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

Percentage Accurate: 90.2% → 93.8%

Time: 10.6s

Alternatives: 14

Speedup: 0.6×

• 47.8% 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

real(8) function code(x, y, z, t, a, b, c, i)
    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: 90.2% 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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.8% accurate, 0.4× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ (* y x) (* t z)) (* i (* (+ (* c b) a) c)))))
   (if (<= t_1 INFINITY)
     (* 2.0 t_1)
     (*
      (* (+ (* (fma (/ (- c) t) (/ (* (fma b c a) i) y) (/ z y)) t) x) y)
      2.0))))

C

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

Julia

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

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(y * x), $MachinePrecision] + N[(t * z), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(2.0 * t$95$1), $MachinePrecision], N[(N[(N[(N[(N[(N[((-c) / t), $MachinePrecision] * N[(N[(N[(b * c + a), $MachinePrecision] * i), $MachinePrecision] / y), $MachinePrecision] + N[(z / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] + x), $MachinePrecision] * y), $MachinePrecision] * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.4%

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

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i))

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   5. Applied rewrites 38.5%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 84.6%

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

4. Final simplification 95.8%

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

Alternative 2: 81.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+106}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(b, c, a\right) \cdot c\right) \cdot i\right) \cdot -2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right) \cdot 2\\ \mathbf{elif}\;t\_1 \leq 10^{+234}:\\ \;\;\;\;\mathsf{fma}\left(\left(-a\right) \cdot c, i, t \cdot z\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot -2\right) \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* (+ (* c b) a) c))))
   (if (<= t_1 -1e+106)
     (* (* (* (fma b c a) c) i) -2.0)
     (if (<= t_1 5e-9)
       (* (fma t z (* y x)) 2.0)
       (if (<= t_1 1e+234)
         (* (fma (* (- a) c) i (* t z)) 2.0)
         (* (* (* (fma c b a) i) -2.0) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i * (((c * b) + a) * c);
	double tmp;
	if (t_1 <= -1e+106) {
		tmp = ((fma(b, c, a) * c) * i) * -2.0;
	} else if (t_1 <= 5e-9) {
		tmp = fma(t, z, (y * x)) * 2.0;
	} else if (t_1 <= 1e+234) {
		tmp = fma((-a * c), i, (t * z)) * 2.0;
	} else {
		tmp = ((fma(c, b, a) * i) * -2.0) * c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if (t_1 <= -1e+106)
		tmp = Float64(Float64(Float64(fma(b, c, a) * c) * i) * -2.0);
	elseif (t_1 <= 5e-9)
		tmp = Float64(fma(t, z, Float64(y * x)) * 2.0);
	elseif (t_1 <= 1e+234)
		tmp = Float64(fma(Float64(Float64(-a) * c), i, Float64(t * z)) * 2.0);
	else
		tmp = Float64(Float64(Float64(fma(c, b, a) * i) * -2.0) * c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+106], N[(N[(N[(N[(b * c + a), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[t$95$1, 5e-9], N[(N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+234], N[(N[(N[((-a) * c), $MachinePrecision] * i + N[(t * z), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision] * -2.0), $MachinePrecision] * c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -1.00000000000000009e106

   1. Initial program 86.5%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. lower-*.f64 N/A

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

      7. distribute-lft-out N/A

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

      8. associate-*r* N/A

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

      9. distribute-rgt-in N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 78.3

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

   5. Applied rewrites 78.3%

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

   7. Applied rewrites 81.7%

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

   if -1.00000000000000009e106 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.0000000000000001e-9

   1. Initial program 99.1%

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

   3. Taylor expanded in c around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 89.7

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

   5. Applied rewrites 89.7%

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

   if 5.0000000000000001e-9 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1.00000000000000002e234

   1. Initial program 95.7%

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

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. neg-mul-1 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 80.4

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

   5. Applied rewrites 80.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 81.1%

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

   if 1.00000000000000002e234 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 79.9%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. lower-*.f64 N/A

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

      7. distribute-lft-out N/A

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

      8. associate-*r* N/A

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

      9. distribute-rgt-in N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 93.3

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

   5. Applied rewrites 93.3%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -1 \cdot 10^{+106}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(b, c, a\right) \cdot c\right) \cdot i\right) \cdot -2\\ \mathbf{elif}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 5 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right) \cdot 2\\ \mathbf{elif}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 10^{+234}:\\ \;\;\;\;\mathsf{fma}\left(\left(-a\right) \cdot c, i, t \cdot z\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot -2\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+263}:\\ \;\;\;\;\left(\left(\frac{a}{c} + b\right) \cdot i\right) \cdot \left(\left(c \cdot c\right) \cdot -2\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+157}:\\ \;\;\;\;\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \left(\left(-a\right) \cdot c\right) \cdot i\right)\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot -2\right) \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* (+ (* c b) a) c))))
   (if (<= t_1 -4e+263)
     (* (* (+ (/ a c) b) i) (* (* c c) -2.0))
     (if (<= t_1 1e+157)
       (* (fma z t (fma x y (* (* (- a) c) i))) 2.0)
       (* (* (* (fma c b a) i) -2.0) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i * (((c * b) + a) * c);
	double tmp;
	if (t_1 <= -4e+263) {
		tmp = (((a / c) + b) * i) * ((c * c) * -2.0);
	} else if (t_1 <= 1e+157) {
		tmp = fma(z, t, fma(x, y, ((-a * c) * i))) * 2.0;
	} else {
		tmp = ((fma(c, b, a) * i) * -2.0) * c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if (t_1 <= -4e+263)
		tmp = Float64(Float64(Float64(Float64(a / c) + b) * i) * Float64(Float64(c * c) * -2.0));
	elseif (t_1 <= 1e+157)
		tmp = Float64(fma(z, t, fma(x, y, Float64(Float64(Float64(-a) * c) * i))) * 2.0);
	else
		tmp = Float64(Float64(Float64(fma(c, b, a) * i) * -2.0) * c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+263], N[(N[(N[(N[(a / c), $MachinePrecision] + b), $MachinePrecision] * i), $MachinePrecision] * N[(N[(c * c), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+157], N[(N[(z * t + N[(x * y + N[(N[((-a) * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision] * -2.0), $MachinePrecision] * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.00000000000000006e263

   1. Initial program 81.8%

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

   3. Taylor expanded in c around inf

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

      1. distribute-lft-out N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. lower-/.f64 90.7

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

   5. Applied rewrites 90.7%

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

   if -4.00000000000000006e263 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 9.99999999999999983e156

   1. Initial program 99.2%

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

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. neg-mul-1 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 94.7

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

   5. Applied rewrites 94.7%

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

   7. Applied rewrites 94.7%

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

   if 9.99999999999999983e156 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.7%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. lower-*.f64 N/A

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

      7. distribute-lft-out N/A

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

      8. associate-*r* N/A

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

      9. distribute-rgt-in N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 88.3

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

   5. Applied rewrites 88.3%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -4 \cdot 10^{+263}:\\ \;\;\;\;\left(\left(\frac{a}{c} + b\right) \cdot i\right) \cdot \left(\left(c \cdot c\right) \cdot -2\right)\\ \mathbf{elif}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 10^{+157}:\\ \;\;\;\;\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \left(\left(-a\right) \cdot c\right) \cdot i\right)\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot -2\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+304}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(b, c, a\right) \cdot c\right) \cdot i\right) \cdot -2\\ \mathbf{elif}\;t\_1 \leq 10^{+157}:\\ \;\;\;\;\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \left(\left(-a\right) \cdot c\right) \cdot i\right)\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot -2\right) \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* (+ (* c b) a) c))))
   (if (<= t_1 -2e+304)
     (* (* (* (fma b c a) c) i) -2.0)
     (if (<= t_1 1e+157)
       (* (fma z t (fma x y (* (* (- a) c) i))) 2.0)
       (* (* (* (fma c b a) i) -2.0) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i * (((c * b) + a) * c);
	double tmp;
	if (t_1 <= -2e+304) {
		tmp = ((fma(b, c, a) * c) * i) * -2.0;
	} else if (t_1 <= 1e+157) {
		tmp = fma(z, t, fma(x, y, ((-a * c) * i))) * 2.0;
	} else {
		tmp = ((fma(c, b, a) * i) * -2.0) * c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if (t_1 <= -2e+304)
		tmp = Float64(Float64(Float64(fma(b, c, a) * c) * i) * -2.0);
	elseif (t_1 <= 1e+157)
		tmp = Float64(fma(z, t, fma(x, y, Float64(Float64(Float64(-a) * c) * i))) * 2.0);
	else
		tmp = Float64(Float64(Float64(fma(c, b, a) * i) * -2.0) * c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+304], N[(N[(N[(N[(b * c + a), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+157], N[(N[(z * t + N[(x * y + N[(N[((-a) * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision] * -2.0), $MachinePrecision] * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -1.9999999999999999e304

   1. Initial program 81.4%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. lower-*.f64 N/A

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

      7. distribute-lft-out N/A

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

      8. associate-*r* N/A

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

      9. distribute-rgt-in N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 86.0

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

   5. Applied rewrites 86.0%

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

   7. Applied rewrites 86.2%

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

   if -1.9999999999999999e304 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 9.99999999999999983e156

   1. Initial program 99.2%

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

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. neg-mul-1 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 94.7

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

   5. Applied rewrites 94.7%

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

   7. Applied rewrites 94.7%

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

   if 9.99999999999999983e156 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.7%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. lower-*.f64 N/A

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

      7. distribute-lft-out N/A

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

      8. associate-*r* N/A

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

      9. distribute-rgt-in N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 88.3

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

   5. Applied rewrites 88.3%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -2 \cdot 10^{+304}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(b, c, a\right) \cdot c\right) \cdot i\right) \cdot -2\\ \mathbf{elif}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 10^{+157}:\\ \;\;\;\;\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \left(\left(-a\right) \cdot c\right) \cdot i\right)\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot -2\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+106}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(b, c, a\right) \cdot c\right) \cdot i\right) \cdot -2\\ \mathbf{elif}\;t\_1 \leq 10^{+157}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot -2\right) \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* (+ (* c b) a) c))))
   (if (<= t_1 -1e+106)
     (* (* (* (fma b c a) c) i) -2.0)
     (if (<= t_1 1e+157)
       (* (fma t z (* y x)) 2.0)
       (* (* (* (fma c b a) i) -2.0) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i * (((c * b) + a) * c);
	double tmp;
	if (t_1 <= -1e+106) {
		tmp = ((fma(b, c, a) * c) * i) * -2.0;
	} else if (t_1 <= 1e+157) {
		tmp = fma(t, z, (y * x)) * 2.0;
	} else {
		tmp = ((fma(c, b, a) * i) * -2.0) * c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if (t_1 <= -1e+106)
		tmp = Float64(Float64(Float64(fma(b, c, a) * c) * i) * -2.0);
	elseif (t_1 <= 1e+157)
		tmp = Float64(fma(t, z, Float64(y * x)) * 2.0);
	else
		tmp = Float64(Float64(Float64(fma(c, b, a) * i) * -2.0) * c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+106], N[(N[(N[(N[(b * c + a), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+157], N[(N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision] * -2.0), $MachinePrecision] * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -1.00000000000000009e106

   1. Initial program 86.5%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. lower-*.f64 N/A

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

      7. distribute-lft-out N/A

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

      8. associate-*r* N/A

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

      9. distribute-rgt-in N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 78.3

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

   5. Applied rewrites 78.3%

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

   7. Applied rewrites 81.7%

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

   if -1.00000000000000009e106 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 9.99999999999999983e156

   1. Initial program 99.2%

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

   3. Taylor expanded in c around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 85.2

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

   5. Applied rewrites 85.2%

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

   if 9.99999999999999983e156 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.7%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. lower-*.f64 N/A

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

      7. distribute-lft-out N/A

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

      8. associate-*r* N/A

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

      9. distribute-rgt-in N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 88.3

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

   5. Applied rewrites 88.3%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -1 \cdot 10^{+106}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(b, c, a\right) \cdot c\right) \cdot i\right) \cdot -2\\ \mathbf{elif}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 10^{+157}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot -2\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot -2\right) \cdot c\\ t_2 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+157}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (* (fma c b a) i) -2.0) c)) (t_2 (* i (* (+ (* c b) a) c))))
   (if (<= t_2 -1e+106)
     t_1
     (if (<= t_2 1e+157) (* (fma t z (* y x)) 2.0) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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) * -2.0) * c;
	double t_2 = i * (((c * b) + a) * c);
	double tmp;
	if (t_2 <= -1e+106) {
		tmp = t_1;
	} else if (t_2 <= 1e+157) {
		tmp = fma(t, z, (y * x)) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(fma(c, b, a) * i) * -2.0) * c)
	t_2 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if (t_2 <= -1e+106)
		tmp = t_1;
	elseif (t_2 <= 1e+157)
		tmp = Float64(fma(t, z, Float64(y * x)) * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision] * -2.0), $MachinePrecision] * c), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+106], t$95$1, If[LessEqual[t$95$2, 1e+157], 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) < -1.00000000000000009e106 or 9.99999999999999983e156 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 83.4%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. lower-*.f64 N/A

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

      7. distribute-lft-out N/A

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

      8. associate-*r* N/A

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

      9. distribute-rgt-in N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 83.6

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

   5. Applied rewrites 83.6%

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

   if -1.00000000000000009e106 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 9.99999999999999983e156

   1. Initial program 99.2%

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

   3. Taylor expanded in c around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 85.2

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

   5. Applied rewrites 85.2%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -1 \cdot 10^{+106}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot -2\right) \cdot c\\ \mathbf{elif}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 10^{+157}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot -2\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(i \cdot c\right) \cdot b\right) \cdot -2\right) \cdot c\\ t_2 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+157}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (* (* i c) b) -2.0) c)) (t_2 (* i (* (+ (* c b) a) c))))
   (if (<= t_2 -2e+304)
     t_1
     (if (<= t_2 1e+157) (* (fma t z (* y x)) 2.0) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((i * c) * b) * -2.0) * c;
	double t_2 = i * (((c * b) + a) * c);
	double tmp;
	if (t_2 <= -2e+304) {
		tmp = t_1;
	} else if (t_2 <= 1e+157) {
		tmp = fma(t, z, (y * x)) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(i * c) * b) * -2.0) * c)
	t_2 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if (t_2 <= -2e+304)
		tmp = t_1;
	elseif (t_2 <= 1e+157)
		tmp = Float64(fma(t, z, Float64(y * x)) * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(i * c), $MachinePrecision] * b), $MachinePrecision] * -2.0), $MachinePrecision] * c), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+304], t$95$1, If[LessEqual[t$95$2, 1e+157], 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) < -1.9999999999999999e304 or 9.99999999999999983e156 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 81.0%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 68.1

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

   5. Applied rewrites 68.1%

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

   if -1.9999999999999999e304 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 9.99999999999999983e156

   1. Initial program 99.2%

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

   3. Taylor expanded in c around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 79.5

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

   5. Applied rewrites 79.5%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -2 \cdot 10^{+304}:\\ \;\;\;\;\left(\left(\left(i \cdot c\right) \cdot b\right) \cdot -2\right) \cdot c\\ \mathbf{elif}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 10^{+157}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(i \cdot c\right) \cdot b\right) \cdot -2\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+304}:\\ \;\;\;\;\left(\left(\left(i \cdot b\right) \cdot c\right) \cdot -2\right) \cdot c\\ \mathbf{elif}\;t\_1 \leq 10^{+157}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-2 \cdot b\right) \cdot c\right) \cdot \left(i \cdot c\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* (+ (* c b) a) c))))
   (if (<= t_1 -2e+304)
     (* (* (* (* i b) c) -2.0) c)
     (if (<= t_1 1e+157)
       (* (fma t z (* y x)) 2.0)
       (* (* (* -2.0 b) c) (* i c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i * (((c * b) + a) * c);
	double tmp;
	if (t_1 <= -2e+304) {
		tmp = (((i * b) * c) * -2.0) * c;
	} else if (t_1 <= 1e+157) {
		tmp = fma(t, z, (y * x)) * 2.0;
	} else {
		tmp = ((-2.0 * b) * c) * (i * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if (t_1 <= -2e+304)
		tmp = Float64(Float64(Float64(Float64(i * b) * c) * -2.0) * c);
	elseif (t_1 <= 1e+157)
		tmp = Float64(fma(t, z, Float64(y * x)) * 2.0);
	else
		tmp = Float64(Float64(Float64(-2.0 * b) * c) * Float64(i * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+304], N[(N[(N[(N[(i * b), $MachinePrecision] * c), $MachinePrecision] * -2.0), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t$95$1, 1e+157], N[(N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(N[(-2.0 * b), $MachinePrecision] * c), $MachinePrecision] * N[(i * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -1.9999999999999999e304

   1. Initial program 81.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 74.1

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

   5. Applied rewrites 74.1%

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

   7. Applied rewrites 71.8%

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

   if -1.9999999999999999e304 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 9.99999999999999983e156

   1. Initial program 99.2%

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

   3. Taylor expanded in c around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 79.5

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

   5. Applied rewrites 79.5%

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

   if 9.99999999999999983e156 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.7%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

   7. Applied rewrites 63.0%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -2 \cdot 10^{+304}:\\ \;\;\;\;\left(\left(\left(i \cdot b\right) \cdot c\right) \cdot -2\right) \cdot c\\ \mathbf{elif}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 10^{+157}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-2 \cdot b\right) \cdot c\right) \cdot \left(i \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(-2 \cdot b\right) \cdot c\right) \cdot \left(i \cdot c\right)\\ t_2 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+157}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (* -2.0 b) c) (* i c))) (t_2 (* i (* (+ (* c b) a) c))))
   (if (<= t_2 -2e+304)
     t_1
     (if (<= t_2 1e+157) (* (fma t z (* y x)) 2.0) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((-2.0 * b) * c) * (i * c);
	double t_2 = i * (((c * b) + a) * c);
	double tmp;
	if (t_2 <= -2e+304) {
		tmp = t_1;
	} else if (t_2 <= 1e+157) {
		tmp = fma(t, z, (y * x)) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(-2.0 * b) * c) * Float64(i * c))
	t_2 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if (t_2 <= -2e+304)
		tmp = t_1;
	elseif (t_2 <= 1e+157)
		tmp = Float64(fma(t, z, Float64(y * x)) * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(-2.0 * b), $MachinePrecision] * c), $MachinePrecision] * N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+304], t$95$1, If[LessEqual[t$95$2, 1e+157], 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) < -1.9999999999999999e304 or 9.99999999999999983e156 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 81.0%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 68.1

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

   5. Applied rewrites 68.1%

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

   7. Applied rewrites 66.4%

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

   if -1.9999999999999999e304 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 9.99999999999999983e156

   1. Initial program 99.2%

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

   3. Taylor expanded in c around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 79.5

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

   5. Applied rewrites 79.5%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -2 \cdot 10^{+304}:\\ \;\;\;\;\left(\left(-2 \cdot b\right) \cdot c\right) \cdot \left(i \cdot c\right)\\ \mathbf{elif}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 10^{+157}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-2 \cdot b\right) \cdot c\right) \cdot \left(i \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ t_2 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+214}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (* i c) a) -2.0)) (t_2 (* i (* (+ (* c b) a) c))))
   (if (<= t_2 -1e+106)
     t_1
     (if (<= t_2 2e+214) (* (fma t z (* y x)) 2.0) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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 = i * (((c * b) + a) * c);
	double tmp;
	if (t_2 <= -1e+106) {
		tmp = t_1;
	} else if (t_2 <= 2e+214) {
		tmp = fma(t, z, (y * x)) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(i * c) * a) * -2.0)
	t_2 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if (t_2 <= -1e+106)
		tmp = t_1;
	elseif (t_2 <= 2e+214)
		tmp = Float64(fma(t, z, Float64(y * x)) * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+106], t$95$1, If[LessEqual[t$95$2, 2e+214], 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) < -1.00000000000000009e106 or 1.9999999999999999e214 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 83.4%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 46.2

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

   5. Applied rewrites 46.2%

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

   if -1.00000000000000009e106 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1.9999999999999999e214

   1. Initial program 98.5%

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

   3. Taylor expanded in c around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 83.0

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

   5. Applied rewrites 83.0%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -1 \cdot 10^{+106}:\\ \;\;\;\;\left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ \mathbf{elif}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 2 \cdot 10^{+214}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 92.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+296}:\\ \;\;\;\;2 \cdot \left(\left(y \cdot x + t \cdot z\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot -2\right) \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* (+ (* c b) a) c))))
   (if (<= t_1 2e+296)
     (* 2.0 (- (+ (* y x) (* t z)) t_1))
     (* (* (* (fma c b a) i) -2.0) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i * (((c * b) + a) * c);
	double tmp;
	if (t_1 <= 2e+296) {
		tmp = 2.0 * (((y * x) + (t * z)) - t_1);
	} else {
		tmp = ((fma(c, b, a) * i) * -2.0) * c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if (t_1 <= 2e+296)
		tmp = Float64(2.0 * Float64(Float64(Float64(y * x) + Float64(t * z)) - t_1));
	else
		tmp = Float64(Float64(Float64(fma(c, b, a) * i) * -2.0) * c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+296], N[(2.0 * N[(N[(N[(y * x), $MachinePrecision] + N[(t * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision] * -2.0), $MachinePrecision] * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1.99999999999999996e296

   1. Initial program 95.0%

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

   if 1.99999999999999996e296 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 78.4%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. lower-*.f64 N/A

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

      7. distribute-lft-out N/A

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

      8. associate-*r* N/A

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

      9. distribute-rgt-in N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 94.5

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

   5. Applied rewrites 94.5%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 2 \cdot 10^{+296}:\\ \;\;\;\;2 \cdot \left(\left(y \cdot x + t \cdot z\right) - i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot -2\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := 2 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;t \cdot z \leq -1 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \cdot z \leq 10^{-319}:\\ \;\;\;\;\left(y \cdot x\right) \cdot 2\\ \mathbf{elif}\;t \cdot z \leq 2 \cdot 10^{+214}:\\ \;\;\;\;\left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* t z))))
   (if (<= (* t z) -1e+25)
     t_1
     (if (<= (* t z) 1e-319)
       (* (* y x) 2.0)
       (if (<= (* t z) 2e+214) (* (* (* i c) a) -2.0) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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);
	double tmp;
	if ((t * z) <= -1e+25) {
		tmp = t_1;
	} else if ((t * z) <= 1e-319) {
		tmp = (y * x) * 2.0;
	} else if ((t * z) <= 2e+214) {
		tmp = ((i * c) * a) * -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    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 = 2.0d0 * (t * z)
    if ((t * z) <= (-1d+25)) then
        tmp = t_1
    else if ((t * z) <= 1d-319) then
        tmp = (y * x) * 2.0d0
    else if ((t * z) <= 2d+214) then
        tmp = ((i * c) * a) * (-2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static 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);
	double tmp;
	if ((t * z) <= -1e+25) {
		tmp = t_1;
	} else if ((t * z) <= 1e-319) {
		tmp = (y * x) * 2.0;
	} else if ((t * z) <= 2e+214) {
		tmp = ((i * c) * a) * -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (t * z)
	tmp = 0
	if (t * z) <= -1e+25:
		tmp = t_1
	elif (t * z) <= 1e-319:
		tmp = (y * x) * 2.0
	elif (t * z) <= 2e+214:
		tmp = ((i * c) * a) * -2.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(t * z))
	tmp = 0.0
	if (Float64(t * z) <= -1e+25)
		tmp = t_1;
	elseif (Float64(t * z) <= 1e-319)
		tmp = Float64(Float64(y * x) * 2.0);
	elseif (Float64(t * z) <= 2e+214)
		tmp = Float64(Float64(Float64(i * c) * a) * -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (t * z);
	tmp = 0.0;
	if ((t * z) <= -1e+25)
		tmp = t_1;
	elseif ((t * z) <= 1e-319)
		tmp = (y * x) * 2.0;
	elseif ((t * z) <= 2e+214)
		tmp = ((i * c) * a) * -2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t * z), $MachinePrecision], -1e+25], t$95$1, If[LessEqual[N[(t * z), $MachinePrecision], 1e-319], N[(N[(y * x), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[N[(t * z), $MachinePrecision], 2e+214], N[(N[(N[(i * c), $MachinePrecision] * a), $MachinePrecision] * -2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1.00000000000000009e25 or 1.9999999999999999e214 < (*.f64 z t)

   1. Initial program 89.2%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 67.4

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

   5. Applied rewrites 67.4%

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

   if -1.00000000000000009e25 < (*.f64 z t) < 9.99989e-320

   1. Initial program 93.4%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 46.5

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

   5. Applied rewrites 46.5%

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

   if 9.99989e-320 < (*.f64 z t) < 1.9999999999999999e214

   1. Initial program 92.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 34.6

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

   5. Applied rewrites 34.6%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq -1 \cdot 10^{+25}:\\ \;\;\;\;2 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;t \cdot z \leq 10^{-319}:\\ \;\;\;\;\left(y \cdot x\right) \cdot 2\\ \mathbf{elif}\;t \cdot z \leq 2 \cdot 10^{+214}:\\ \;\;\;\;\left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 44.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := 2 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;t \cdot z \leq -1 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \cdot z \leq 5 \cdot 10^{+67}:\\ \;\;\;\;\left(y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* t z))))
   (if (<= (* t z) -1e+25) t_1 (if (<= (* t z) 5e+67) (* (* y x) 2.0) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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);
	double tmp;
	if ((t * z) <= -1e+25) {
		tmp = t_1;
	} else if ((t * z) <= 5e+67) {
		tmp = (y * x) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    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 = 2.0d0 * (t * z)
    if ((t * z) <= (-1d+25)) then
        tmp = t_1
    else if ((t * z) <= 5d+67) then
        tmp = (y * x) * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static 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);
	double tmp;
	if ((t * z) <= -1e+25) {
		tmp = t_1;
	} else if ((t * z) <= 5e+67) {
		tmp = (y * x) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (t * z)
	tmp = 0
	if (t * z) <= -1e+25:
		tmp = t_1
	elif (t * z) <= 5e+67:
		tmp = (y * x) * 2.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(t * z))
	tmp = 0.0
	if (Float64(t * z) <= -1e+25)
		tmp = t_1;
	elseif (Float64(t * z) <= 5e+67)
		tmp = Float64(Float64(y * x) * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (t * z);
	tmp = 0.0;
	if ((t * z) <= -1e+25)
		tmp = t_1;
	elseif ((t * z) <= 5e+67)
		tmp = (y * x) * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t * z), $MachinePrecision], -1e+25], t$95$1, If[LessEqual[N[(t * z), $MachinePrecision], 5e+67], N[(N[(y * x), $MachinePrecision] * 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1.00000000000000009e25 or 4.99999999999999976e67 < (*.f64 z t)

   1. Initial program 89.6%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 62.9

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

   5. Applied rewrites 62.9%

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

   if -1.00000000000000009e25 < (*.f64 z t) < 4.99999999999999976e67

   1. Initial program 93.1%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 37.6

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

   5. Applied rewrites 37.6%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq -1 \cdot 10^{+25}:\\ \;\;\;\;2 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;t \cdot z \leq 5 \cdot 10^{+67}:\\ \;\;\;\;\left(y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ 2 \cdot \left(t \cdot z\right) \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (* 2.0 (* t z)))

C

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

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = 2.0d0 * (t * z)
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (t * z);
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.5%

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

3. Taylor expanded in z around inf

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 32.4

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

5. Applied rewrites 32.4%

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

Developer Target 1: 94.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024327 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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