, (z * t)) - ((a * c) * i));
	} else {
		tmp = 2.0 * ((y * x) - (t_1 * c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(fma(c, b, a) * i)
	t_2 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_2 <= -5e+229)
		tmp = Float64(Float64(-2.0 * t_1) * c);
	elseif (t_2 <= 2e+243)
		tmp = Float64(2.0 * Float64(fma(x, y, Float64(z * t)) - Float64(Float64(a * c) * i)));
	else
		tmp = Float64(2.0 * Float64(Float64(y * x) - Float64(t_1 * c)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+229], N[(N[(-2.0 * t$95$1), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t$95$2, 2e+243], N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(a * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(y * x), $MachinePrecision] - N[(t$95$1 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000005e229

   1. Initial program 76.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -2 \cdot \left(\left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      2. associate-*l* N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot \color{blue}{c} \]

      3. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      4. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      5. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      6. lower-*.f64 N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot \color{blue}{c} \]

      7. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      8. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      9. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c \]

      10. lower-*.f64 N/A

          \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c \]

      11. *-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot c \]

      12. lower-*.f64 N/A

          \[\leadsto \left(-2 \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot c \]

      13. +-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(b \cdot c + a\right) \cdot i\right)\right) \cdot c \]

      14. *-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(c \cdot b + a\right) \cdot i\right)\right) \cdot c \]

      15. lower-fma.f64 85.6

          \[\leadsto \left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c \]

   4. Applied rewrites 85.6%

      \[\leadsto \color{blue}{\left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c} \]

   if -5.0000000000000005e229 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 2.0000000000000001e243

   1. Initial program 99.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   3. Applied rewrites 99.3%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(i, \left(\left(-b\right) \cdot c\right) \cdot c - c \cdot a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)} \]

   4. Taylor expanded in b around 0

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

   6. Applied rewrites 91.4%

      \[\leadsto 2 \cdot \color{blue}{\left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot c\right) \cdot i\right)} \]

   if 2.0000000000000001e243 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 79.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

         \[\leadsto 2 \cdot \left(x \cdot y - \color{blue}{c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{c} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{c} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      6. *-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(a + b \cdot c\right) \cdot i\right) \cdot c\right) \]

      7. lower-*.f64 N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(a + b \cdot c\right) \cdot i\right) \cdot c\right) \]

      8. +-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(b \cdot c + a\right) \cdot i\right) \cdot c\right) \]

      9. *-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(c \cdot b + a\right) \cdot i\right) \cdot c\right) \]

      10. lower-fma.f64 85.0

          \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right) \]

   4. Applied rewrites 85.0%

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

Alternative 4: 88.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+229}:\\ \;\;\;\;\left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+303}:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(t, z, y \cdot x\right) - \left(i \cdot c\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \left(\left(c \cdot \left(\frac{a}{b} + c\right)\right) \cdot i\right)\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (<= t_1 -5e+229)
     (* (* -2.0 (* (fma c b a) i)) c)
     (if (<= t_1 4e+303)
       (* 2.0 (- (fma t z (* y x)) (* (* i c) a)))
       (* (* -2.0 (* (* c (+ (/ a b) c)) i)) b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_1 <= -5e+229) {
		tmp = (-2.0 * (fma(c, b, a) * i)) * c;
	} else if (t_1 <= 4e+303) {
		tmp = 2.0 * (fma(t, z, (y * x)) - ((i * c) * a));
	} else {
		tmp = (-2.0 * ((c * ((a / b) + c)) * i)) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_1 <= -5e+229)
		tmp = Float64(Float64(-2.0 * Float64(fma(c, b, a) * i)) * c);
	elseif (t_1 <= 4e+303)
		tmp = Float64(2.0 * Float64(fma(t, z, Float64(y * x)) - Float64(Float64(i * c) * a)));
	else
		tmp = Float64(Float64(-2.0 * Float64(Float64(c * Float64(Float64(a / b) + c)) * i)) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+229], N[(N[(-2.0 * N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t$95$1, 4e+303], N[(2.0 * N[(N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision] - N[(N[(i * c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-2.0 * N[(N[(c * N[(N[(a / b), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000005e229

   1. Initial program 76.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -2 \cdot \left(\left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      2. associate-*l* N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot \color{blue}{c} \]

      3. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      4. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      5. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      6. lower-*.f64 N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot \color{blue}{c} \]

      7. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      8. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      9. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c \]

      10. lower-*.f64 N/A

          \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c \]

      11. *-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot c \]

      12. lower-*.f64 N/A

          \[\leadsto \left(-2 \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot c \]

      13. +-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(b \cdot c + a\right) \cdot i\right)\right) \cdot c \]

      14. *-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(c \cdot b + a\right) \cdot i\right)\right) \cdot c \]

      15. lower-fma.f64 85.6

          \[\leadsto \left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c \]

   4. Applied rewrites 85.6%

      \[\leadsto \color{blue}{\left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c} \]

   if -5.0000000000000005e229 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4e303

   1. Initial program 99.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. cancel-sign-sub-inv N/A

         \[\leadsto 2 \cdot \left(t \cdot z + \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(a\right)\right) \cdot \left(c \cdot i\right)}\right)\right) \]

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

         \[\leadsto 2 \cdot \left(t \cdot z + \left(x \cdot y + \left(\mathsf{neg}\left(a \cdot \left(c \cdot i\right)\right)\right)\right)\right) \]

      4. mul-1-neg N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-+l+ N/A

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

      9. mul-1-neg N/A

         \[\leadsto 2 \cdot \left(t \cdot z + \left(x \cdot y + \left(\mathsf{neg}\left(a \cdot \left(c \cdot i\right)\right)\right)\right)\right) \]

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

          \[\leadsto 2 \cdot \left(t \cdot z + \left(x \cdot y + \left(\mathsf{neg}\left(a\right)\right) \cdot \color{blue}{\left(c \cdot i\right)}\right)\right) \]

      11. cancel-sign-sub-inv N/A

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

      12. associate--l+ N/A

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

      13. lower--.f64 N/A

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

   4. Applied rewrites 89.8%

      \[\leadsto 2 \cdot \color{blue}{\left(\mathsf{fma}\left(t, z, y \cdot x\right) - \left(i \cdot c\right) \cdot a\right)} \]

   if 4e303 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 76.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   3. Applied rewrites 70.5%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(i, \left(\left(-b\right) \cdot c\right) \cdot c - c \cdot a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)} \]

   4. Taylor expanded in b around 0

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

   6. Applied rewrites 45.4%

      \[\leadsto 2 \cdot \color{blue}{\left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot c\right) \cdot i\right)} \]

   7. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{-2} \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{-2} \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto -2 \cdot \left(\left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      4. associate-*l* N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot \color{blue}{c} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      6. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      7. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      8. lower-*.f64 N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot \color{blue}{c} \]

   9. Applied rewrites 89.0%

      \[\leadsto \color{blue}{\left(\left(i \cdot \mathsf{fma}\left(c, b, a\right)\right) \cdot -2\right) \cdot c} \]

   10. Taylor expanded in b around inf

       \[\leadsto b \cdot \color{blue}{\left(-2 \cdot \left({c}^{2} \cdot i\right) + -2 \cdot \frac{a \cdot \left(c \cdot i\right)}{b}\right)} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left(-2 \cdot \left({c}^{2} \cdot i\right) + -2 \cdot \frac{a \cdot \left(c \cdot i\right)}{b}\right) \cdot b \]

       2. lower-*.f64 N/A

          \[\leadsto \left(-2 \cdot \left({c}^{2} \cdot i\right) + -2 \cdot \frac{a \cdot \left(c \cdot i\right)}{b}\right) \cdot b \]

   12. Applied rewrites 85.6%

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

Alternative 5: 82.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y \cdot x - \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-17}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* y x) (* (* (fma c b a) i) c))))
        (t_2 (* (* (+ a (* b c)) c) i)))
   (if (<= t_2 -1e+74) t_1 (if (<= t_2 5e-17) (* 2.0 (fma t z (* y x))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((y * x) - ((fma(c, b, a) * i) * c));
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -1e+74) {
		tmp = t_1;
	} else if (t_2 <= 5e-17) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(y * x) - Float64(Float64(fma(c, b, a) * i) * c)))
	t_2 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_2 <= -1e+74)
		tmp = t_1;
	elseif (t_2 <= 5e-17)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(y * x), $MachinePrecision] - N[(N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+74], t$95$1, If[LessEqual[t$95$2, 5e-17], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -9.99999999999999952e73 or 4.9999999999999999e-17 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 84.3%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

         \[\leadsto 2 \cdot \left(x \cdot y - \color{blue}{c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{c} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{c} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      6. *-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(a + b \cdot c\right) \cdot i\right) \cdot c\right) \]

      7. lower-*.f64 N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(a + b \cdot c\right) \cdot i\right) \cdot c\right) \]

      8. +-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(b \cdot c + a\right) \cdot i\right) \cdot c\right) \]

      9. *-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(c \cdot b + a\right) \cdot i\right) \cdot c\right) \]

      10. lower-fma.f64 78.0

          \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right) \]

   4. Applied rewrites 78.0%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)} \]

   if -9.99999999999999952e73 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.9999999999999999e-17

   1. Initial program 99.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, \color{blue}{z}, x \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

      3. lower-*.f64 90.4

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

   4. Applied rewrites 90.4%

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

Alternative 6: 81.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ t_3 := 2 \cdot \left(y \cdot x - \left(a \cdot c\right) \cdot i\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+74}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-17}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+289}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* -2.0 (* (fma c b a) i)) c))
        (t_2 (* (* (+ a (* b c)) c) i))
        (t_3 (* 2.0 (- (* y x) (* (* a c) i)))))
   (if (<= t_2 -5e+229)
     t_1
     (if (<= t_2 -1e+74)
       t_3
       (if (<= t_2 5e-17)
         (* 2.0 (fma t z (* y x)))
         (if (<= t_2 2e+289) t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (-2.0 * (fma(c, b, a) * i)) * c;
	double t_2 = ((a + (b * c)) * c) * i;
	double t_3 = 2.0 * ((y * x) - ((a * c) * i));
	double tmp;
	if (t_2 <= -5e+229) {
		tmp = t_1;
	} else if (t_2 <= -1e+74) {
		tmp = t_3;
	} else if (t_2 <= 5e-17) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else if (t_2 <= 2e+289) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-2.0 * Float64(fma(c, b, a) * i)) * c)
	t_2 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	t_3 = Float64(2.0 * Float64(Float64(y * x) - Float64(Float64(a * c) * i)))
	tmp = 0.0
	if (t_2 <= -5e+229)
		tmp = t_1;
	elseif (t_2 <= -1e+74)
		tmp = t_3;
	elseif (t_2 <= 5e-17)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	elseif (t_2 <= 2e+289)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(-2.0 * N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(N[(y * x), $MachinePrecision] - N[(N[(a * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+229], t$95$1, If[LessEqual[t$95$2, -1e+74], t$95$3, If[LessEqual[t$95$2, 5e-17], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+289], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000005e229 or 2.0000000000000001e289 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 77.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -2 \cdot \left(\left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      2. associate-*l* N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot \color{blue}{c} \]

      3. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      4. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      5. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      6. lower-*.f64 N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot \color{blue}{c} \]

      7. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      8. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      9. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c \]

      10. lower-*.f64 N/A

          \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c \]

      11. *-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot c \]

      12. lower-*.f64 N/A

          \[\leadsto \left(-2 \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot c \]

      13. +-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(b \cdot c + a\right) \cdot i\right)\right) \cdot c \]

      14. *-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(c \cdot b + a\right) \cdot i\right)\right) \cdot c \]

      15. lower-fma.f64 86.6

          \[\leadsto \left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c \]

   4. Applied rewrites 86.6%

      \[\leadsto \color{blue}{\left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c} \]

   if -5.0000000000000005e229 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -9.99999999999999952e73 or 4.9999999999999999e-17 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 2.0000000000000001e289

   1. Initial program 99.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

         \[\leadsto 2 \cdot \left(x \cdot y - \color{blue}{c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{c} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{c} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      6. *-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(a + b \cdot c\right) \cdot i\right) \cdot c\right) \]

      7. lower-*.f64 N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(a + b \cdot c\right) \cdot i\right) \cdot c\right) \]

      8. +-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(b \cdot c + a\right) \cdot i\right) \cdot c\right) \]

      9. *-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(c \cdot b + a\right) \cdot i\right) \cdot c\right) \]

      10. lower-fma.f64 61.0

          \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right) \]

   4. Applied rewrites 61.0%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)} \]

   5. Taylor expanded in a around inf

      \[\leadsto 2 \cdot \left(y \cdot x - a \cdot \color{blue}{\left(c \cdot i\right)}\right) \]
   6. Step-by-step derivation

      1. *-lft-identity N/A

         \[\leadsto 2 \cdot \left(y \cdot x - 1 \cdot \left(a \cdot \color{blue}{\left(c \cdot i\right)}\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(a \cdot \left(\color{blue}{c} \cdot i\right)\right)\right) \]

      3. distribute-lft-neg-in N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(c \cdot i\right)\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot \left(c \cdot i\right)\right)\right)\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\left(a \cdot c\right) \cdot i\right)\right)\right)\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot c\right)\right) \cdot i\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(\left(-1 \cdot \left(a \cdot c\right)\right) \cdot i\right)\right)\right) \]

      8. distribute-lft-neg-in N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot c\right)\right)\right) \cdot i\right) \]

      9. lower-*.f64 N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot c\right)\right)\right) \cdot i\right) \]

      10. *-commutative N/A

          \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(\left(a \cdot c\right) \cdot -1\right)\right) \cdot i\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(a \cdot c\right) \cdot \left(\mathsf{neg}\left(-1\right)\right)\right) \cdot i\right) \]

      12. metadata-eval N/A

          \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(a \cdot c\right) \cdot 1\right) \cdot i\right) \]

      13. *-rgt-identity N/A

          \[\leadsto 2 \cdot \left(y \cdot x - \left(a \cdot c\right) \cdot i\right) \]

      14. lower-*.f64 54.1

          \[\leadsto 2 \cdot \left(y \cdot x - \left(a \cdot c\right) \cdot i\right) \]

   7. Applied rewrites 54.1%

      \[\leadsto 2 \cdot \left(y \cdot x - \left(a \cdot c\right) \cdot \color{blue}{i}\right) \]

   if -9.99999999999999952e73 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.9999999999999999e-17

   1. Initial program 99.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, \color{blue}{z}, x \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

      3. lower-*.f64 90.4

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

   4. Applied rewrites 90.4%

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

Alternative 7: 81.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+229}:\\ \;\;\;\;\left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+74}:\\ \;\;\;\;2 \cdot \left(y \cdot x - \left(a \cdot c\right) \cdot i\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+110}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(-i\right) \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (<= t_1 -5e+229)
     (* (* -2.0 (* (fma c b a) i)) c)
     (if (<= t_1 -1e+74)
       (* 2.0 (- (* y x) (* (* a c) i)))
       (if (<= t_1 5e+110)
         (* 2.0 (fma t z (* y x)))
         (* 2.0 (* (- i) (* (fma c b a) c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_1 <= -5e+229) {
		tmp = (-2.0 * (fma(c, b, a) * i)) * c;
	} else if (t_1 <= -1e+74) {
		tmp = 2.0 * ((y * x) - ((a * c) * i));
	} else if (t_1 <= 5e+110) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else {
		tmp = 2.0 * (-i * (fma(c, b, a) * c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_1 <= -5e+229)
		tmp = Float64(Float64(-2.0 * Float64(fma(c, b, a) * i)) * c);
	elseif (t_1 <= -1e+74)
		tmp = Float64(2.0 * Float64(Float64(y * x) - Float64(Float64(a * c) * i)));
	elseif (t_1 <= 5e+110)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	else
		tmp = Float64(2.0 * Float64(Float64(-i) * Float64(fma(c, b, a) * c)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+229], N[(N[(-2.0 * N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t$95$1, -1e+74], N[(2.0 * N[(N[(y * x), $MachinePrecision] - N[(N[(a * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+110], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[((-i) * N[(N[(c * b + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000005e229

   1. Initial program 76.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -2 \cdot \left(\left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      2. associate-*l* N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot \color{blue}{c} \]

      3. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      4. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      5. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      6. lower-*.f64 N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot \color{blue}{c} \]

      7. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      8. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      9. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c \]

      10. lower-*.f64 N/A

          \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c \]

      11. *-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot c \]

      12. lower-*.f64 N/A

          \[\leadsto \left(-2 \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot c \]

      13. +-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(b \cdot c + a\right) \cdot i\right)\right) \cdot c \]

      14. *-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(c \cdot b + a\right) \cdot i\right)\right) \cdot c \]

      15. lower-fma.f64 85.6

          \[\leadsto \left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c \]

   4. Applied rewrites 85.6%

      \[\leadsto \color{blue}{\left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c} \]

   if -5.0000000000000005e229 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -9.99999999999999952e73

   1. Initial program 99.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

         \[\leadsto 2 \cdot \left(x \cdot y - \color{blue}{c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{c} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{c} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      6. *-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(a + b \cdot c\right) \cdot i\right) \cdot c\right) \]

      7. lower-*.f64 N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(a + b \cdot c\right) \cdot i\right) \cdot c\right) \]

      8. +-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(b \cdot c + a\right) \cdot i\right) \cdot c\right) \]

      9. *-commutative N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(c \cdot b + a\right) \cdot i\right) \cdot c\right) \]

      10. lower-fma.f64 61.7

          \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right) \]

   4. Applied rewrites 61.7%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)} \]

   5. Taylor expanded in a around inf

      \[\leadsto 2 \cdot \left(y \cdot x - a \cdot \color{blue}{\left(c \cdot i\right)}\right) \]
   6. Step-by-step derivation

      1. *-lft-identity N/A

         \[\leadsto 2 \cdot \left(y \cdot x - 1 \cdot \left(a \cdot \color{blue}{\left(c \cdot i\right)}\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(a \cdot \left(\color{blue}{c} \cdot i\right)\right)\right) \]

      3. distribute-lft-neg-in N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(c \cdot i\right)\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot \left(c \cdot i\right)\right)\right)\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\left(a \cdot c\right) \cdot i\right)\right)\right)\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot c\right)\right) \cdot i\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(\left(-1 \cdot \left(a \cdot c\right)\right) \cdot i\right)\right)\right) \]

      8. distribute-lft-neg-in N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot c\right)\right)\right) \cdot i\right) \]

      9. lower-*.f64 N/A

         \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot c\right)\right)\right) \cdot i\right) \]

      10. *-commutative N/A

          \[\leadsto 2 \cdot \left(y \cdot x - \left(\mathsf{neg}\left(\left(a \cdot c\right) \cdot -1\right)\right) \cdot i\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(a \cdot c\right) \cdot \left(\mathsf{neg}\left(-1\right)\right)\right) \cdot i\right) \]

      12. metadata-eval N/A

          \[\leadsto 2 \cdot \left(y \cdot x - \left(\left(a \cdot c\right) \cdot 1\right) \cdot i\right) \]

      13. *-rgt-identity N/A

          \[\leadsto 2 \cdot \left(y \cdot x - \left(a \cdot c\right) \cdot i\right) \]

      14. lower-*.f64 52.0

          \[\leadsto 2 \cdot \left(y \cdot x - \left(a \cdot c\right) \cdot i\right) \]

   7. Applied rewrites 52.0%

      \[\leadsto 2 \cdot \left(y \cdot x - \left(a \cdot c\right) \cdot \color{blue}{i}\right) \]

   if -9.99999999999999952e73 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999978e110

   1. Initial program 99.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, \color{blue}{z}, x \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

      3. lower-*.f64 87.6

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

   4. Applied rewrites 87.6%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(t, z, y \cdot x\right)} \]

   if 4.99999999999999978e110 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 83.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in i around inf

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 2 \cdot \left(\mathsf{neg}\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right) \]

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

         \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(c\right)\right) \cdot \color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto 2 \cdot \left(\left(-1 \cdot c\right) \cdot \left(\color{blue}{i} \cdot \left(a + b \cdot c\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto 2 \cdot \left(\left(-1 \cdot c\right) \cdot \left(\left(a + b \cdot c\right) \cdot \color{blue}{i}\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto 2 \cdot \left(\left(\left(-1 \cdot c\right) \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{i}\right) \]

      6. associate-*r* N/A

         \[\leadsto 2 \cdot \left(\left(-1 \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right) \cdot i\right) \]

      7. mul-1-neg N/A

         \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(c \cdot \left(a + b \cdot c\right)\right)\right) \cdot i\right) \]

      8. *-commutative N/A

         \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(a + b \cdot c\right) \cdot c\right)\right) \cdot i\right) \]

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

         \[\leadsto 2 \cdot \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      10. *-commutative N/A

          \[\leadsto 2 \cdot \left(\mathsf{neg}\left(i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)\right)\right) \]

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

          \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(i\right)\right) \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right)}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(i\right)\right) \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right)}\right) \]

      13. lower-neg.f64 N/A

          \[\leadsto 2 \cdot \left(\left(-i\right) \cdot \left(\color{blue}{\left(a + b \cdot c\right)} \cdot c\right)\right) \]

      14. lift-+.f64 N/A

          \[\leadsto 2 \cdot \left(\left(-i\right) \cdot \left(\left(a + b \cdot c\right) \cdot c\right)\right) \]

      15. lift-*.f64 N/A

          \[\leadsto 2 \cdot \left(\left(-i\right) \cdot \left(\left(a + b \cdot c\right) \cdot c\right)\right) \]

      16. lift-*.f64 76.6

          \[\leadsto 2 \cdot \left(\left(-i\right) \cdot \left(\left(a + b \cdot c\right) \cdot \color{blue}{c}\right)\right) \]

      17. lift-*.f64 N/A

          \[\leadsto 2 \cdot \left(\left(-i\right) \cdot \left(\left(a + b \cdot c\right) \cdot c\right)\right) \]

      18. lift-+.f64 N/A

          \[\leadsto 2 \cdot \left(\left(-i\right) \cdot \left(\left(a + b \cdot c\right) \cdot c\right)\right) \]

      19. +-commutative N/A

          \[\leadsto 2 \cdot \left(\left(-i\right) \cdot \left(\left(b \cdot c + a\right) \cdot c\right)\right) \]

      20. *-commutative N/A

          \[\leadsto 2 \cdot \left(\left(-i\right) \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\right) \]

      21. lower-fma.f64 76.6

          \[\leadsto 2 \cdot \left(\left(-i\right) \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot c\right)\right) \]

   4. Applied rewrites 76.6%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(-i\right) \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot c\right)\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 79.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+74}:\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(a \cdot c\right) \cdot i\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-9}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* -2.0 (* (fma c b a) i)) c)) (t_2 (* (* (+ a (* b c)) c) i)))
   (if (<= t_2 -1e+205)
     t_1
     (if (<= t_2 -1e+74)
       (* 2.0 (- (* t z) (* (* a c) i)))
       (if (<= t_2 5e-9) (* 2.0 (fma t z (* y x))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (-2.0 * (fma(c, b, a) * i)) * c;
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -1e+205) {
		tmp = t_1;
	} else if (t_2 <= -1e+74) {
		tmp = 2.0 * ((t * z) - ((a * c) * i));
	} else if (t_2 <= 5e-9) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-2.0 * Float64(fma(c, b, a) * i)) * c)
	t_2 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_2 <= -1e+205)
		tmp = t_1;
	elseif (t_2 <= -1e+74)
		tmp = Float64(2.0 * Float64(Float64(t * z) - Float64(Float64(a * c) * i)));
	elseif (t_2 <= 5e-9)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(-2.0 * N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+205], t$95$1, If[LessEqual[t$95$2, -1e+74], N[(2.0 * N[(N[(t * z), $MachinePrecision] - N[(N[(a * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e-9], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -1.00000000000000002e205 or 5.0000000000000001e-9 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 82.6%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -2 \cdot \left(\left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      2. associate-*l* N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot \color{blue}{c} \]

      3. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      4. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      5. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      6. lower-*.f64 N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot \color{blue}{c} \]

      7. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      8. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      9. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c \]

      10. lower-*.f64 N/A

          \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c \]

      11. *-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot c \]

      12. lower-*.f64 N/A

          \[\leadsto \left(-2 \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot c \]

      13. +-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(b \cdot c + a\right) \cdot i\right)\right) \cdot c \]

      14. *-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(c \cdot b + a\right) \cdot i\right)\right) \cdot c \]

      15. lower-fma.f64 74.6

          \[\leadsto \left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c \]

   4. Applied rewrites 74.6%

      \[\leadsto \color{blue}{\left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c} \]

   if -1.00000000000000002e205 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -9.99999999999999952e73

   1. Initial program 99.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   3. Applied rewrites 99.1%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(i, \left(\left(-b\right) \cdot c\right) \cdot c - c \cdot a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)} \]

   4. Taylor expanded in b around 0

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

   6. Applied rewrites 76.8%

      \[\leadsto 2 \cdot \color{blue}{\left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot c\right) \cdot i\right)} \]

   7. Taylor expanded in x around 0

      \[\leadsto 2 \cdot \left(t \cdot z - \color{blue}{\left(a \cdot c\right)} \cdot i\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 55.0

         \[\leadsto 2 \cdot \left(t \cdot z - \left(a \cdot \color{blue}{c}\right) \cdot i\right) \]

   9. Applied rewrites 55.0%

      \[\leadsto 2 \cdot \left(t \cdot z - \color{blue}{\left(a \cdot c\right)} \cdot i\right) \]

   if -9.99999999999999952e73 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.0000000000000001e-9

   1. Initial program 99.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, \color{blue}{z}, x \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

      3. lower-*.f64 90.3

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

   4. Applied rewrites 90.3%

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

Alternative 9: 79.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-9}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* -2.0 (* (fma c b a) i)) c)) (t_2 (* (* (+ a (* b c)) c) i)))
   (if (<= t_2 -5e+179) t_1 (if (<= t_2 5e-9) (* 2.0 (fma t z (* y x))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (-2.0 * (fma(c, b, a) * i)) * c;
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -5e+179) {
		tmp = t_1;
	} else if (t_2 <= 5e-9) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-2.0 * Float64(fma(c, b, a) * i)) * c)
	t_2 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_2 <= -5e+179)
		tmp = t_1;
	elseif (t_2 <= 5e-9)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(-2.0 * N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+179], t$95$1, If[LessEqual[t$95$2, 5e-9], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5e179 or 5.0000000000000001e-9 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 82.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -2 \cdot \left(\left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      2. associate-*l* N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot \color{blue}{c} \]

      3. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      4. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      5. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      6. lower-*.f64 N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot \color{blue}{c} \]

      7. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      8. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      9. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c \]

      10. lower-*.f64 N/A

          \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c \]

      11. *-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot c \]

      12. lower-*.f64 N/A

          \[\leadsto \left(-2 \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot c \]

      13. +-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(b \cdot c + a\right) \cdot i\right)\right) \cdot c \]

      14. *-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(c \cdot b + a\right) \cdot i\right)\right) \cdot c \]

      15. lower-fma.f64 74.2

          \[\leadsto \left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c \]

   4. Applied rewrites 74.2%

      \[\leadsto \color{blue}{\left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c} \]

   if -5e179 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.0000000000000001e-9

   1. Initial program 99.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, \color{blue}{z}, x \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

      3. lower-*.f64 86.3

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

   4. Applied rewrites 86.3%

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

Alternative 10: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+229}:\\ \;\;\;\;\left(\left(\left(\left(-i\right) \cdot b\right) \cdot c\right) \cdot c\right) \cdot 2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+303}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(i \cdot c\right) \cdot b\right) \cdot -2\right) \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (<= t_1 -5e+229)
     (* (* (* (* (- i) b) c) c) 2.0)
     (if (<= t_1 4e+303)
       (* 2.0 (fma t z (* y x)))
       (* (* (* (* i c) b) -2.0) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_1 <= -5e+229) {
		tmp = (((-i * b) * c) * c) * 2.0;
	} else if (t_1 <= 4e+303) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else {
		tmp = (((i * c) * b) * -2.0) * c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_1 <= -5e+229)
		tmp = Float64(Float64(Float64(Float64(Float64(-i) * b) * c) * c) * 2.0);
	elseif (t_1 <= 4e+303)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	else
		tmp = Float64(Float64(Float64(Float64(i * c) * b) * -2.0) * c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+229], N[(N[(N[(N[((-i) * b), $MachinePrecision] * c), $MachinePrecision] * c), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[t$95$1, 4e+303], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(i * c), $MachinePrecision] * b), $MachinePrecision] * -2.0), $MachinePrecision] * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000005e229

   1. Initial program 76.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left({c}^{2} \cdot i\right)\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto 2 \cdot \left(\left(-1 \cdot b\right) \cdot \color{blue}{\left({c}^{2} \cdot i\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(\color{blue}{{c}^{2}} \cdot i\right)\right) \]

      3. *-commutative N/A

         \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(i \cdot \color{blue}{{c}^{2}}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto 2 \cdot \left(\left(\left(\mathsf{neg}\left(b\right)\right) \cdot i\right) \cdot \color{blue}{{c}^{2}}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto 2 \cdot \left(\left(\left(\mathsf{neg}\left(b\right)\right) \cdot i\right) \cdot \color{blue}{{c}^{2}}\right) \]

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

         \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(b \cdot i\right)\right) \cdot {\color{blue}{c}}^{2}\right) \]

      7. *-commutative N/A

         \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(i \cdot b\right)\right) \cdot {c}^{2}\right) \]

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

         \[\leadsto 2 \cdot \left(\left(\left(\mathsf{neg}\left(i\right)\right) \cdot b\right) \cdot {\color{blue}{c}}^{2}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto 2 \cdot \left(\left(\left(\mathsf{neg}\left(i\right)\right) \cdot b\right) \cdot {\color{blue}{c}}^{2}\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto 2 \cdot \left(\left(\left(-i\right) \cdot b\right) \cdot {c}^{2}\right) \]

      11. unpow2 N/A

          \[\leadsto 2 \cdot \left(\left(\left(-i\right) \cdot b\right) \cdot \left(c \cdot \color{blue}{c}\right)\right) \]

      12. lower-*.f64 64.9

          \[\leadsto 2 \cdot \left(\left(\left(-i\right) \cdot b\right) \cdot \left(c \cdot \color{blue}{c}\right)\right) \]

   4. Applied rewrites 64.9%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(\left(-i\right) \cdot b\right) \cdot \left(c \cdot c\right)\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \left(\left(\left(-i\right) \cdot b\right) \cdot \left(c \cdot c\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(-i\right) \cdot b\right) \cdot \left(c \cdot c\right)\right) \cdot 2} \]

      3. lower-*.f64 64.9

         \[\leadsto \color{blue}{\left(\left(\left(-i\right) \cdot b\right) \cdot \left(c \cdot c\right)\right) \cdot 2} \]

   6. Applied rewrites 66.4%

      \[\leadsto \color{blue}{\left(\left(\left(\left(-i\right) \cdot b\right) \cdot c\right) \cdot c\right) \cdot 2} \]

   if -5.0000000000000005e229 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4e303

   1. Initial program 99.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, \color{blue}{z}, x \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

      3. lower-*.f64 77.6

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

   4. Applied rewrites 77.6%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(t, z, y \cdot x\right)} \]

   if 4e303 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 76.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{-2 \cdot \left(b \cdot \left({c}^{2} \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-2 \cdot b\right) \cdot \color{blue}{\left({c}^{2} \cdot i\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(-2 \cdot b\right) \cdot \left(i \cdot \color{blue}{{c}^{2}}\right) \]

      3. unpow2 N/A

         \[\leadsto \left(-2 \cdot b\right) \cdot \left(i \cdot \left(c \cdot \color{blue}{c}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \left(-2 \cdot b\right) \cdot \left(\left(i \cdot c\right) \cdot \color{blue}{c}\right) \]

      5. *-commutative N/A

         \[\leadsto \left(-2 \cdot b\right) \cdot \left(\left(c \cdot i\right) \cdot c\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\left(-2 \cdot b\right) \cdot \left(c \cdot i\right)\right) \cdot \color{blue}{c} \]

      7. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      8. lower-*.f64 N/A

         \[\leadsto \left(-2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot \color{blue}{c} \]

      9. *-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(c \cdot i\right)\right) \cdot -2\right) \cdot c \]

      10. lower-*.f64 N/A

          \[\leadsto \left(\left(b \cdot \left(c \cdot i\right)\right) \cdot -2\right) \cdot c \]

      11. *-commutative N/A

          \[\leadsto \left(\left(\left(c \cdot i\right) \cdot b\right) \cdot -2\right) \cdot c \]

      12. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(c \cdot i\right) \cdot b\right) \cdot -2\right) \cdot c \]

      13. *-commutative N/A

          \[\leadsto \left(\left(\left(i \cdot c\right) \cdot b\right) \cdot -2\right) \cdot c \]

      14. lower-*.f64 71.5

          \[\leadsto \left(\left(\left(i \cdot c\right) \cdot b\right) \cdot -2\right) \cdot c \]

   4. Applied rewrites 71.5%

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

Alternative 11: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+229}:\\ \;\;\;\;\left(\left(i \cdot \left(c \cdot b\right)\right) \cdot -2\right) \cdot c\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+303}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(i \cdot c\right) \cdot b\right) \cdot -2\right) \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (<= t_1 -5e+229)
     (* (* (* i (* c b)) -2.0) c)
     (if (<= t_1 4e+303)
       (* 2.0 (fma t z (* y x)))
       (* (* (* (* i c) b) -2.0) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_1 <= -5e+229) {
		tmp = ((i * (c * b)) * -2.0) * c;
	} else if (t_1 <= 4e+303) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else {
		tmp = (((i * c) * b) * -2.0) * c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_1 <= -5e+229)
		tmp = Float64(Float64(Float64(i * Float64(c * b)) * -2.0) * c);
	elseif (t_1 <= 4e+303)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	else
		tmp = Float64(Float64(Float64(Float64(i * c) * b) * -2.0) * c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+229], N[(N[(N[(i * N[(c * b), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t$95$1, 4e+303], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(i * c), $MachinePrecision] * b), $MachinePrecision] * -2.0), $MachinePrecision] * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000005e229

   1. Initial program 76.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   3. Applied rewrites 69.7%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(i, \left(\left(-b\right) \cdot c\right) \cdot c - c \cdot a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)} \]

   4. Taylor expanded in b around 0

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

   6. Applied rewrites 42.6%

      \[\leadsto 2 \cdot \color{blue}{\left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot c\right) \cdot i\right)} \]

   7. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{-2} \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{-2} \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto -2 \cdot \left(\left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      4. associate-*l* N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot \color{blue}{c} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      6. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      7. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      8. lower-*.f64 N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot \color{blue}{c} \]

   9. Applied rewrites 85.6%

      \[\leadsto \color{blue}{\left(\left(i \cdot \mathsf{fma}\left(c, b, a\right)\right) \cdot -2\right) \cdot c} \]

   10. Taylor expanded in a around 0

       \[\leadsto \left(\left(i \cdot \left(b \cdot c\right)\right) \cdot -2\right) \cdot c \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left(\left(i \cdot \left(c \cdot b\right)\right) \cdot -2\right) \cdot c \]

       2. lower-*.f64 66.0

          \[\leadsto \left(\left(i \cdot \left(c \cdot b\right)\right) \cdot -2\right) \cdot c \]

   12. Applied rewrites 66.0%

       \[\leadsto \left(\left(i \cdot \left(c \cdot b\right)\right) \cdot -2\right) \cdot c \]

   if -5.0000000000000005e229 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4e303

   1. Initial program 99.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, \color{blue}{z}, x \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

      3. lower-*.f64 77.6

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

   4. Applied rewrites 77.6%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(t, z, y \cdot x\right)} \]

   if 4e303 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 76.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{-2 \cdot \left(b \cdot \left({c}^{2} \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-2 \cdot b\right) \cdot \color{blue}{\left({c}^{2} \cdot i\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(-2 \cdot b\right) \cdot \left(i \cdot \color{blue}{{c}^{2}}\right) \]

      3. unpow2 N/A

         \[\leadsto \left(-2 \cdot b\right) \cdot \left(i \cdot \left(c \cdot \color{blue}{c}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \left(-2 \cdot b\right) \cdot \left(\left(i \cdot c\right) \cdot \color{blue}{c}\right) \]

      5. *-commutative N/A

         \[\leadsto \left(-2 \cdot b\right) \cdot \left(\left(c \cdot i\right) \cdot c\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\left(-2 \cdot b\right) \cdot \left(c \cdot i\right)\right) \cdot \color{blue}{c} \]

      7. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      8. lower-*.f64 N/A

         \[\leadsto \left(-2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot \color{blue}{c} \]

      9. *-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(c \cdot i\right)\right) \cdot -2\right) \cdot c \]

      10. lower-*.f64 N/A

          \[\leadsto \left(\left(b \cdot \left(c \cdot i\right)\right) \cdot -2\right) \cdot c \]

      11. *-commutative N/A

          \[\leadsto \left(\left(\left(c \cdot i\right) \cdot b\right) \cdot -2\right) \cdot c \]

      12. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(c \cdot i\right) \cdot b\right) \cdot -2\right) \cdot c \]

      13. *-commutative N/A

          \[\leadsto \left(\left(\left(i \cdot c\right) \cdot b\right) \cdot -2\right) \cdot c \]

      14. lower-*.f64 71.5

          \[\leadsto \left(\left(\left(i \cdot c\right) \cdot b\right) \cdot -2\right) \cdot c \]

   4. Applied rewrites 71.5%

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

Alternative 12: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+229}:\\ \;\;\;\;\left(\left(i \cdot \left(c \cdot b\right)\right) \cdot -2\right) \cdot c\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+303}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (<= t_1 -5e+229)
     (* (* (* i (* c b)) -2.0) c)
     (if (<= t_1 4e+303)
       (* 2.0 (fma t z (* y x)))
       (* (* (* (* c c) i) b) -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_1 <= -5e+229) {
		tmp = ((i * (c * b)) * -2.0) * c;
	} else if (t_1 <= 4e+303) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else {
		tmp = (((c * c) * i) * b) * -2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_1 <= -5e+229)
		tmp = Float64(Float64(Float64(i * Float64(c * b)) * -2.0) * c);
	elseif (t_1 <= 4e+303)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	else
		tmp = Float64(Float64(Float64(Float64(c * c) * i) * b) * -2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+229], N[(N[(N[(i * N[(c * b), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t$95$1, 4e+303], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(c * c), $MachinePrecision] * i), $MachinePrecision] * b), $MachinePrecision] * -2.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000005e229

   1. Initial program 76.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   3. Applied rewrites 69.7%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(i, \left(\left(-b\right) \cdot c\right) \cdot c - c \cdot a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)} \]

   4. Taylor expanded in b around 0

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

   6. Applied rewrites 42.6%

      \[\leadsto 2 \cdot \color{blue}{\left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot c\right) \cdot i\right)} \]

   7. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{-2} \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{-2} \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto -2 \cdot \left(\left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      4. associate-*l* N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot \color{blue}{c} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      6. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      7. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      8. lower-*.f64 N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot \color{blue}{c} \]

   9. Applied rewrites 85.6%

      \[\leadsto \color{blue}{\left(\left(i \cdot \mathsf{fma}\left(c, b, a\right)\right) \cdot -2\right) \cdot c} \]

   10. Taylor expanded in a around 0

       \[\leadsto \left(\left(i \cdot \left(b \cdot c\right)\right) \cdot -2\right) \cdot c \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left(\left(i \cdot \left(c \cdot b\right)\right) \cdot -2\right) \cdot c \]

       2. lower-*.f64 66.0

          \[\leadsto \left(\left(i \cdot \left(c \cdot b\right)\right) \cdot -2\right) \cdot c \]

   12. Applied rewrites 66.0%

       \[\leadsto \left(\left(i \cdot \left(c \cdot b\right)\right) \cdot -2\right) \cdot c \]

   if -5.0000000000000005e229 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4e303

   1. Initial program 99.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, \color{blue}{z}, x \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

      3. lower-*.f64 77.6

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

   4. Applied rewrites 77.6%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(t, z, y \cdot x\right)} \]

   if 4e303 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 76.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   3. Applied rewrites 70.5%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(i, \left(\left(-b\right) \cdot c\right) \cdot c - c \cdot a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)} \]

   4. Taylor expanded in b around inf

      \[\leadsto \color{blue}{-2 \cdot \left(b \cdot \left({c}^{2} \cdot i\right)\right)} \]

   6. Applied rewrites 71.1%

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

Alternative 13: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+229}:\\ \;\;\;\;\left(\left(i \cdot \left(c \cdot b\right)\right) \cdot -2\right) \cdot c\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+303}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(i \cdot b\right) \cdot \left(c \cdot c\right)\right) \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (<= t_1 -5e+229)
     (* (* (* i (* c b)) -2.0) c)
     (if (<= t_1 4e+303)
       (* 2.0 (fma t z (* y x)))
       (* (* (* i b) (* c c)) -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_1 <= -5e+229) {
		tmp = ((i * (c * b)) * -2.0) * c;
	} else if (t_1 <= 4e+303) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else {
		tmp = ((i * b) * (c * c)) * -2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_1 <= -5e+229)
		tmp = Float64(Float64(Float64(i * Float64(c * b)) * -2.0) * c);
	elseif (t_1 <= 4e+303)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	else
		tmp = Float64(Float64(Float64(i * b) * Float64(c * c)) * -2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+229], N[(N[(N[(i * N[(c * b), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t$95$1, 4e+303], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(i * b), $MachinePrecision] * N[(c * c), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000005e229

   1. Initial program 76.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   3. Applied rewrites 69.7%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(i, \left(\left(-b\right) \cdot c\right) \cdot c - c \cdot a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)} \]

   4. Taylor expanded in b around 0

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

   6. Applied rewrites 42.6%

      \[\leadsto 2 \cdot \color{blue}{\left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot c\right) \cdot i\right)} \]

   7. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{-2} \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{-2} \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto -2 \cdot \left(\left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{c}\right) \]

      4. associate-*l* N/A

         \[\leadsto \left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot \color{blue}{c} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \left(b \cdot c\right) \cdot i\right)\right) \cdot c \]

      6. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      7. distribute-lft-out N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c \]

      8. lower-*.f64 N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot \color{blue}{c} \]

   9. Applied rewrites 85.6%

      \[\leadsto \color{blue}{\left(\left(i \cdot \mathsf{fma}\left(c, b, a\right)\right) \cdot -2\right) \cdot c} \]

   10. Taylor expanded in a around 0

       \[\leadsto \left(\left(i \cdot \left(b \cdot c\right)\right) \cdot -2\right) \cdot c \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left(\left(i \cdot \left(c \cdot b\right)\right) \cdot -2\right) \cdot c \]

       2. lower-*.f64 66.0

          \[\leadsto \left(\left(i \cdot \left(c \cdot b\right)\right) \cdot -2\right) \cdot c \]

   12. Applied rewrites 66.0%

       \[\leadsto \left(\left(i \cdot \left(c \cdot b\right)\right) \cdot -2\right) \cdot c \]

   if -5.0000000000000005e229 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4e303

   1. Initial program 99.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, \color{blue}{z}, x \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

      3. lower-*.f64 77.6

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

   4. Applied rewrites 77.6%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(t, z, y \cdot x\right)} \]

   if 4e303 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 76.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   3. Applied rewrites 70.5%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(i, \left(\left(-b\right) \cdot c\right) \cdot c - c \cdot a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)} \]

   4. Taylor expanded in b around inf

      \[\leadsto \color{blue}{-2 \cdot \left(b \cdot \left({c}^{2} \cdot i\right)\right)} \]

   6. Applied rewrites 71.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2 \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2 \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2 \]

      4. *-commutative N/A

         \[\leadsto \left(b \cdot \left(\left(c \cdot c\right) \cdot i\right)\right) \cdot -2 \]

      5. pow2 N/A

         \[\leadsto \left(b \cdot \left({c}^{2} \cdot i\right)\right) \cdot -2 \]

      6. *-commutative N/A

         \[\leadsto \left(b \cdot \left(i \cdot {c}^{2}\right)\right) \cdot -2 \]

      7. associate-*r* N/A

         \[\leadsto \left(\left(b \cdot i\right) \cdot {c}^{2}\right) \cdot -2 \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(b \cdot i\right) \cdot {c}^{2}\right) \cdot -2 \]

      9. *-commutative N/A

         \[\leadsto \left(\left(i \cdot b\right) \cdot {c}^{2}\right) \cdot -2 \]

      10. lower-*.f64 N/A

          \[\leadsto \left(\left(i \cdot b\right) \cdot {c}^{2}\right) \cdot -2 \]

      11. pow2 N/A

          \[\leadsto \left(\left(i \cdot b\right) \cdot \left(c \cdot c\right)\right) \cdot -2 \]

      12. lift-*.f64 69.7

          \[\leadsto \left(\left(i \cdot b\right) \cdot \left(c \cdot c\right)\right) \cdot -2 \]

   8. Applied rewrites 69.7%

      \[\leadsto \left(\left(i \cdot b\right) \cdot \left(c \cdot c\right)\right) \cdot -2 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+229}:\\ \;\;\;\;\left(\left(c \cdot b\right) \cdot \left(i \cdot c\right)\right) \cdot -2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+303}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(i \cdot b\right) \cdot \left(c \cdot c\right)\right) \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (<= t_1 -5e+229)
     (* (* (* c b) (* i c)) -2.0)
     (if (<= t_1 4e+303)
       (* 2.0 (fma t z (* y x)))
       (* (* (* i b) (* c c)) -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_1 <= -5e+229) {
		tmp = ((c * b) * (i * c)) * -2.0;
	} else if (t_1 <= 4e+303) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else {
		tmp = ((i * b) * (c * c)) * -2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_1 <= -5e+229)
		tmp = Float64(Float64(Float64(c * b) * Float64(i * c)) * -2.0);
	elseif (t_1 <= 4e+303)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	else
		tmp = Float64(Float64(Float64(i * b) * Float64(c * c)) * -2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+229], N[(N[(N[(c * b), $MachinePrecision] * N[(i * c), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[t$95$1, 4e+303], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(i * b), $MachinePrecision] * N[(c * c), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000005e229

   1. Initial program 76.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   3. Applied rewrites 69.7%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(i, \left(\left(-b\right) \cdot c\right) \cdot c - c \cdot a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)} \]

   4. Taylor expanded in b around inf

      \[\leadsto \color{blue}{-2 \cdot \left(b \cdot \left({c}^{2} \cdot i\right)\right)} \]

   6. Applied rewrites 67.2%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2 \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2 \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2 \]

      4. *-commutative N/A

         \[\leadsto \left(b \cdot \left(\left(c \cdot c\right) \cdot i\right)\right) \cdot -2 \]

      5. associate-*l* N/A

         \[\leadsto \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2 \]

      6. associate-*r* N/A

         \[\leadsto \left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot -2 \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot -2 \]

      8. *-commutative N/A

         \[\leadsto \left(\left(c \cdot b\right) \cdot \left(c \cdot i\right)\right) \cdot -2 \]

      9. lower-*.f64 N/A

         \[\leadsto \left(\left(c \cdot b\right) \cdot \left(c \cdot i\right)\right) \cdot -2 \]

      10. *-commutative N/A

          \[\leadsto \left(\left(c \cdot b\right) \cdot \left(i \cdot c\right)\right) \cdot -2 \]

      11. lower-*.f64 67.0

          \[\leadsto \left(\left(c \cdot b\right) \cdot \left(i \cdot c\right)\right) \cdot -2 \]

   8. Applied rewrites 67.0%

      \[\leadsto \left(\left(c \cdot b\right) \cdot \left(i \cdot c\right)\right) \cdot -2 \]

   if -5.0000000000000005e229 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4e303

   1. Initial program 99.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, \color{blue}{z}, x \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

      3. lower-*.f64 77.6

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

   4. Applied rewrites 77.6%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(t, z, y \cdot x\right)} \]

   if 4e303 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 76.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   3. Applied rewrites 70.5%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(i, \left(\left(-b\right) \cdot c\right) \cdot c - c \cdot a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)} \]

   4. Taylor expanded in b around inf

      \[\leadsto \color{blue}{-2 \cdot \left(b \cdot \left({c}^{2} \cdot i\right)\right)} \]

   6. Applied rewrites 71.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2 \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2 \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2 \]

      4. *-commutative N/A

         \[\leadsto \left(b \cdot \left(\left(c \cdot c\right) \cdot i\right)\right) \cdot -2 \]

      5. pow2 N/A

         \[\leadsto \left(b \cdot \left({c}^{2} \cdot i\right)\right) \cdot -2 \]

      6. *-commutative N/A

         \[\leadsto \left(b \cdot \left(i \cdot {c}^{2}\right)\right) \cdot -2 \]

      7. associate-*r* N/A

         \[\leadsto \left(\left(b \cdot i\right) \cdot {c}^{2}\right) \cdot -2 \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(b \cdot i\right) \cdot {c}^{2}\right) \cdot -2 \]

      9. *-commutative N/A

         \[\leadsto \left(\left(i \cdot b\right) \cdot {c}^{2}\right) \cdot -2 \]

      10. lower-*.f64 N/A

          \[\leadsto \left(\left(i \cdot b\right) \cdot {c}^{2}\right) \cdot -2 \]

      11. pow2 N/A

          \[\leadsto \left(\left(i \cdot b\right) \cdot \left(c \cdot c\right)\right) \cdot -2 \]

      12. lift-*.f64 69.7

          \[\leadsto \left(\left(i \cdot b\right) \cdot \left(c \cdot c\right)\right) \cdot -2 \]

   8. Applied rewrites 69.7%

      \[\leadsto \left(\left(i \cdot b\right) \cdot \left(c \cdot c\right)\right) \cdot -2 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(c \cdot b\right) \cdot \left(i \cdot c\right)\right) \cdot -2\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+303}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (* c b) (* i c)) -2.0)) (t_2 (* (* (+ a (* b c)) c) i)))
   (if (<= t_2 -5e+229)
     t_1
     (if (<= t_2 4e+303) (* 2.0 (fma t z (* y x))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((c * b) * (i * c)) * -2.0;
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -5e+229) {
		tmp = t_1;
	} else if (t_2 <= 4e+303) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(c * b) * Float64(i * c)) * -2.0)
	t_2 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_2 <= -5e+229)
		tmp = t_1;
	elseif (t_2 <= 4e+303)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(c * b), $MachinePrecision] * N[(i * c), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+229], t$95$1, If[LessEqual[t$95$2, 4e+303], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000005e229 or 4e303 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 76.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   3. Applied rewrites 70.1%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(i, \left(\left(-b\right) \cdot c\right) \cdot c - c \cdot a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)} \]

   4. Taylor expanded in b around inf

      \[\leadsto \color{blue}{-2 \cdot \left(b \cdot \left({c}^{2} \cdot i\right)\right)} \]

   6. Applied rewrites 69.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2 \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2 \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2 \]

      4. *-commutative N/A

         \[\leadsto \left(b \cdot \left(\left(c \cdot c\right) \cdot i\right)\right) \cdot -2 \]

      5. associate-*l* N/A

         \[\leadsto \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2 \]

      6. associate-*r* N/A

         \[\leadsto \left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot -2 \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot -2 \]

      8. *-commutative N/A

         \[\leadsto \left(\left(c \cdot b\right) \cdot \left(c \cdot i\right)\right) \cdot -2 \]

      9. lower-*.f64 N/A

         \[\leadsto \left(\left(c \cdot b\right) \cdot \left(c \cdot i\right)\right) \cdot -2 \]

      10. *-commutative N/A

          \[\leadsto \left(\left(c \cdot b\right) \cdot \left(i \cdot c\right)\right) \cdot -2 \]

      11. lower-*.f64 68.6

          \[\leadsto \left(\left(c \cdot b\right) \cdot \left(i \cdot c\right)\right) \cdot -2 \]

   8. Applied rewrites 68.6%

      \[\leadsto \left(\left(c \cdot b\right) \cdot \left(i \cdot c\right)\right) \cdot -2 \]

   if -5.0000000000000005e229 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4e303

   1. Initial program 99.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, \color{blue}{z}, x \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

      3. lower-*.f64 77.6

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

   4. Applied rewrites 77.6%

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

Alternative 16: 62.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+158}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (* i c) a) -2.0)) (t_2 (* (* (+ a (* b c)) c) i)))
   (if (<= t_2 -2e+217)
     t_1
     (if (<= t_2 1e+158) (* 2.0 (fma t z (* y x))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((i * c) * a) * -2.0;
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -2e+217) {
		tmp = t_1;
	} else if (t_2 <= 1e+158) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(i * c) * a) * -2.0)
	t_2 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_2 <= -2e+217)
		tmp = t_1;
	elseif (t_2 <= 1e+158)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(i * c), $MachinePrecision] * a), $MachinePrecision] * -2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+217], t$95$1, If[LessEqual[t$95$2, 1e+158], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -1.99999999999999992e217 or 9.99999999999999953e157 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 79.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot \left(c \cdot i\right)\right) \cdot \color{blue}{-2} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot \left(c \cdot i\right)\right) \cdot \color{blue}{-2} \]

      3. *-commutative N/A

         \[\leadsto \left(\left(c \cdot i\right) \cdot a\right) \cdot -2 \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(c \cdot i\right) \cdot a\right) \cdot -2 \]

      5. *-commutative N/A

         \[\leadsto \left(\left(i \cdot c\right) \cdot a\right) \cdot -2 \]

      6. lower-*.f64 40.3

         \[\leadsto \left(\left(i \cdot c\right) \cdot a\right) \cdot -2 \]

   4. Applied rewrites 40.3%

      \[\leadsto \color{blue}{\left(\left(i \cdot c\right) \cdot a\right) \cdot -2} \]

   if -1.99999999999999992e217 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 9.99999999999999953e157

   1. Initial program 99.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, \color{blue}{z}, x \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

      3. lower-*.f64 82.3

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right) \]

   4. Applied rewrites 82.3%

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

Alternative 17: 44.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + z\right) \cdot t\\ \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-74}:\\ \;\;\;\;\left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-51}:\\ \;\;\;\;\left(x + x\right) \cdot y\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+27}:\\ \;\;\;\;\left(\left(a \cdot c\right) \cdot i\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ z z) t)))
   (if (<= (* z t) -1e+87)
     t_1
     (if (<= (* z t) -2e-74)
       (* (* (* i c) a) -2.0)
       (if (<= (* z t) 2e-51)
         (* (+ x x) y)
         (if (<= (* z t) 2e+27) (* (* (* a c) i) -2.0) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z + z) * t;
	double tmp;
	if ((z * t) <= -1e+87) {
		tmp = t_1;
	} else if ((z * t) <= -2e-74) {
		tmp = ((i * c) * a) * -2.0;
	} else if ((z * t) <= 2e-51) {
		tmp = (x + x) * y;
	} else if ((z * t) <= 2e+27) {
		tmp = ((a * c) * i) * -2.0;
	} 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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + z) * t
    if ((z * t) <= (-1d+87)) then
        tmp = t_1
    else if ((z * t) <= (-2d-74)) then
        tmp = ((i * c) * a) * (-2.0d0)
    else if ((z * t) <= 2d-51) then
        tmp = (x + x) * y
    else if ((z * t) <= 2d+27) then
        tmp = ((a * c) * i) * (-2.0d0)
    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 c, double i) {
	double t_1 = (z + z) * t;
	double tmp;
	if ((z * t) <= -1e+87) {
		tmp = t_1;
	} else if ((z * t) <= -2e-74) {
		tmp = ((i * c) * a) * -2.0;
	} else if ((z * t) <= 2e-51) {
		tmp = (x + x) * y;
	} else if ((z * t) <= 2e+27) {
		tmp = ((a * c) * i) * -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z + z) * t
	tmp = 0
	if (z * t) <= -1e+87:
		tmp = t_1
	elif (z * t) <= -2e-74:
		tmp = ((i * c) * a) * -2.0
	elif (z * t) <= 2e-51:
		tmp = (x + x) * y
	elif (z * t) <= 2e+27:
		tmp = ((a * c) * i) * -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z + z) * t)
	tmp = 0.0
	if (Float64(z * t) <= -1e+87)
		tmp = t_1;
	elseif (Float64(z * t) <= -2e-74)
		tmp = Float64(Float64(Float64(i * c) * a) * -2.0);
	elseif (Float64(z * t) <= 2e-51)
		tmp = Float64(Float64(x + x) * y);
	elseif (Float64(z * t) <= 2e+27)
		tmp = Float64(Float64(Float64(a * c) * i) * -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z + z) * t;
	tmp = 0.0;
	if ((z * t) <= -1e+87)
		tmp = t_1;
	elseif ((z * t) <= -2e-74)
		tmp = ((i * c) * a) * -2.0;
	elseif ((z * t) <= 2e-51)
		tmp = (x + x) * y;
	elseif ((z * t) <= 2e+27)
		tmp = ((a * c) * i) * -2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z + z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1e+87], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], -2e-74], N[(N[(N[(i * c), $MachinePrecision] * a), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e-51], N[(N[(x + x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+27], N[(N[(N[(a * c), $MachinePrecision] * i), $MachinePrecision] * -2.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 z t) < -9.9999999999999996e86 or 2e27 < (*.f64 z t)

   1. Initial program 87.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 2 \cdot \left(z \cdot \color{blue}{t}\right) \]

      2. associate-*l* N/A

         \[\leadsto \left(2 \cdot z\right) \cdot \color{blue}{t} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(2 \cdot z\right) \cdot \color{blue}{t} \]

      4. count-2-rev N/A

         \[\leadsto \left(z + z\right) \cdot t \]

      5. lower-+.f64 55.6

         \[\leadsto \left(z + z\right) \cdot t \]

   4. Applied rewrites 55.6%

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

   if -9.9999999999999996e86 < (*.f64 z t) < -1.99999999999999992e-74

   1. Initial program 91.4%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot \left(c \cdot i\right)\right) \cdot \color{blue}{-2} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot \left(c \cdot i\right)\right) \cdot \color{blue}{-2} \]

      3. *-commutative N/A

         \[\leadsto \left(\left(c \cdot i\right) \cdot a\right) \cdot -2 \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(c \cdot i\right) \cdot a\right) \cdot -2 \]

      5. *-commutative N/A

         \[\leadsto \left(\left(i \cdot c\right) \cdot a\right) \cdot -2 \]

      6. lower-*.f64 27.0

         \[\leadsto \left(\left(i \cdot c\right) \cdot a\right) \cdot -2 \]

   4. Applied rewrites 27.0%

      \[\leadsto \color{blue}{\left(\left(i \cdot c\right) \cdot a\right) \cdot -2} \]

   if -1.99999999999999992e-74 < (*.f64 z t) < 2e-51

   1. Initial program 92.4%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   3. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(2 \cdot x\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(2 \cdot x\right) \cdot \color{blue}{y} \]

      3. count-2-rev N/A

         \[\leadsto \left(x + x\right) \cdot y \]

      4. lower-+.f64 40.1

         \[\leadsto \left(x + x\right) \cdot y \]

   4. Applied rewrites 40.1%

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

   if 2e-51 < (*.f64 z t) < 2e27

   1. Initial program 91.5%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot \left(c \cdot i\right)\right) \cdot \color{blue}{-2} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot \left(c \cdot i\right)\right) \cdot \color{blue}{-2} \]

      3. *-commutative N/A

         \[\leadsto \left(\left(c \cdot i\right) \cdot a\right) \cdot -2 \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(c \cdot i\right) \cdot a\right) \cdot -2 \]

      5. *-commutative N/A

         \[\leadsto \left(\left(i \cdot c\right) \cdot a\right) \cdot -2 \]

      6. lower-*.f64 32.2

         \[\leadsto \left(\left(i \cdot c\right) \cdot a\right) \cdot -2 \]

   4. Applied rewrites 32.2%

      \[\leadsto \color{blue}{\left(\left(i \cdot c\right) \cdot a\right) \cdot -2} \]

   6. Applied rewrites 29.1%

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

Alternative 18: 44.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + x\right) \cdot y\\ \mathbf{if}\;x \cdot y \leq -5000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-57}:\\ \;\;\;\;\left(\left(i \cdot a\right) \cdot c\right) \cdot -2\\ \mathbf{elif}\;x \cdot y \leq 0.02:\\ \;\;\;\;\left(z + z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ x x) y)))
   (if (<= (* x y) -5000000.0)
     t_1
     (if (<= (* x y) -5e-57)
       (* (* (* i a) c) -2.0)
       (if (<= (* x y) 0.02) (* (+ z z) t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + x) * y;
	double tmp;
	if ((x * y) <= -5000000.0) {
		tmp = t_1;
	} else if ((x * y) <= -5e-57) {
		tmp = ((i * a) * c) * -2.0;
	} else if ((x * y) <= 0.02) {
		tmp = (z + z) * t;
	} 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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + x) * y
    if ((x * y) <= (-5000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= (-5d-57)) then
        tmp = ((i * a) * c) * (-2.0d0)
    else if ((x * y) <= 0.02d0) then
        tmp = (z + z) * t
    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 c, double i) {
	double t_1 = (x + x) * y;
	double tmp;
	if ((x * y) <= -5000000.0) {
		tmp = t_1;
	} else if ((x * y) <= -5e-57) {
		tmp = ((i * a) * c) * -2.0;
	} else if ((x * y) <= 0.02) {
		tmp = (z + z) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + x) * y
	tmp = 0
	if (x * y) <= -5000000.0:
		tmp = t_1
	elif (x * y) <= -5e-57:
		tmp = ((i * a) * c) * -2.0
	elif (x * y) <= 0.02:
		tmp = (z + z) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + x) * y)
	tmp = 0.0
	if (Float64(x * y) <= -5000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= -5e-57)
		tmp = Float64(Float64(Float64(i * a) * c) * -2.0);
	elseif (Float64(x * y) <= 0.02)
		tmp = Float64(Float64(z + z) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + x) * y;
	tmp = 0.0;
	if ((x * y) <= -5000000.0)
		tmp = t_1;
	elseif ((x * y) <= -5e-57)
		tmp = ((i * a) * c) * -2.0;
	elseif ((x * y) <= 0.02)
		tmp = (z + z) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5e-57], N[(N[(N[(i * a), $MachinePrecision] * c), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 0.02], N[(N[(z + z), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5e6 or 0.0200000000000000004 < (*.f64 x y)

   1. Initial program 88.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   3. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(2 \cdot x\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(2 \cdot x\right) \cdot \color{blue}{y} \]

      3. count-2-rev N/A

         \[\leadsto \left(x + x\right) \cdot y \]

      4. lower-+.f64 50.7

         \[\leadsto \left(x + x\right) \cdot y \]

   4. Applied rewrites 50.7%

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

   if -5e6 < (*.f64 x y) < -5.0000000000000002e-57

   1. Initial program 93.5%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot \left(c \cdot i\right)\right) \cdot \color{blue}{-2} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot \left(c \cdot i\right)\right) \cdot \color{blue}{-2} \]

      3. *-commutative N/A

         \[\leadsto \left(\left(c \cdot i\right) \cdot a\right) \cdot -2 \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(c \cdot i\right) \cdot a\right) \cdot -2 \]

      5. *-commutative N/A

         \[\leadsto \left(\left(i \cdot c\right) \cdot a\right) \cdot -2 \]

      6. lower-*.f64 26.1

         \[\leadsto \left(\left(i \cdot c\right) \cdot a\right) \cdot -2 \]

   4. Applied rewrites 26.1%

      \[\leadsto \color{blue}{\left(\left(i \cdot c\right) \cdot a\right) \cdot -2} \]

   6. Applied rewrites 24.5%

      \[\leadsto \color{blue}{\left(\left(a \cdot c\right) \cdot i\right) \cdot -2} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(a \cdot c\right) \cdot i\right) \cdot -2 \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(a \cdot c\right) \cdot i\right) \cdot -2 \]

      3. associate-*l* N/A

         \[\leadsto \left(a \cdot \left(c \cdot i\right)\right) \cdot -2 \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot \left(i \cdot c\right)\right) \cdot -2 \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(a \cdot i\right) \cdot c\right) \cdot -2 \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\left(a \cdot i\right) \cdot c\right) \cdot -2 \]

      7. *-commutative N/A

         \[\leadsto \left(\left(i \cdot a\right) \cdot c\right) \cdot -2 \]

      8. lower-*.f64 23.2

         \[\leadsto \left(\left(i \cdot a\right) \cdot c\right) \cdot -2 \]

   8. Applied rewrites 23.2%

      \[\leadsto \left(\left(i \cdot a\right) \cdot c\right) \cdot -2 \]

   if -5.0000000000000002e-57 < (*.f64 x y) < 0.0200000000000000004

   1. Initial program 91.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 2 \cdot \left(z \cdot \color{blue}{t}\right) \]

      2. associate-*l* N/A

         \[\leadsto \left(2 \cdot z\right) \cdot \color{blue}{t} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(2 \cdot z\right) \cdot \color{blue}{t} \]

      4. count-2-rev N/A

         \[\leadsto \left(z + z\right) \cdot t \]

      5. lower-+.f64 38.0

         \[\leadsto \left(z + z\right) \cdot t \]

   4. Applied rewrites 38.0%

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

Alternative 19: 43.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + z\right) \cdot t\\ \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-51}:\\ \;\;\;\;\left(x + x\right) \cdot y\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+27}:\\ \;\;\;\;\left(\left(a \cdot c\right) \cdot i\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ z z) t)))
   (if (<= (* z t) -2e+128)
     t_1
     (if (<= (* z t) 2e-51)
       (* (+ x x) y)
       (if (<= (* z t) 2e+27) (* (* (* a c) i) -2.0) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z + z) * t;
	double tmp;
	if ((z * t) <= -2e+128) {
		tmp = t_1;
	} else if ((z * t) <= 2e-51) {
		tmp = (x + x) * y;
	} else if ((z * t) <= 2e+27) {
		tmp = ((a * c) * i) * -2.0;
	} 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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + z) * t
    if ((z * t) <= (-2d+128)) then
        tmp = t_1
    else if ((z * t) <= 2d-51) then
        tmp = (x + x) * y
    else if ((z * t) <= 2d+27) then
        tmp = ((a * c) * i) * (-2.0d0)
    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 c, double i) {
	double t_1 = (z + z) * t;
	double tmp;
	if ((z * t) <= -2e+128) {
		tmp = t_1;
	} else if ((z * t) <= 2e-51) {
		tmp = (x + x) * y;
	} else if ((z * t) <= 2e+27) {
		tmp = ((a * c) * i) * -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z + z) * t
	tmp = 0
	if (z * t) <= -2e+128:
		tmp = t_1
	elif (z * t) <= 2e-51:
		tmp = (x + x) * y
	elif (z * t) <= 2e+27:
		tmp = ((a * c) * i) * -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z + z) * t)
	tmp = 0.0
	if (Float64(z * t) <= -2e+128)
		tmp = t_1;
	elseif (Float64(z * t) <= 2e-51)
		tmp = Float64(Float64(x + x) * y);
	elseif (Float64(z * t) <= 2e+27)
		tmp = Float64(Float64(Float64(a * c) * i) * -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z + z) * t;
	tmp = 0.0;
	if ((z * t) <= -2e+128)
		tmp = t_1;
	elseif ((z * t) <= 2e-51)
		tmp = (x + x) * y;
	elseif ((z * t) <= 2e+27)
		tmp = ((a * c) * i) * -2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z + z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -2e+128], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 2e-51], N[(N[(x + x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+27], N[(N[(N[(a * c), $MachinePrecision] * i), $MachinePrecision] * -2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -2.0000000000000002e128 or 2e27 < (*.f64 z t)

   1. Initial program 86.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 2 \cdot \left(z \cdot \color{blue}{t}\right) \]

      2. associate-*l* N/A

         \[\leadsto \left(2 \cdot z\right) \cdot \color{blue}{t} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(2 \cdot z\right) \cdot \color{blue}{t} \]

      4. count-2-rev N/A

         \[\leadsto \left(z + z\right) \cdot t \]

      5. lower-+.f64 57.0

         \[\leadsto \left(z + z\right) \cdot t \]

   4. Applied rewrites 57.0%

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

   if -2.0000000000000002e128 < (*.f64 z t) < 2e-51

   1. Initial program 92.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   3. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(2 \cdot x\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(2 \cdot x\right) \cdot \color{blue}{y} \]

      3. count-2-rev N/A

         \[\leadsto \left(x + x\right) \cdot y \]

      4. lower-+.f64 37.4

         \[\leadsto \left(x + x\right) \cdot y \]

   4. Applied rewrites 37.4%

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

   if 2e-51 < (*.f64 z t) < 2e27

   1. Initial program 91.5%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot \left(c \cdot i\right)\right) \cdot \color{blue}{-2} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot \left(c \cdot i\right)\right) \cdot \color{blue}{-2} \]

      3. *-commutative N/A

         \[\leadsto \left(\left(c \cdot i\right) \cdot a\right) \cdot -2 \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(c \cdot i\right) \cdot a\right) \cdot -2 \]

      5. *-commutative N/A

         \[\leadsto \left(\left(i \cdot c\right) \cdot a\right) \cdot -2 \]

      6. lower-*.f64 32.2

         \[\leadsto \left(\left(i \cdot c\right) \cdot a\right) \cdot -2 \]

   4. Applied rewrites 32.2%

      \[\leadsto \color{blue}{\left(\left(i \cdot c\right) \cdot a\right) \cdot -2} \]

   6. Applied rewrites 29.1%

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

Alternative 20: 40.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + x\right) \cdot y\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.7:\\ \;\;\;\;\left(z + z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ x x) y)))
   (if (<= x -2.1e+34) t_1 (if (<= x 2.7) (* (+ z z) t) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + x) * y;
	double tmp;
	if (x <= -2.1e+34) {
		tmp = t_1;
	} else if (x <= 2.7) {
		tmp = (z + z) * t;
	} 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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + x) * y
    if (x <= (-2.1d+34)) then
        tmp = t_1
    else if (x <= 2.7d0) then
        tmp = (z + z) * t
    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 c, double i) {
	double t_1 = (x + x) * y;
	double tmp;
	if (x <= -2.1e+34) {
		tmp = t_1;
	} else if (x <= 2.7) {
		tmp = (z + z) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + x) * y
	tmp = 0
	if x <= -2.1e+34:
		tmp = t_1
	elif x <= 2.7:
		tmp = (z + z) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + x) * y)
	tmp = 0.0
	if (x <= -2.1e+34)
		tmp = t_1;
	elseif (x <= 2.7)
		tmp = Float64(Float64(z + z) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + x) * y;
	tmp = 0.0;
	if (x <= -2.1e+34)
		tmp = t_1;
	elseif (x <= 2.7)
		tmp = (z + z) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[x, -2.1e+34], t$95$1, If[LessEqual[x, 2.7], N[(N[(z + z), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.10000000000000017e34 or 2.7000000000000002 < x

   1. Initial program 87.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   3. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(2 \cdot x\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(2 \cdot x\right) \cdot \color{blue}{y} \]

      3. count-2-rev N/A

         \[\leadsto \left(x + x\right) \cdot y \]

      4. lower-+.f64 45.8

         \[\leadsto \left(x + x\right) \cdot y \]

   4. Applied rewrites 45.8%

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

   if -2.10000000000000017e34 < x < 2.7000000000000002

   1. Initial program 92.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 2 \cdot \left(z \cdot \color{blue}{t}\right) \]

      2. associate-*l* N/A

         \[\leadsto \left(2 \cdot z\right) \cdot \color{blue}{t} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(2 \cdot z\right) \cdot \color{blue}{t} \]

      4. count-2-rev N/A

         \[\leadsto \left(z + z\right) \cdot t \]

      5. lower-+.f64 35.7

         \[\leadsto \left(z + z\right) \cdot t \]

   4. Applied rewrites 35.7%

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

Alternative 21: 29.0% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \left(x + x\right) \cdot y \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (* (+ x x) y))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (x + x) * 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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    code = (x + x) * y
end function

Java

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

Python

def code(x, y, z, t, a, b, c, i):
	return (x + x) * y

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.1%

   \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

2. Taylor expanded in x around inf

   \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
3. Step-by-step derivation

   1. associate-*r* N/A

      \[\leadsto \left(2 \cdot x\right) \cdot \color{blue}{y} \]

   2. lower-*.f64 N/A

      \[\leadsto \left(2 \cdot x\right) \cdot \color{blue}{y} \]

   3. count-2-rev N/A

      \[\leadsto \left(x + x\right) \cdot y \]

   4. lower-+.f64 29.0

      \[\leadsto \left(x + x\right) \cdot y \]

4. Applied rewrites 29.0%

   \[\leadsto \color{blue}{\left(x + x\right) \cdot y} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025130 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))