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

Percentage Accurate: 90.1% → 93.4%

Time: 4.6s

Alternatives: 17

Speedup: 0.7×

• 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: 93.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;i \leq -1.36 \cdot 10^{+183}:\\ \;\;\;\;2 \cdot \left(t\_1 - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+171}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(\left(-b\right) \cdot \left(i \cdot c\right) - i \cdot a, c, \mathsf{fma}\left(t, z, y \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t\_1 - \mathsf{fma}\left(c, a, \left(c \cdot b\right) \cdot c\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= i -1.36e+183)
     (* 2.0 (- t_1 (* (* (+ a (* b c)) c) i)))
     (if (<= i 1.75e+171)
       (* 2.0 (fma (- (* (- b) (* i c)) (* i a)) c (fma t z (* y x))))
       (* 2.0 (- t_1 (* (fma c a (* (* c b) c)) i)))))))

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 (i <= -1.36e+183) {
		tmp = 2.0 * (t_1 - (((a + (b * c)) * c) * i));
	} else if (i <= 1.75e+171) {
		tmp = 2.0 * fma(((-b * (i * c)) - (i * a)), c, fma(t, z, (y * x)));
	} else {
		tmp = 2.0 * (t_1 - (fma(c, a, ((c * b) * c)) * i));
	}
	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 (i <= -1.36e+183)
		tmp = Float64(2.0 * Float64(t_1 - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)));
	elseif (i <= 1.75e+171)
		tmp = Float64(2.0 * fma(Float64(Float64(Float64(-b) * Float64(i * c)) - Float64(i * a)), c, fma(t, z, Float64(y * x))));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(fma(c, a, Float64(Float64(c * b) * c)) * i)));
	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[i, -1.36e+183], N[(2.0 * N[(t$95$1 - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.75e+171], N[(2.0 * N[(N[(N[((-b) * N[(i * c), $MachinePrecision]), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision] * c + N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(N[(c * a + N[(N[(c * b), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.35999999999999995e183

   1. Initial program 90.1%

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

   if -1.35999999999999995e183 < i < 1.75e171

   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 c around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(-1 \cdot \left(b \cdot \left(c \cdot i\right)\right) - a \cdot i, c, t \cdot z + x \cdot y\right) \]

      4. associate-*r* N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(\left(-1 \cdot b\right) \cdot \left(c \cdot i\right) - a \cdot i, c, t \cdot z + x \cdot y\right) \]

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 88.9

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

   4. Applied rewrites 88.9%

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

   if 1.75e171 < i

   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. 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

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

      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. *-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 89.4

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

   3. Applied rewrites 89.4%

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

Alternative 2: 91.9% accurate, 0.5× speedup

Math

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

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

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, a, ((c * b) * c)) * i));
	} else {
		tmp = fma(t, z, (y * x)) * 2.0;
	}
	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, a, Float64(Float64(c * b) * c)) * i)));
	else
		tmp = Float64(fma(t, z, Float64(y * x)) * 2.0);
	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 * a + N[(N[(c * b), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision] * 2.0), $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 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. 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

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

      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. *-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 89.4

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

   3. Applied rewrites 89.4%

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

   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 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 c around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 54.9

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

   4. Applied rewrites 54.9%

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

Alternative 3: 91.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision] * 2.0), $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 90.1%

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

   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 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 c around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 54.9

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

   4. Applied rewrites 54.9%

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

Alternative 4: 88.5% accurate, 0.5× speedup

Math

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

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 -5e+229)
     (* -2.0 t_1)
     (if (<= t_2 2e+243)
       (* 2.0 (- (fma t z (* y x)) (* (* i c) a)))
       (* 2.0 (- (* 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 = (fma(c, b, a) * i) * c;
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -5e+229) {
		tmp = -2.0 * t_1;
	} else if (t_2 <= 2e+243) {
		tmp = 2.0 * (fma(t, z, (y * x)) - ((i * c) * a));
	} else {
		tmp = 2.0 * ((y * x) - 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 <= -5e+229)
		tmp = Float64(-2.0 * t_1);
	elseif (t_2 <= 2e+243)
		tmp = Float64(2.0 * Float64(fma(t, z, Float64(y * x)) - Float64(Float64(i * c) * a)));
	else
		tmp = Float64(2.0 * Float64(Float64(y * x) - 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, -5e+229], N[(-2.0 * t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 2e+243], N[(2.0 * N[(N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision] - N[(N[(i * c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(y * x), $MachinePrecision] - t$95$1), $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 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 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. 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 47.7

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

   4. Applied rewrites 47.7%

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

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

   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 c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 73.4

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

   7. Applied rewrites 73.4%

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

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

   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 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 69.3

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

   4. Applied rewrites 69.3%

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

Alternative 5: 83.0% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (<= t_1 -1e+74)
     (* 2.0 (- (* t z) (* (* (fma c b a) c) i)))
     (if (<= t_1 5e-17)
       (* (fma t z (* y x)) 2.0)
       (* 2.0 (- (* y x) (* (* (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 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_1 <= -1e+74) {
		tmp = 2.0 * ((t * z) - ((fma(c, b, a) * c) * i));
	} else if (t_1 <= 5e-17) {
		tmp = fma(t, z, (y * x)) * 2.0;
	} else {
		tmp = 2.0 * ((y * x) - ((fma(c, b, a) * i) * 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 <= -1e+74)
		tmp = Float64(2.0 * Float64(Float64(t * z) - Float64(Float64(fma(c, b, a) * c) * i)));
	elseif (t_1 <= 5e-17)
		tmp = Float64(fma(t, z, Float64(y * x)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(y * x) - 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[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+74], N[(2.0 * N[(N[(t * z), $MachinePrecision] - N[(N[(N[(c * b + a), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-17], N[(N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(N[(y * x), $MachinePrecision] - N[(N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   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 c around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(-1 \cdot \left(b \cdot \left(c \cdot i\right)\right) - a \cdot i, c, t \cdot z + x \cdot y\right) \]

      4. associate-*r* N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(\left(-1 \cdot b\right) \cdot \left(c \cdot i\right) - a \cdot i, c, t \cdot z + x \cdot y\right) \]

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 88.9

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

   4. Applied rewrites 88.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   6. 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. +-commutative N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. lift-fma.f64 69.3

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

   7. Applied rewrites 69.3%

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

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

   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 c around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 54.9

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

   4. Applied rewrites 54.9%

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

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

   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 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 69.3

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

   4. Applied rewrites 69.3%

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

Alternative 6: 82.6% accurate, 0.3× speedup

Math

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

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) (* (* i c) a)))))
   (if (<= t_2 -5e+229)
     t_1
     (if (<= t_2 -1e+74)
       t_3
       (if (<= t_2 5e-17)
         (* (fma t z (* y x)) 2.0)
         (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) - ((i * c) * a));
	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 = fma(t, z, (y * x)) * 2.0;
	} 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(-2.0 * Float64(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(i * c) * a)))
	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(fma(t, z, Float64(y * x)) * 2.0);
	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[(-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]}, Block[{t$95$3 = N[(2.0 * N[(N[(y * x), $MachinePrecision] - N[(N[(i * c), $MachinePrecision] * a), $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[(N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision] * 2.0), $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 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 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. 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 47.7

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

   4. Applied rewrites 47.7%

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

   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 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 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 69.3

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

   4. Applied rewrites 69.3%

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

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 49.4

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

   7. Applied rewrites 49.4%

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

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

   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 c around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 54.9

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

   4. Applied rewrites 54.9%

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

Alternative 7: 81.6% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* t z) (* (* (fma c b a) c) i))))
        (t_2 (* (* (+ a (* b c)) c) i)))
   (if (<= t_2 -1e+74) t_1 (if (<= t_2 5e-9) (* (fma t z (* y x)) 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 = 2.0 * ((t * z) - ((fma(c, b, a) * c) * i));
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -1e+74) {
		tmp = t_1;
	} else if (t_2 <= 5e-9) {
		tmp = fma(t, z, (y * x)) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(t * z) - Float64(Float64(fma(c, b, a) * c) * i)))
	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-9)
		tmp = Float64(fma(t, z, Float64(y * x)) * 2.0);
	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[(t * z), $MachinePrecision] - N[(N[(N[(c * b + a), $MachinePrecision] * c), $MachinePrecision] * i), $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-9], N[(N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision] * 2.0), $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 5.0000000000000001e-9 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   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 c around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(-1 \cdot \left(b \cdot \left(c \cdot i\right)\right) - a \cdot i, c, t \cdot z + x \cdot y\right) \]

      4. associate-*r* N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(\left(-1 \cdot b\right) \cdot \left(c \cdot i\right) - a \cdot i, c, t \cdot z + x \cdot y\right) \]

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 88.9

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

   4. Applied rewrites 88.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   6. 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. +-commutative N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. lift-fma.f64 69.3

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

   7. Applied rewrites 69.3%

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

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

   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 c around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 54.9

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

   4. Applied rewrites 54.9%

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

Alternative 8: 79.7% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -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) (* (* i c) a)))
       (if (<= t_2 5e-9) (* (fma t z (* y x)) 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 = -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) - ((i * c) * a));
	} else if (t_2 <= 5e-9) {
		tmp = fma(t, z, (y * x)) * 2.0;
	} 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 <= -1e+205)
		tmp = t_1;
	elseif (t_2 <= -1e+74)
		tmp = Float64(2.0 * Float64(Float64(t * z) - Float64(Float64(i * c) * a)));
	elseif (t_2 <= 5e-9)
		tmp = Float64(fma(t, z, Float64(y * x)) * 2.0);
	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, -1e+205], t$95$1, If[LessEqual[t$95$2, -1e+74], N[(2.0 * N[(N[(t * z), $MachinePrecision] - N[(N[(i * c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e-9], N[(N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision] * 2.0), $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 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 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. 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 47.7

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

   4. Applied rewrites 47.7%

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

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

   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 c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 73.4

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

   7. Applied rewrites 73.4%

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

   8. Taylor expanded in x around 0

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

      1. lift-*.f64 49.8

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

   10. Applied rewrites 49.8%

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

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

   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 c around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 54.9

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

   4. Applied rewrites 54.9%

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

Alternative 9: 79.6% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -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) (* (fma t z (* y x)) 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 = -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 = fma(t, z, (y * x)) * 2.0;
	} 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+179)
		tmp = t_1;
	elseif (t_2 <= 5e-9)
		tmp = Float64(fma(t, z, Float64(y * x)) * 2.0);
	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+179], t$95$1, If[LessEqual[t$95$2, 5e-9], N[(N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision] * 2.0), $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 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 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. 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 47.7

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

   4. Applied rewrites 47.7%

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

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

   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 c around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 54.9

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

   4. Applied rewrites 54.9%

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

Alternative 10: 74.3% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (<= t_1 -5e+229)
     (* (* c (* c (* i b))) -2.0)
     (if (<= t_1 4e+303)
       (* (fma t z (* y x)) 2.0)
       (* (* (* 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+229) {
		tmp = (c * (c * (i * b))) * -2.0;
	} else if (t_1 <= 4e+303) {
		tmp = fma(t, z, (y * x)) * 2.0;
	} 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+229)
		tmp = Float64(Float64(c * Float64(c * Float64(i * b))) * -2.0);
	elseif (t_1 <= 4e+303)
		tmp = Float64(fma(t, z, Float64(y * x)) * 2.0);
	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+229], N[(N[(c * N[(c * N[(i * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[t$95$1, 4e+303], N[(N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision] * 2.0), $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) < -5.0000000000000005e229

   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 b around inf

      \[\leadsto \color{blue}{-2 \cdot \left(b \cdot \left({c}^{2} \cdot i\right)\right)} \]
   3. 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 33.6

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

   4. Applied rewrites 33.6%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2} \]
   5. 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. pow2 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. pow2 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 32.4

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

   6. Applied rewrites 32.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 33.6

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

   8. Applied rewrites 33.6%

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

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

   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 c around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 54.9

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

   4. Applied rewrites 54.9%

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

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

   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 b around inf

      \[\leadsto \color{blue}{-2 \cdot \left(b \cdot \left({c}^{2} \cdot i\right)\right)} \]
   3. 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 33.6

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

   4. Applied rewrites 33.6%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2} \]
   5. 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. lift-*.f64 34.6

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

   6. Applied rewrites 34.6%

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

Alternative 11: 73.9% accurate, 0.6× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

      \[\leadsto \color{blue}{-2 \cdot \left(b \cdot \left({c}^{2} \cdot i\right)\right)} \]
   3. 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 33.6

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

   4. Applied rewrites 33.6%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2} \]
   5. 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. pow2 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. pow2 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 32.4

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

   6. Applied rewrites 32.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 33.6

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

   8. Applied rewrites 33.6%

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

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

   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 c around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 54.9

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

   4. Applied rewrites 54.9%

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

Alternative 12: 73.4% accurate, 0.6× speedup

Math

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

FPCore

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

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-2.0 * Float64(i * b)) * Float64(c * c))
	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(fma(t, z, Float64(y * x)) * 2.0);
	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[(i * b), $MachinePrecision]), $MachinePrecision] * N[(c * 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+229], t$95$1, If[LessEqual[t$95$2, 4e+303], N[(N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision] * 2.0), $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 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 c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. distribute-lft-out N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. unpow2 N/A

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

      11. lower-*.f64 40.7

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

   4. Applied rewrites 40.7%

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

   5. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 32.4

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

   7. Applied rewrites 32.4%

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

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

   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 c around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 54.9

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

   4. Applied rewrites 54.9%

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

Alternative 13: 62.8% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (* i c) a) -2.0)) (t_2 (* (* (+ a (* b c)) c) i)))
   (if (<= t_2 -2e+217)
     t_1
     (if (<= t_2 1e+158) (* (fma t z (* y x)) 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 = ((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 = fma(t, z, (y * x)) * 2.0;
	} 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(fma(t, z, Float64(y * x)) * 2.0);
	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[(N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision] * 2.0), $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 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 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 25.2

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

   4. Applied rewrites 25.2%

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

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

   1. Initial program 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 c around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 54.9

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

   4. Applied rewrites 54.9%

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

Alternative 14: 44.5% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ t t) z)))
   (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) (* (* (* c a) 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 = (t + t) * z;
	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 = ((c * a) * 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 = (t + t) * z
    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 = ((c * a) * 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 = (t + t) * z;
	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 = ((c * a) * i) * -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t + t) * z
	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 = ((c * a) * i) * -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t + t) * z)
	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(c * a) * 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 = (t + t) * z;
	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 = ((c * a) * 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[(t + t), $MachinePrecision] * z), $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[(c * a), $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 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 z around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 29.3

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

   4. Applied rewrites 29.3%

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

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

   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 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 25.2

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

   4. Applied rewrites 25.2%

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

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

   1. Initial program 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%

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

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

   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 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 25.2

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

   4. Applied rewrites 25.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 23.8

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

   6. Applied rewrites 23.8%

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

Alternative 15: 44.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + t\right) \cdot z\\ \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-51}:\\ \;\;\;\;\left(x + x\right) \cdot y\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+27}:\\ \;\;\;\;\left(\left(c \cdot a\right) \cdot i\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ t t) z)))
   (if (<= (* z t) -2e+128)
     t_1
     (if (<= (* z t) 2e-51)
       (* (+ x x) y)
       (if (<= (* z t) 2e+27) (* (* (* c a) 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 = (t + t) * z;
	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 = ((c * a) * 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 = (t + t) * z
    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 = ((c * a) * 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 = (t + t) * z;
	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 = ((c * a) * i) * -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t + t) * z
	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 = ((c * a) * i) * -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t + t) * z)
	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(c * a) * 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 = (t + t) * z;
	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 = ((c * a) * 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[(t + t), $MachinePrecision] * z), $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[(c * a), $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 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 z around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 29.3

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

   4. Applied rewrites 29.3%

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

   if -2.0000000000000002e128 < (*.f64 z t) < 2e-51

   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%

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

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

   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 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 25.2

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

   4. Applied rewrites 25.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 23.8

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

   6. Applied rewrites 23.8%

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

Alternative 16: 40.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + x\right) \cdot y\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 0.96:\\ \;\;\;\;\left(t + t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ x x) y)))
   (if (<= x -5.8e+34) t_1 (if (<= x 0.96) (* (+ t 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 = (x + x) * y;
	double tmp;
	if (x <= -5.8e+34) {
		tmp = t_1;
	} else if (x <= 0.96) {
		tmp = (t + t) * z;
	} 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 <= (-5.8d+34)) then
        tmp = t_1
    else if (x <= 0.96d0) then
        tmp = (t + t) * z
    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 <= -5.8e+34) {
		tmp = t_1;
	} else if (x <= 0.96) {
		tmp = (t + t) * z;
	} 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 <= -5.8e+34:
		tmp = t_1
	elif x <= 0.96:
		tmp = (t + t) * z
	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 <= -5.8e+34)
		tmp = t_1;
	elseif (x <= 0.96)
		tmp = Float64(Float64(t + t) * z);
	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 <= -5.8e+34)
		tmp = t_1;
	elseif (x <= 0.96)
		tmp = (t + t) * z;
	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, -5.8e+34], t$95$1, If[LessEqual[x, 0.96], N[(N[(t + t), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.8000000000000003e34 or 0.95999999999999996 < x

   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%

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

   if -5.8000000000000003e34 < x < 0.95999999999999996

   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 z around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 29.3

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

   4. Applied rewrites 29.3%

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

Alternative 17: 29.3% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   1. associate-*r* N/A

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

   2. lower-*.f64 N/A

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

   3. count-2-rev N/A

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

   4. lower-+.f64 29.3

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

4. Applied rewrites 29.3%

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