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

Percentage Accurate: 89.5% → 93.8%

Time: 5.7s

Alternatives: 12

Speedup: 0.5×

• 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: 89.5% 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: 93.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;-2 \cdot t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+226}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, t \cdot z - \left(\mathsf{fma}\left(c, b, a\right) \cdot c\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t \cdot z - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (fma c b a) i) c)) (t_2 (* (* (+ a (* b c)) c) i)))
   (if (<= t_2 (- INFINITY))
     (* -2.0 t_1)
     (if (<= t_2 1e+226)
       (* 2.0 (fma y x (- (* t z) (* (* (fma c b a) c) i))))
       (* 2.0 (- (* t z) t_1))))))

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) * c;
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = -2.0 * t_1;
	} else if (t_2 <= 1e+226) {
		tmp = 2.0 * fma(y, x, ((t * z) - ((fma(c, b, a) * c) * i)));
	} else {
		tmp = 2.0 * ((t * z) - t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = 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 <= Float64(-Inf))
		tmp = Float64(-2.0 * t_1);
	elseif (t_2 <= 1e+226)
		tmp = Float64(2.0 * fma(y, x, Float64(Float64(t * z) - Float64(Float64(fma(c, b, a) * c) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(t * z) - 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 + a), $MachinePrecision] * i), $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, (-Infinity)], N[(-2.0 * t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 1e+226], N[(2.0 * N[(y * x + N[(N[(t * z), $MachinePrecision] - N[(N[(N[(c * b + a), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(t * z), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0

   1. Initial program 83.8%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 96.5

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

   5. Applied rewrites 96.5%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 9.99999999999999961e225

   1. Initial program 99.3%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate--l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. lift-+.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 99.3

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

   4. Applied rewrites 99.3%

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

   if 9.99999999999999961e225 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 65.8%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 89.3

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

   5. Applied rewrites 89.3%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq -\infty:\\ \;\;\;\;-2 \cdot \left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \mathbf{elif}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq 10^{+226}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, t \cdot z - \left(\mathsf{fma}\left(c, b, a\right) \cdot c\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2000000000000:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+189}:\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(a \cdot i\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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+100)
     t_1
     (if (<= t_2 2000000000000.0)
       (* 2.0 (fma t z (* y x)))
       (if (<= t_2 1e+189) (* 2.0 (- (* t z) (* (* a i) c))) 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+100) {
		tmp = t_1;
	} else if (t_2 <= 2000000000000.0) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else if (t_2 <= 1e+189) {
		tmp = 2.0 * ((t * z) - ((a * i) * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-2.0 * 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 <= -5e+100)
		tmp = t_1;
	elseif (t_2 <= 2000000000000.0)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	elseif (t_2 <= 1e+189)
		tmp = Float64(2.0 * Float64(Float64(t * z) - Float64(Float64(a * i) * c)));
	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[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+100], t$95$1, If[LessEqual[t$95$2, 2000000000000.0], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+189], N[(2.0 * N[(N[(t * z), $MachinePrecision] - N[(N[(a * i), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.9999999999999999e100 or 1e189 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.3%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 85.0

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

   5. Applied rewrites 85.0%

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

   if -4.9999999999999999e100 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 2e12

   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. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]
   4. 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 94.8

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

   5. Applied rewrites 94.8%

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

   if 2e12 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1e189

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 90.8

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

   5. Applied rewrites 90.8%

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

   6. Taylor expanded in a around inf

      \[\leadsto 2 \cdot \left(t \cdot z - \left(a \cdot i\right) \cdot c\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 78.6%

      \[\leadsto 2 \cdot \left(t \cdot z - \left(a \cdot i\right) \cdot c\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq -5 \cdot 10^{+100}:\\ \;\;\;\;-2 \cdot \left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \mathbf{elif}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq 2000000000000:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{elif}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq 10^{+189}:\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(a \cdot i\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 98.0

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

   4. Applied rewrites 98.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 70.4

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

   5. Applied rewrites 70.4%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \leq \infty:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \mathsf{fma}\left(c, b, a\right) \cdot \left(i \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+234} \lor \neg \left(t\_1 \leq 10^{+176}\right):\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a \cdot c\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (or (<= t_1 -5e+234) (not (<= t_1 1e+176)))
     (* 2.0 (- (* t z) (* (* (fma c b a) i) c)))
     (* 2.0 (- (+ (* x y) (* z t)) (* (* a c) i))))))

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+234) || !(t_1 <= 1e+176)) {
		tmp = 2.0 * ((t * z) - ((fma(c, b, a) * i) * c));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - ((a * c) * i));
	}
	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+234) || !(t_1 <= 1e+176))
		tmp = Float64(2.0 * Float64(Float64(t * z) - Float64(Float64(fma(c, b, a) * i) * c)));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(a * c) * i)));
	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[Or[LessEqual[t$95$1, -5e+234], N[Not[LessEqual[t$95$1, 1e+176]], $MachinePrecision]], N[(2.0 * N[(N[(t * z), $MachinePrecision] - N[(N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(a * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000003e234 or 1e176 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 79.1%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 91.6

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

   5. Applied rewrites 91.6%

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

   if -5.0000000000000003e234 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1e176

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 96.7%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq -5 \cdot 10^{+234} \lor \neg \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq 10^{+176}\right):\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a \cdot c\right) \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+100} \lor \neg \left(t\_1 \leq 2000000000000\right):\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (or (<= t_1 -5e+100) (not (<= t_1 2000000000000.0)))
     (* 2.0 (- (* t z) (* (* (fma c b a) i) c)))
     (* 2.0 (fma t z (* y x))))))

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+100) || !(t_1 <= 2000000000000.0)) {
		tmp = 2.0 * ((t * z) - ((fma(c, b, a) * i) * c));
	} else {
		tmp = 2.0 * fma(t, z, (y * x));
	}
	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+100) || !(t_1 <= 2000000000000.0))
		tmp = Float64(2.0 * Float64(Float64(t * z) - Float64(Float64(fma(c, b, a) * i) * c)));
	else
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	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[Or[LessEqual[t$95$1, -5e+100], N[Not[LessEqual[t$95$1, 2000000000000.0]], $MachinePrecision]], N[(2.0 * N[(N[(t * z), $MachinePrecision] - N[(N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.9999999999999999e100 or 2e12 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 83.3%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 89.9

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

   5. Applied rewrites 89.9%

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

   if -4.9999999999999999e100 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 2e12

   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. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]
   4. 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 94.8

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

   5. Applied rewrites 94.8%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq -5 \cdot 10^{+100} \lor \neg \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq 2000000000000\right):\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+100} \lor \neg \left(t\_1 \leq 10^{+189}\right):\\ \;\;\;\;-2 \cdot \left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (or (<= t_1 -5e+100) (not (<= t_1 1e+189)))
     (* -2.0 (* (* (fma c b a) i) c))
     (* 2.0 (fma t z (* y x))))))

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+100) || !(t_1 <= 1e+189)) {
		tmp = -2.0 * ((fma(c, b, a) * i) * c);
	} else {
		tmp = 2.0 * fma(t, z, (y * x));
	}
	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+100) || !(t_1 <= 1e+189))
		tmp = Float64(-2.0 * Float64(Float64(fma(c, b, a) * i) * c));
	else
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	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[Or[LessEqual[t$95$1, -5e+100], N[Not[LessEqual[t$95$1, 1e+189]], $MachinePrecision]], N[(-2.0 * N[(N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.9999999999999999e100 or 1e189 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.3%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 85.0

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

   5. Applied rewrites 85.0%

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

   if -4.9999999999999999e100 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1e189

   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. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]
   4. 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 87.8

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

   5. Applied rewrites 87.8%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq -5 \cdot 10^{+100} \lor \neg \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq 10^{+189}\right):\\ \;\;\;\;-2 \cdot \left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+234} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+216}\right):\\ \;\;\;\;\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (or (<= t_1 -5e+234) (not (<= t_1 2e+216)))
     (* (* (* (* c c) i) b) -2.0)
     (* 2.0 (fma t z (* y x))))))

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+234) || !(t_1 <= 2e+216)) {
		tmp = (((c * c) * i) * b) * -2.0;
	} else {
		tmp = 2.0 * fma(t, z, (y * x));
	}
	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+234) || !(t_1 <= 2e+216))
		tmp = Float64(Float64(Float64(Float64(c * c) * i) * b) * -2.0);
	else
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	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[Or[LessEqual[t$95$1, -5e+234], N[Not[LessEqual[t$95$1, 2e+216]], $MachinePrecision]], N[(N[(N[(N[(c * c), $MachinePrecision] * i), $MachinePrecision] * b), $MachinePrecision] * -2.0), $MachinePrecision], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000003e234 or 2e216 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 78.2%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 65.8

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

   5. Applied rewrites 65.8%

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

   if -5.0000000000000003e234 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 2e216

   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. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]
   4. 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 83.4

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

   5. Applied rewrites 83.4%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq -5 \cdot 10^{+234} \lor \neg \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq 2 \cdot 10^{+216}\right):\\ \;\;\;\;\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+234}:\\ \;\;\;\;\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+216}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot \left(i \cdot c\right)\right) \cdot b\right) \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (<= t_1 -5e+234)
     (* (* (* (* c c) i) b) -2.0)
     (if (<= t_1 2e+216)
       (* 2.0 (fma t z (* y x)))
       (* (* (* c (* i c)) 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+234) {
		tmp = (((c * c) * i) * b) * -2.0;
	} else if (t_1 <= 2e+216) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else {
		tmp = ((c * (i * c)) * 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+234)
		tmp = Float64(Float64(Float64(Float64(c * c) * i) * b) * -2.0);
	elseif (t_1 <= 2e+216)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	else
		tmp = Float64(Float64(Float64(c * Float64(i * c)) * 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+234], N[(N[(N[(N[(c * c), $MachinePrecision] * i), $MachinePrecision] * b), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+216], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(c * N[(i * c), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] * -2.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000003e234

   1. Initial program 86.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 71.2

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

   5. Applied rewrites 71.2%

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

   if -5.0000000000000003e234 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 2e216

   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. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]
   4. 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 83.4

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

   5. Applied rewrites 83.4%

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

   if 2e216 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 66.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 89.2

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

   4. Applied rewrites 89.2%

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

   5. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. pow2 N/A

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

      7. lift-*.f64 58.2

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

   7. Applied rewrites 58.2%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2} \]
   8. 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. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 62.1

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

   9. Applied rewrites 62.1%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq -5 \cdot 10^{+234}:\\ \;\;\;\;\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2\\ \mathbf{elif}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq 2 \cdot 10^{+216}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot \left(i \cdot c\right)\right) \cdot b\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+234}:\\ \;\;\;\;\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2\\ \mathbf{elif}\;t\_1 \leq 10^{+189}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot \left(c \cdot b\right)\right) \cdot i\right) \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (<= t_1 -5e+234)
     (* (* (* (* c c) i) b) -2.0)
     (if (<= t_1 1e+189)
       (* 2.0 (fma t z (* y x)))
       (* (* (* c (* c b)) i) -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+234) {
		tmp = (((c * c) * i) * b) * -2.0;
	} else if (t_1 <= 1e+189) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else {
		tmp = ((c * (c * b)) * i) * -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+234)
		tmp = Float64(Float64(Float64(Float64(c * c) * i) * b) * -2.0);
	elseif (t_1 <= 1e+189)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	else
		tmp = Float64(Float64(Float64(c * Float64(c * b)) * i) * -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+234], N[(N[(N[(N[(c * c), $MachinePrecision] * i), $MachinePrecision] * b), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+189], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(c * N[(c * b), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * -2.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000003e234

   1. Initial program 86.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 71.2

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

   5. Applied rewrites 71.2%

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

   if -5.0000000000000003e234 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1e189

   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. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]
   4. 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 84.5

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

   5. Applied rewrites 84.5%

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

   if 1e189 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 68.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 87.9

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

   4. Applied rewrites 87.9%

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

   5. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. pow2 N/A

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

      7. lift-*.f64 54.9

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

   7. Applied rewrites 54.9%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2} \]
   8. 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. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 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. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. pow2 N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 56.9

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

   9. Applied rewrites 56.9%

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

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-*l* N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. *-commutative N/A

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

       7. lower-*.f64 58.7

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

   11. Applied rewrites 58.7%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq -5 \cdot 10^{+234}:\\ \;\;\;\;\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2\\ \mathbf{elif}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq 10^{+189}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot \left(c \cdot b\right)\right) \cdot i\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+100} \lor \neg \left(t\_1 \leq 10^{+189}\right):\\ \;\;\;\;\left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (or (<= t_1 -5e+100) (not (<= t_1 1e+189)))
     (* (* (* i c) a) -2.0)
     (* 2.0 (fma t z (* y x))))))

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+100) || !(t_1 <= 1e+189)) {
		tmp = ((i * c) * a) * -2.0;
	} else {
		tmp = 2.0 * fma(t, z, (y * x));
	}
	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+100) || !(t_1 <= 1e+189))
		tmp = Float64(Float64(Float64(i * c) * a) * -2.0);
	else
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	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[Or[LessEqual[t$95$1, -5e+100], N[Not[LessEqual[t$95$1, 1e+189]], $MachinePrecision]], N[(N[(N[(i * c), $MachinePrecision] * a), $MachinePrecision] * -2.0), $MachinePrecision], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.9999999999999999e100 or 1e189 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.3%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   4. 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 40.5

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

   5. Applied rewrites 40.5%

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

   if -4.9999999999999999e100 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1e189

   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. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]
   4. 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 87.8

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

   5. Applied rewrites 87.8%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq -5 \cdot 10^{+100} \lor \neg \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq 10^{+189}\right):\\ \;\;\;\;\left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+177} \lor \neg \left(x \cdot y \leq 10^{+27}\right):\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2e+177) (not (<= (* x y) 1e+27)))
   (* 2.0 (* y x))
   (* 2.0 (* t z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2e+177) || !((x * y) <= 1e+27)) {
		tmp = 2.0 * (y * x);
	} else {
		tmp = 2.0 * (t * z);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, 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) :: tmp
    if (((x * y) <= (-2d+177)) .or. (.not. ((x * y) <= 1d+27))) then
        tmp = 2.0d0 * (y * x)
    else
        tmp = 2.0d0 * (t * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2e+177) || !((x * y) <= 1e+27)) {
		tmp = 2.0 * (y * x);
	} else {
		tmp = 2.0 * (t * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -2e+177) or not ((x * y) <= 1e+27):
		tmp = 2.0 * (y * x)
	else:
		tmp = 2.0 * (t * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+177) || !(Float64(x * y) <= 1e+27))
		tmp = Float64(2.0 * Float64(y * x));
	else
		tmp = Float64(2.0 * Float64(t * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -2e+177) || ~(((x * y) <= 1e+27)))
		tmp = 2.0 * (y * x);
	else
		tmp = 2.0 * (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+177], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+27]], $MachinePrecision]], N[(2.0 * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2e177 or 1e27 < (*.f64 x y)

   1. Initial program 86.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 55.3

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

   5. Applied rewrites 55.3%

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

   if -2e177 < (*.f64 x y) < 1e27

   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. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 42.1

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

   5. Applied rewrites 42.1%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+177} \lor \neg \left(x \cdot y \leq 10^{+27}\right):\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 28.5% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(t \cdot z\right) \end{array} \]

FPCore

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

C

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

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 * (t * z)
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 * (t * z);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.2%

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

3. Taylor expanded in z around inf

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

   1. lower-*.f64 32.2

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

5. Applied rewrites 32.2%

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

Developer Target 1: 94.0% accurate, 1.0× speedup

Math

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

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(a + Float64(b * c)) * Float64(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[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2025037 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (* 2 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i)))))

  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))