Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, E

Percentage Accurate: 85.8% → 90.2%

Time: 26.5s

Alternatives: 24

Speedup: 1.0×

• 51.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

Alternative 1: 90.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -7.5 \cdot 10^{-212}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), \mathsf{fma}\left(t, -4 \cdot a, \mathsf{fma}\left(b, c, k \cdot \left(j \cdot -27\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), -4 \cdot a\right), b \cdot c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= i -7.5e-212)
   (fma
    x
    (fma 18.0 (* t (* y z)) (* i -4.0))
    (fma t (* -4.0 a) (fma b c (* k (* j -27.0)))))
   (fma
    j
    (* k -27.0)
    (fma x (* i -4.0) (fma t (fma x (* 18.0 (* y z)) (* -4.0 a)) (* b c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (i <= -7.5e-212) {
		tmp = fma(x, fma(18.0, (t * (y * z)), (i * -4.0)), fma(t, (-4.0 * a), fma(b, c, (k * (j * -27.0)))));
	} else {
		tmp = fma(j, (k * -27.0), fma(x, (i * -4.0), fma(t, fma(x, (18.0 * (y * z)), (-4.0 * a)), (b * c))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (i <= -7.5e-212)
		tmp = fma(x, fma(18.0, Float64(t * Float64(y * z)), Float64(i * -4.0)), fma(t, Float64(-4.0 * a), fma(b, c, Float64(k * Float64(j * -27.0)))));
	else
		tmp = fma(j, Float64(k * -27.0), fma(x, Float64(i * -4.0), fma(t, fma(x, Float64(18.0 * Float64(y * z)), Float64(-4.0 * a)), Float64(b * c))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[i, -7.5e-212], N[(x * N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(-4.0 * a), $MachinePrecision] + N[(b * c + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision] + N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -7.50000000000000012e-212

   1. Initial program 83.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, k \cdot \left(j \cdot -27\right)\right)\right)\right)} \]

   if -7.50000000000000012e-212 < i

   1. Initial program 84.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 84.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. +-commutative 84.7%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 84.7%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 84.7%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 87.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 87.4%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 87.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 87.4%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 87.4%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 87.4%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 87.4%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 87.4%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.5 \cdot 10^{-212}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), \mathsf{fma}\left(t, -4 \cdot a, \mathsf{fma}\left(b, c, k \cdot \left(j \cdot -27\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), -4 \cdot a\right), b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 2: 90.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), -4 \cdot a\right), b \cdot c\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (fma
  j
  (* k -27.0)
  (fma x (* i -4.0) (fma t (fma x (* 18.0 (* y z)) (* -4.0 a)) (* b c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return fma(j, (k * -27.0), fma(x, (i * -4.0), fma(t, fma(x, (18.0 * (y * z)), (-4.0 * a)), (b * c))));
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return fma(j, Float64(k * -27.0), fma(x, Float64(i * -4.0), fma(t, fma(x, Float64(18.0 * Float64(y * z)), Float64(-4.0 * a)), Float64(b * c))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(j * N[(k * -27.0), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision] + N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.1%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Step-by-step derivation

   1. sub-neg 84.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

   2. +-commutative 84.1%

      \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

   3. associate-*l* 84.1%

      \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

   4. distribute-rgt-neg-in 84.1%

      \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

   5. fma-def 86.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

   6. *-commutative 86.1%

      \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

   7. distribute-rgt-neg-in 86.1%

      \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

   8. metadata-eval 86.1%

      \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

   9. sub-neg 86.1%

      \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

   10. +-commutative 86.1%

       \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

   11. associate-*l* 86.1%

       \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   12. distribute-rgt-neg-in 86.1%

       \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

3. Simplified 90.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

4. Final simplification 90.8%

   \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), -4 \cdot a\right), b \cdot c\right)\right)\right) \]

Alternative 3: 92.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (-
           (+ (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))) (* b c))
           (* i (* x 4.0)))
          (* k (* j 27.0)))))
   (if (<= t_1 INFINITY) t_1 (* x (- (* 18.0 (* y (* t z))) (* i 4.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = x * ((18.0 * (y * (t * z))) - (i * 4.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(i * 4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k)) < +inf.0

   1. Initial program 96.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 0.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 0.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 0.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 0.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 18.2%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 21.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 21.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 21.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 21.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 21.2%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 21.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 61.1%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right) \leq \infty:\\ \;\;\;\;\left(\left(\left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]

Alternative 4: 87.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.2 \cdot 10^{+194}:\\ \;\;\;\;\left(t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x 6.2e+194)
   (-
    (+ (* t (- (* (* y z) (* x 18.0)) (* a 4.0))) (* b c))
    (+ (* x (* i 4.0)) (* j (* k 27.0))))
   (* x (- (* 18.0 (* y (* t z))) (* i 4.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= 6.2e+194) {
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (b * c)) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= 6.2d+194) then
        tmp = ((t * (((y * z) * (x * 18.0d0)) - (a * 4.0d0))) + (b * c)) - ((x * (i * 4.0d0)) + (j * (k * 27.0d0)))
    else
        tmp = x * ((18.0d0 * (y * (t * z))) - (i * 4.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= 6.2e+194) {
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (b * c)) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= 6.2e+194:
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (b * c)) - ((x * (i * 4.0)) + (j * (k * 27.0)))
	else:
		tmp = x * ((18.0 * (y * (t * z))) - (i * 4.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= 6.2e+194)
		tmp = Float64(Float64(Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(i * 4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= 6.2e+194)
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (b * c)) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	else
		tmp = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, 6.2e+194], N[(N[(N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.1999999999999999e194

   1. Initial program 86.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 86.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 86.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 86.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 86.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 89.0%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 88.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 88.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 88.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 88.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 88.6%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 88.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   if 6.1999999999999999e194 < x

   1. Initial program 57.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 57.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 57.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 57.4%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 57.4%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 57.4%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 57.4%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 57.4%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 57.4%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 57.4%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 57.4%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 57.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 81.1%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.2 \cdot 10^{+194}:\\ \;\;\;\;\left(t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]

Alternative 5: 58.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := b \cdot c + t_1\\ t_3 := 27 \cdot \left(k \cdot j\right)\\ t_4 := x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{+119}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{+21}:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-276}:\\ \;\;\;\;t_1 - t_3\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+84}:\\ \;\;\;\;b \cdot c - t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t a)))
        (t_2 (+ (* b c) t_1))
        (t_3 (* 27.0 (* k j)))
        (t_4 (* x (- (* 18.0 (* y (* t z))) (* i 4.0)))))
   (if (<= x -9.2e+119)
     t_4
     (if (<= x -1.08e+21)
       (+ (* -4.0 (* i x)) (* j (* k -27.0)))
       (if (<= x -5.6e-39)
         (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))
         (if (<= x -6.5e-126)
           t_2
           (if (<= x 1.45e-276)
             (- t_1 t_3)
             (if (<= x 3.8e-206)
               t_2
               (if (<= x 1.9e+84) (- (* b c) t_3) t_4)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double t_2 = (b * c) + t_1;
	double t_3 = 27.0 * (k * j);
	double t_4 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	double tmp;
	if (x <= -9.2e+119) {
		tmp = t_4;
	} else if (x <= -1.08e+21) {
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0));
	} else if (x <= -5.6e-39) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (x <= -6.5e-126) {
		tmp = t_2;
	} else if (x <= 1.45e-276) {
		tmp = t_1 - t_3;
	} else if (x <= 3.8e-206) {
		tmp = t_2;
	} else if (x <= 1.9e+84) {
		tmp = (b * c) - t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * a)
    t_2 = (b * c) + t_1
    t_3 = 27.0d0 * (k * j)
    t_4 = x * ((18.0d0 * (y * (t * z))) - (i * 4.0d0))
    if (x <= (-9.2d+119)) then
        tmp = t_4
    else if (x <= (-1.08d+21)) then
        tmp = ((-4.0d0) * (i * x)) + (j * (k * (-27.0d0)))
    else if (x <= (-5.6d-39)) then
        tmp = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    else if (x <= (-6.5d-126)) then
        tmp = t_2
    else if (x <= 1.45d-276) then
        tmp = t_1 - t_3
    else if (x <= 3.8d-206) then
        tmp = t_2
    else if (x <= 1.9d+84) then
        tmp = (b * c) - t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double t_2 = (b * c) + t_1;
	double t_3 = 27.0 * (k * j);
	double t_4 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	double tmp;
	if (x <= -9.2e+119) {
		tmp = t_4;
	} else if (x <= -1.08e+21) {
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0));
	} else if (x <= -5.6e-39) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (x <= -6.5e-126) {
		tmp = t_2;
	} else if (x <= 1.45e-276) {
		tmp = t_1 - t_3;
	} else if (x <= 3.8e-206) {
		tmp = t_2;
	} else if (x <= 1.9e+84) {
		tmp = (b * c) - t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (t * a)
	t_2 = (b * c) + t_1
	t_3 = 27.0 * (k * j)
	t_4 = x * ((18.0 * (y * (t * z))) - (i * 4.0))
	tmp = 0
	if x <= -9.2e+119:
		tmp = t_4
	elif x <= -1.08e+21:
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0))
	elif x <= -5.6e-39:
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	elif x <= -6.5e-126:
		tmp = t_2
	elif x <= 1.45e-276:
		tmp = t_1 - t_3
	elif x <= 3.8e-206:
		tmp = t_2
	elif x <= 1.9e+84:
		tmp = (b * c) - t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(t * a))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(27.0 * Float64(k * j))
	t_4 = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -9.2e+119)
		tmp = t_4;
	elseif (x <= -1.08e+21)
		tmp = Float64(Float64(-4.0 * Float64(i * x)) + Float64(j * Float64(k * -27.0)));
	elseif (x <= -5.6e-39)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	elseif (x <= -6.5e-126)
		tmp = t_2;
	elseif (x <= 1.45e-276)
		tmp = Float64(t_1 - t_3);
	elseif (x <= 3.8e-206)
		tmp = t_2;
	elseif (x <= 1.9e+84)
		tmp = Float64(Float64(b * c) - t_3);
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (t * a);
	t_2 = (b * c) + t_1;
	t_3 = 27.0 * (k * j);
	t_4 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	tmp = 0.0;
	if (x <= -9.2e+119)
		tmp = t_4;
	elseif (x <= -1.08e+21)
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0));
	elseif (x <= -5.6e-39)
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	elseif (x <= -6.5e-126)
		tmp = t_2;
	elseif (x <= 1.45e-276)
		tmp = t_1 - t_3;
	elseif (x <= 3.8e-206)
		tmp = t_2;
	elseif (x <= 1.9e+84)
		tmp = (b * c) - t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.2e+119], t$95$4, If[LessEqual[x, -1.08e+21], N[(N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.6e-39], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.5e-126], t$95$2, If[LessEqual[x, 1.45e-276], N[(t$95$1 - t$95$3), $MachinePrecision], If[LessEqual[x, 3.8e-206], t$95$2, If[LessEqual[x, 1.9e+84], N[(N[(b * c), $MachinePrecision] - t$95$3), $MachinePrecision], t$95$4]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -9.2000000000000003e119 or 1.9e84 < x

   1. Initial program 68.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 68.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 68.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 68.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 68.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 70.6%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 73.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 73.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 73.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 73.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 73.7%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 73.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 72.9%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

   if -9.2000000000000003e119 < x < -1.08e21

   1. Initial program 89.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 84.2%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around 0 69.0%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 69.0%

         \[\leadsto \color{blue}{-\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]

      2. *-commutative 69.0%

         \[\leadsto -\left(4 \cdot \color{blue}{\left(x \cdot i\right)} + 27 \cdot \left(k \cdot j\right)\right) \]

      3. distribute-neg-in 69.0%

         \[\leadsto \color{blue}{\left(-4 \cdot \left(x \cdot i\right)\right) + \left(-27 \cdot \left(k \cdot j\right)\right)} \]

      4. distribute-lft-neg-in 69.0%

         \[\leadsto \color{blue}{\left(-4\right) \cdot \left(x \cdot i\right)} + \left(-27 \cdot \left(k \cdot j\right)\right) \]

      5. metadata-eval 69.0%

         \[\leadsto \color{blue}{-4} \cdot \left(x \cdot i\right) + \left(-27 \cdot \left(k \cdot j\right)\right) \]

      6. distribute-lft-neg-in 69.0%

         \[\leadsto -4 \cdot \left(x \cdot i\right) + \color{blue}{\left(-27\right) \cdot \left(k \cdot j\right)} \]

      7. metadata-eval 69.0%

         \[\leadsto -4 \cdot \left(x \cdot i\right) + \color{blue}{-27} \cdot \left(k \cdot j\right) \]

      8. associate-*r* 69.1%

         \[\leadsto -4 \cdot \left(x \cdot i\right) + \color{blue}{\left(-27 \cdot k\right) \cdot j} \]

   5. Simplified 69.1%

      \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right) + \left(-27 \cdot k\right) \cdot j} \]

   if -1.08e21 < x < -5.6000000000000003e-39

   1. Initial program 80.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 80.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 80.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 80.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 80.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 93.6%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 93.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 93.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 93.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 93.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 93.6%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 61.8%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   if -5.6000000000000003e-39 < x < -6.50000000000000014e-126 or 1.44999999999999994e-276 < x < 3.80000000000000003e-206

   1. Initial program 99.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 99.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 99.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 99.9%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 97.4%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 97.4%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 97.4%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 97.4%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 97.4%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 97.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 88.5%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in x around 0 81.4%

      \[\leadsto \color{blue}{c \cdot b + -4 \cdot \left(a \cdot t\right)} \]

   if -6.50000000000000014e-126 < x < 1.44999999999999994e-276

   1. Initial program 92.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around -inf 74.5%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(-18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - -4 \cdot a\right) \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in y around 0 70.6%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) - 27 \cdot \left(k \cdot j\right)} \]

   if 3.80000000000000003e-206 < x < 1.9e84

   1. Initial program 93.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 81.2%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 65.4%

      \[\leadsto \color{blue}{c \cdot b - 27 \cdot \left(k \cdot j\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{+21}:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-126}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-276}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-206}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+84}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]

Alternative 6: 61.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_2 := t_1 - 27 \cdot \left(k \cdot j\right)\\ t_3 := b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{if}\;y \leq -3.75 \cdot 10^{+164}:\\ \;\;\;\;t_1 - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-18}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-59}:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+27}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* y (* t (* x z)))))
        (t_2 (- t_1 (* 27.0 (* k j))))
        (t_3 (- (* b c) (+ (* 4.0 (* i x)) (* 4.0 (* t a))))))
   (if (<= y -3.75e+164)
     (- t_1 (* j (* k 27.0)))
     (if (<= y -1.85e+112)
       (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))
       (if (<= y -3.8e+71)
         t_2
         (if (<= y -6.5e-18)
           t_3
           (if (<= y -2.8e-59)
             (+ (* -4.0 (* i x)) (* j (* k -27.0)))
             (if (<= y 1.65e+27) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (y * (t * (x * z)));
	double t_2 = t_1 - (27.0 * (k * j));
	double t_3 = (b * c) - ((4.0 * (i * x)) + (4.0 * (t * a)));
	double tmp;
	if (y <= -3.75e+164) {
		tmp = t_1 - (j * (k * 27.0));
	} else if (y <= -1.85e+112) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (y <= -3.8e+71) {
		tmp = t_2;
	} else if (y <= -6.5e-18) {
		tmp = t_3;
	} else if (y <= -2.8e-59) {
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0));
	} else if (y <= 1.65e+27) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 18.0d0 * (y * (t * (x * z)))
    t_2 = t_1 - (27.0d0 * (k * j))
    t_3 = (b * c) - ((4.0d0 * (i * x)) + (4.0d0 * (t * a)))
    if (y <= (-3.75d+164)) then
        tmp = t_1 - (j * (k * 27.0d0))
    else if (y <= (-1.85d+112)) then
        tmp = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    else if (y <= (-3.8d+71)) then
        tmp = t_2
    else if (y <= (-6.5d-18)) then
        tmp = t_3
    else if (y <= (-2.8d-59)) then
        tmp = ((-4.0d0) * (i * x)) + (j * (k * (-27.0d0)))
    else if (y <= 1.65d+27) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (y * (t * (x * z)));
	double t_2 = t_1 - (27.0 * (k * j));
	double t_3 = (b * c) - ((4.0 * (i * x)) + (4.0 * (t * a)));
	double tmp;
	if (y <= -3.75e+164) {
		tmp = t_1 - (j * (k * 27.0));
	} else if (y <= -1.85e+112) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (y <= -3.8e+71) {
		tmp = t_2;
	} else if (y <= -6.5e-18) {
		tmp = t_3;
	} else if (y <= -2.8e-59) {
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0));
	} else if (y <= 1.65e+27) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (y * (t * (x * z)))
	t_2 = t_1 - (27.0 * (k * j))
	t_3 = (b * c) - ((4.0 * (i * x)) + (4.0 * (t * a)))
	tmp = 0
	if y <= -3.75e+164:
		tmp = t_1 - (j * (k * 27.0))
	elif y <= -1.85e+112:
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	elif y <= -3.8e+71:
		tmp = t_2
	elif y <= -6.5e-18:
		tmp = t_3
	elif y <= -2.8e-59:
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0))
	elif y <= 1.65e+27:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))))
	t_2 = Float64(t_1 - Float64(27.0 * Float64(k * j)))
	t_3 = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(i * x)) + Float64(4.0 * Float64(t * a))))
	tmp = 0.0
	if (y <= -3.75e+164)
		tmp = Float64(t_1 - Float64(j * Float64(k * 27.0)));
	elseif (y <= -1.85e+112)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	elseif (y <= -3.8e+71)
		tmp = t_2;
	elseif (y <= -6.5e-18)
		tmp = t_3;
	elseif (y <= -2.8e-59)
		tmp = Float64(Float64(-4.0 * Float64(i * x)) + Float64(j * Float64(k * -27.0)));
	elseif (y <= 1.65e+27)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (y * (t * (x * z)));
	t_2 = t_1 - (27.0 * (k * j));
	t_3 = (b * c) - ((4.0 * (i * x)) + (4.0 * (t * a)));
	tmp = 0.0;
	if (y <= -3.75e+164)
		tmp = t_1 - (j * (k * 27.0));
	elseif (y <= -1.85e+112)
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	elseif (y <= -3.8e+71)
		tmp = t_2;
	elseif (y <= -6.5e-18)
		tmp = t_3;
	elseif (y <= -2.8e-59)
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0));
	elseif (y <= 1.65e+27)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.75e+164], N[(t$95$1 - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.85e+112], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.8e+71], t$95$2, If[LessEqual[y, -6.5e-18], t$95$3, If[LessEqual[y, -2.8e-59], N[(N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+27], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.74999999999999988e164

   1. Initial program 73.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around -inf 61.2%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(-18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - -4 \cdot a\right) \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 52.6%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - 27 \cdot \left(k \cdot j\right)} \]
   4. Step-by-step derivation

      1. pow1 52.6%

         \[\leadsto 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \color{blue}{{\left(27 \cdot \left(k \cdot j\right)\right)}^{1}} \]

   5. Applied egg-rr 52.6%

      \[\leadsto 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \color{blue}{{\left(27 \cdot \left(k \cdot j\right)\right)}^{1}} \]
   6. Step-by-step derivation

      1. unpow1 52.6%

         \[\leadsto 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \color{blue}{27 \cdot \left(k \cdot j\right)} \]

      2. *-commutative 52.6%

         \[\leadsto 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \color{blue}{\left(k \cdot j\right) \cdot 27} \]

      3. *-commutative 52.6%

         \[\leadsto 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \color{blue}{\left(j \cdot k\right)} \cdot 27 \]

      4. associate-*l* 52.6%

         \[\leadsto 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \color{blue}{j \cdot \left(k \cdot 27\right)} \]

   7. Simplified 52.6%

      \[\leadsto 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \color{blue}{j \cdot \left(k \cdot 27\right)} \]

   if -3.74999999999999988e164 < y < -1.85000000000000002e112

   1. Initial program 77.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 77.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 77.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 77.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 77.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 77.8%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 77.8%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 77.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 77.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 77.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 77.8%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 77.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 78.5%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   if -1.85000000000000002e112 < y < -3.8000000000000001e71 or 1.6499999999999999e27 < y

   1. Initial program 78.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around -inf 65.8%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(-18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - -4 \cdot a\right) \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 60.0%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - 27 \cdot \left(k \cdot j\right)} \]

   if -3.8000000000000001e71 < y < -6.50000000000000008e-18 or -2.79999999999999981e-59 < y < 1.6499999999999999e27

   1. Initial program 90.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 85.2%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in j around 0 73.4%

      \[\leadsto \color{blue}{c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)} \]

   if -6.50000000000000008e-18 < y < -2.79999999999999981e-59

   1. Initial program 74.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 51.6%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around 0 59.8%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 59.8%

         \[\leadsto \color{blue}{-\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]

      2. *-commutative 59.8%

         \[\leadsto -\left(4 \cdot \color{blue}{\left(x \cdot i\right)} + 27 \cdot \left(k \cdot j\right)\right) \]

      3. distribute-neg-in 59.8%

         \[\leadsto \color{blue}{\left(-4 \cdot \left(x \cdot i\right)\right) + \left(-27 \cdot \left(k \cdot j\right)\right)} \]

      4. distribute-lft-neg-in 59.8%

         \[\leadsto \color{blue}{\left(-4\right) \cdot \left(x \cdot i\right)} + \left(-27 \cdot \left(k \cdot j\right)\right) \]

      5. metadata-eval 59.8%

         \[\leadsto \color{blue}{-4} \cdot \left(x \cdot i\right) + \left(-27 \cdot \left(k \cdot j\right)\right) \]

      6. distribute-lft-neg-in 59.8%

         \[\leadsto -4 \cdot \left(x \cdot i\right) + \color{blue}{\left(-27\right) \cdot \left(k \cdot j\right)} \]

      7. metadata-eval 59.8%

         \[\leadsto -4 \cdot \left(x \cdot i\right) + \color{blue}{-27} \cdot \left(k \cdot j\right) \]

      8. associate-*r* 59.8%

         \[\leadsto -4 \cdot \left(x \cdot i\right) + \color{blue}{\left(-27 \cdot k\right) \cdot j} \]

   5. Simplified 59.8%

      \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right) + \left(-27 \cdot k\right) \cdot j} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.75 \cdot 10^{+164}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+71}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-18}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-59}:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+27}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - 27 \cdot \left(k \cdot j\right)\\ \end{array} \]

Alternative 7: 71.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 4 \cdot \left(t \cdot a\right)\\ t_2 := x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+18}:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -61:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq -1.06 \cdot 10^{-96}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(i \cdot x\right) + t_1\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+86}:\\ \;\;\;\;\left(b \cdot c - t_1\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* t a))) (t_2 (* x (- (* 18.0 (* y (* t z))) (* i 4.0)))))
   (if (<= x -3.4e+117)
     t_2
     (if (<= x -9e+18)
       (+ (* -4.0 (* i x)) (* j (* k -27.0)))
       (if (<= x -61.0)
         (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))
         (if (<= x -1.06e-96)
           (- (* b c) (+ (* 4.0 (* i x)) t_1))
           (if (<= x 2.2e+86) (- (- (* b c) t_1) (* k (* j 27.0))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (t * a);
	double t_2 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	double tmp;
	if (x <= -3.4e+117) {
		tmp = t_2;
	} else if (x <= -9e+18) {
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0));
	} else if (x <= -61.0) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (x <= -1.06e-96) {
		tmp = (b * c) - ((4.0 * (i * x)) + t_1);
	} else if (x <= 2.2e+86) {
		tmp = ((b * c) - t_1) - (k * (j * 27.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 4.0d0 * (t * a)
    t_2 = x * ((18.0d0 * (y * (t * z))) - (i * 4.0d0))
    if (x <= (-3.4d+117)) then
        tmp = t_2
    else if (x <= (-9d+18)) then
        tmp = ((-4.0d0) * (i * x)) + (j * (k * (-27.0d0)))
    else if (x <= (-61.0d0)) then
        tmp = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    else if (x <= (-1.06d-96)) then
        tmp = (b * c) - ((4.0d0 * (i * x)) + t_1)
    else if (x <= 2.2d+86) then
        tmp = ((b * c) - t_1) - (k * (j * 27.0d0))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (t * a);
	double t_2 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	double tmp;
	if (x <= -3.4e+117) {
		tmp = t_2;
	} else if (x <= -9e+18) {
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0));
	} else if (x <= -61.0) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (x <= -1.06e-96) {
		tmp = (b * c) - ((4.0 * (i * x)) + t_1);
	} else if (x <= 2.2e+86) {
		tmp = ((b * c) - t_1) - (k * (j * 27.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (t * a)
	t_2 = x * ((18.0 * (y * (t * z))) - (i * 4.0))
	tmp = 0
	if x <= -3.4e+117:
		tmp = t_2
	elif x <= -9e+18:
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0))
	elif x <= -61.0:
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	elif x <= -1.06e-96:
		tmp = (b * c) - ((4.0 * (i * x)) + t_1)
	elif x <= 2.2e+86:
		tmp = ((b * c) - t_1) - (k * (j * 27.0))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(t * a))
	t_2 = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -3.4e+117)
		tmp = t_2;
	elseif (x <= -9e+18)
		tmp = Float64(Float64(-4.0 * Float64(i * x)) + Float64(j * Float64(k * -27.0)));
	elseif (x <= -61.0)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	elseif (x <= -1.06e-96)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(i * x)) + t_1));
	elseif (x <= 2.2e+86)
		tmp = Float64(Float64(Float64(b * c) - t_1) - Float64(k * Float64(j * 27.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (t * a);
	t_2 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	tmp = 0.0;
	if (x <= -3.4e+117)
		tmp = t_2;
	elseif (x <= -9e+18)
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0));
	elseif (x <= -61.0)
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	elseif (x <= -1.06e-96)
		tmp = (b * c) - ((4.0 * (i * x)) + t_1);
	elseif (x <= 2.2e+86)
		tmp = ((b * c) - t_1) - (k * (j * 27.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e+117], t$95$2, If[LessEqual[x, -9e+18], N[(N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -61.0], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.06e-96], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+86], N[(N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.4000000000000001e117 or 2.20000000000000003e86 < x

   1. Initial program 68.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 68.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 68.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 68.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 68.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 70.6%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 73.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 73.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 73.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 73.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 73.7%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 73.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 72.9%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

   if -3.4000000000000001e117 < x < -9e18

   1. Initial program 89.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 84.2%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around 0 69.0%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 69.0%

         \[\leadsto \color{blue}{-\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]

      2. *-commutative 69.0%

         \[\leadsto -\left(4 \cdot \color{blue}{\left(x \cdot i\right)} + 27 \cdot \left(k \cdot j\right)\right) \]

      3. distribute-neg-in 69.0%

         \[\leadsto \color{blue}{\left(-4 \cdot \left(x \cdot i\right)\right) + \left(-27 \cdot \left(k \cdot j\right)\right)} \]

      4. distribute-lft-neg-in 69.0%

         \[\leadsto \color{blue}{\left(-4\right) \cdot \left(x \cdot i\right)} + \left(-27 \cdot \left(k \cdot j\right)\right) \]

      5. metadata-eval 69.0%

         \[\leadsto \color{blue}{-4} \cdot \left(x \cdot i\right) + \left(-27 \cdot \left(k \cdot j\right)\right) \]

      6. distribute-lft-neg-in 69.0%

         \[\leadsto -4 \cdot \left(x \cdot i\right) + \color{blue}{\left(-27\right) \cdot \left(k \cdot j\right)} \]

      7. metadata-eval 69.0%

         \[\leadsto -4 \cdot \left(x \cdot i\right) + \color{blue}{-27} \cdot \left(k \cdot j\right) \]

      8. associate-*r* 69.1%

         \[\leadsto -4 \cdot \left(x \cdot i\right) + \color{blue}{\left(-27 \cdot k\right) \cdot j} \]

   5. Simplified 69.1%

      \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right) + \left(-27 \cdot k\right) \cdot j} \]

   if -9e18 < x < -61

   1. Initial program 66.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 66.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 66.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 66.4%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 66.4%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 99.7%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 99.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 99.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 99.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 99.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 99.7%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 83.8%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   if -61 < x < -1.05999999999999998e-96

   1. Initial program 94.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 80.9%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in j around 0 69.5%

      \[\leadsto \color{blue}{c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)} \]

   if -1.05999999999999998e-96 < x < 2.20000000000000003e86

   1. Initial program 95.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 87.0%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+18}:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -61:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq -1.06 \cdot 10^{-96}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+86}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]

Alternative 8: 31.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-18}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-110}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-217}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* k j))) (t_2 (* 18.0 (* y (* t (* x z))))))
   (if (<= y -2.7e+104)
     t_2
     (if (<= y -2.2e+63)
       t_1
       (if (<= y -6.6e-18)
         (* b c)
         (if (<= y -3.6e-81)
           t_1
           (if (<= y -2.8e-110)
             (* i (* x -4.0))
             (if (<= y -1.8e-217)
               (* -4.0 (* t a))
               (if (<= y 5.8e+26) (* b c) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (k * j);
	double t_2 = 18.0 * (y * (t * (x * z)));
	double tmp;
	if (y <= -2.7e+104) {
		tmp = t_2;
	} else if (y <= -2.2e+63) {
		tmp = t_1;
	} else if (y <= -6.6e-18) {
		tmp = b * c;
	} else if (y <= -3.6e-81) {
		tmp = t_1;
	} else if (y <= -2.8e-110) {
		tmp = i * (x * -4.0);
	} else if (y <= -1.8e-217) {
		tmp = -4.0 * (t * a);
	} else if (y <= 5.8e+26) {
		tmp = b * c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-27.0d0) * (k * j)
    t_2 = 18.0d0 * (y * (t * (x * z)))
    if (y <= (-2.7d+104)) then
        tmp = t_2
    else if (y <= (-2.2d+63)) then
        tmp = t_1
    else if (y <= (-6.6d-18)) then
        tmp = b * c
    else if (y <= (-3.6d-81)) then
        tmp = t_1
    else if (y <= (-2.8d-110)) then
        tmp = i * (x * (-4.0d0))
    else if (y <= (-1.8d-217)) then
        tmp = (-4.0d0) * (t * a)
    else if (y <= 5.8d+26) then
        tmp = b * c
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (k * j);
	double t_2 = 18.0 * (y * (t * (x * z)));
	double tmp;
	if (y <= -2.7e+104) {
		tmp = t_2;
	} else if (y <= -2.2e+63) {
		tmp = t_1;
	} else if (y <= -6.6e-18) {
		tmp = b * c;
	} else if (y <= -3.6e-81) {
		tmp = t_1;
	} else if (y <= -2.8e-110) {
		tmp = i * (x * -4.0);
	} else if (y <= -1.8e-217) {
		tmp = -4.0 * (t * a);
	} else if (y <= 5.8e+26) {
		tmp = b * c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (k * j)
	t_2 = 18.0 * (y * (t * (x * z)))
	tmp = 0
	if y <= -2.7e+104:
		tmp = t_2
	elif y <= -2.2e+63:
		tmp = t_1
	elif y <= -6.6e-18:
		tmp = b * c
	elif y <= -3.6e-81:
		tmp = t_1
	elif y <= -2.8e-110:
		tmp = i * (x * -4.0)
	elif y <= -1.8e-217:
		tmp = -4.0 * (t * a)
	elif y <= 5.8e+26:
		tmp = b * c
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(k * j))
	t_2 = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))))
	tmp = 0.0
	if (y <= -2.7e+104)
		tmp = t_2;
	elseif (y <= -2.2e+63)
		tmp = t_1;
	elseif (y <= -6.6e-18)
		tmp = Float64(b * c);
	elseif (y <= -3.6e-81)
		tmp = t_1;
	elseif (y <= -2.8e-110)
		tmp = Float64(i * Float64(x * -4.0));
	elseif (y <= -1.8e-217)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (y <= 5.8e+26)
		tmp = Float64(b * c);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (k * j);
	t_2 = 18.0 * (y * (t * (x * z)));
	tmp = 0.0;
	if (y <= -2.7e+104)
		tmp = t_2;
	elseif (y <= -2.2e+63)
		tmp = t_1;
	elseif (y <= -6.6e-18)
		tmp = b * c;
	elseif (y <= -3.6e-81)
		tmp = t_1;
	elseif (y <= -2.8e-110)
		tmp = i * (x * -4.0);
	elseif (y <= -1.8e-217)
		tmp = -4.0 * (t * a);
	elseif (y <= 5.8e+26)
		tmp = b * c;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+104], t$95$2, If[LessEqual[y, -2.2e+63], t$95$1, If[LessEqual[y, -6.6e-18], N[(b * c), $MachinePrecision], If[LessEqual[y, -3.6e-81], t$95$1, If[LessEqual[y, -2.8e-110], N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.8e-217], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+26], N[(b * c), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.69999999999999985e104 or 5.8e26 < y

   1. Initial program 75.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 75.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 75.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 75.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 75.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 80.1%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 81.0%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 81.0%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 81.0%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 81.0%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 81.1%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 81.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 52.8%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 43.2%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]

   if -2.69999999999999985e104 < y < -2.1999999999999999e63 or -6.6000000000000003e-18 < y < -3.5999999999999999e-81

   1. Initial program 85.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 85.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. +-commutative 85.5%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 85.5%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 85.5%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 85.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 85.5%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 85.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 85.5%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 85.5%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 85.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 85.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 85.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 41.3%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -2.1999999999999999e63 < y < -6.6000000000000003e-18 or -1.79999999999999991e-217 < y < 5.8e26

   1. Initial program 89.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 83.6%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around inf 27.6%

      \[\leadsto \color{blue}{c \cdot b} \]

   if -3.5999999999999999e-81 < y < -2.8e-110

   1. Initial program 100.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 84.6%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in i around inf 34.3%

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

      1. *-commutative 34.3%

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      2. associate-*l* 34.3%

         \[\leadsto \color{blue}{i \cdot \left(x \cdot -4\right)} \]

   5. Simplified 34.3%

      \[\leadsto \color{blue}{i \cdot \left(x \cdot -4\right)} \]

   if -2.8e-110 < y < -1.79999999999999991e-217

   1. Initial program 100.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 94.5%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around inf 37.2%

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

      1. *-commutative 37.2%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

   5. Simplified 37.2%

      \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+104}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+63}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-18}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-81}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-110}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-217}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 9: 31.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+104}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-17}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.76 \cdot 10^{-109}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-219}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* k j))))
   (if (<= y -2.5e+104)
     (* 18.0 (* x (* t (* y z))))
     (if (<= y -4.3e+63)
       t_1
       (if (<= y -1.15e-17)
         (* b c)
         (if (<= y -2.3e-81)
           t_1
           (if (<= y -1.76e-109)
             (* i (* x -4.0))
             (if (<= y -1.36e-219)
               (* -4.0 (* t a))
               (if (<= y 1.8e+26) (* b c) (* 18.0 (* y (* t (* x z)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (k * j);
	double tmp;
	if (y <= -2.5e+104) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (y <= -4.3e+63) {
		tmp = t_1;
	} else if (y <= -1.15e-17) {
		tmp = b * c;
	} else if (y <= -2.3e-81) {
		tmp = t_1;
	} else if (y <= -1.76e-109) {
		tmp = i * (x * -4.0);
	} else if (y <= -1.36e-219) {
		tmp = -4.0 * (t * a);
	} else if (y <= 1.8e+26) {
		tmp = b * c;
	} else {
		tmp = 18.0 * (y * (t * (x * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-27.0d0) * (k * j)
    if (y <= (-2.5d+104)) then
        tmp = 18.0d0 * (x * (t * (y * z)))
    else if (y <= (-4.3d+63)) then
        tmp = t_1
    else if (y <= (-1.15d-17)) then
        tmp = b * c
    else if (y <= (-2.3d-81)) then
        tmp = t_1
    else if (y <= (-1.76d-109)) then
        tmp = i * (x * (-4.0d0))
    else if (y <= (-1.36d-219)) then
        tmp = (-4.0d0) * (t * a)
    else if (y <= 1.8d+26) then
        tmp = b * c
    else
        tmp = 18.0d0 * (y * (t * (x * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (k * j);
	double tmp;
	if (y <= -2.5e+104) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (y <= -4.3e+63) {
		tmp = t_1;
	} else if (y <= -1.15e-17) {
		tmp = b * c;
	} else if (y <= -2.3e-81) {
		tmp = t_1;
	} else if (y <= -1.76e-109) {
		tmp = i * (x * -4.0);
	} else if (y <= -1.36e-219) {
		tmp = -4.0 * (t * a);
	} else if (y <= 1.8e+26) {
		tmp = b * c;
	} else {
		tmp = 18.0 * (y * (t * (x * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (k * j)
	tmp = 0
	if y <= -2.5e+104:
		tmp = 18.0 * (x * (t * (y * z)))
	elif y <= -4.3e+63:
		tmp = t_1
	elif y <= -1.15e-17:
		tmp = b * c
	elif y <= -2.3e-81:
		tmp = t_1
	elif y <= -1.76e-109:
		tmp = i * (x * -4.0)
	elif y <= -1.36e-219:
		tmp = -4.0 * (t * a)
	elif y <= 1.8e+26:
		tmp = b * c
	else:
		tmp = 18.0 * (y * (t * (x * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(k * j))
	tmp = 0.0
	if (y <= -2.5e+104)
		tmp = Float64(18.0 * Float64(x * Float64(t * Float64(y * z))));
	elseif (y <= -4.3e+63)
		tmp = t_1;
	elseif (y <= -1.15e-17)
		tmp = Float64(b * c);
	elseif (y <= -2.3e-81)
		tmp = t_1;
	elseif (y <= -1.76e-109)
		tmp = Float64(i * Float64(x * -4.0));
	elseif (y <= -1.36e-219)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (y <= 1.8e+26)
		tmp = Float64(b * c);
	else
		tmp = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (k * j);
	tmp = 0.0;
	if (y <= -2.5e+104)
		tmp = 18.0 * (x * (t * (y * z)));
	elseif (y <= -4.3e+63)
		tmp = t_1;
	elseif (y <= -1.15e-17)
		tmp = b * c;
	elseif (y <= -2.3e-81)
		tmp = t_1;
	elseif (y <= -1.76e-109)
		tmp = i * (x * -4.0);
	elseif (y <= -1.36e-219)
		tmp = -4.0 * (t * a);
	elseif (y <= 1.8e+26)
		tmp = b * c;
	else
		tmp = 18.0 * (y * (t * (x * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+104], N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.3e+63], t$95$1, If[LessEqual[y, -1.15e-17], N[(b * c), $MachinePrecision], If[LessEqual[y, -2.3e-81], t$95$1, If[LessEqual[y, -1.76e-109], N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.36e-219], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+26], N[(b * c), $MachinePrecision], N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.4999999999999998e104

   1. Initial program 75.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 75.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 75.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 75.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 75.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 77.3%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 79.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 79.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 79.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 79.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 79.7%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 75.0%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in y around inf 40.6%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.8%

         \[\leadsto 18 \cdot \left(y \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)}\right) \]

      2. associate-*r* 47.0%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(y \cdot \left(t \cdot z\right)\right) \cdot x\right)} \]

      3. *-commutative 47.0%

         \[\leadsto 18 \cdot \left(\color{blue}{\left(\left(t \cdot z\right) \cdot y\right)} \cdot x\right) \]

      4. associate-*l* 44.9%

         \[\leadsto 18 \cdot \left(\color{blue}{\left(t \cdot \left(z \cdot y\right)\right)} \cdot x\right) \]

      5. *-commutative 44.9%

         \[\leadsto 18 \cdot \left(\left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) \cdot x\right) \]

   7. Simplified 44.9%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]

   if -2.4999999999999998e104 < y < -4.3e63 or -1.15000000000000004e-17 < y < -2.29999999999999991e-81

   1. Initial program 85.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 85.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. +-commutative 85.5%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 85.5%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 85.5%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 85.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 85.5%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 85.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 85.5%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 85.5%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 85.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 85.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 85.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 41.3%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -4.3e63 < y < -1.15000000000000004e-17 or -1.35999999999999997e-219 < y < 1.80000000000000012e26

   1. Initial program 89.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 83.6%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around inf 27.6%

      \[\leadsto \color{blue}{c \cdot b} \]

   if -2.29999999999999991e-81 < y < -1.7599999999999999e-109

   1. Initial program 100.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 84.6%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in i around inf 34.3%

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

      1. *-commutative 34.3%

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      2. associate-*l* 34.3%

         \[\leadsto \color{blue}{i \cdot \left(x \cdot -4\right)} \]

   5. Simplified 34.3%

      \[\leadsto \color{blue}{i \cdot \left(x \cdot -4\right)} \]

   if -1.7599999999999999e-109 < y < -1.35999999999999997e-219

   1. Initial program 100.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 94.5%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around inf 37.2%

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

      1. *-commutative 37.2%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

   5. Simplified 37.2%

      \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

   if 1.80000000000000012e26 < y

   1. Initial program 75.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 75.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 75.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 75.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 75.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 82.1%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 82.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 82.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 82.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 82.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 82.1%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 51.9%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 45.1%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+104}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{+63}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-17}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-81}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;y \leq -1.76 \cdot 10^{-109}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-219}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 10: 31.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+105}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-17}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.05 \cdot 10^{-109}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-218}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* k j))))
   (if (<= y -1.45e+105)
     (* 18.0 (* x (* t (* y z))))
     (if (<= y -1.95e+63)
       t_1
       (if (<= y -1.7e-17)
         (* b c)
         (if (<= y -8.2e-81)
           t_1
           (if (<= y -4.05e-109)
             (* i (* x -4.0))
             (if (<= y -5.7e-218)
               (* -4.0 (* t a))
               (if (<= y 6.2e+26) (* b c) (* 18.0 (* (* x z) (* t y))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (k * j);
	double tmp;
	if (y <= -1.45e+105) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (y <= -1.95e+63) {
		tmp = t_1;
	} else if (y <= -1.7e-17) {
		tmp = b * c;
	} else if (y <= -8.2e-81) {
		tmp = t_1;
	} else if (y <= -4.05e-109) {
		tmp = i * (x * -4.0);
	} else if (y <= -5.7e-218) {
		tmp = -4.0 * (t * a);
	} else if (y <= 6.2e+26) {
		tmp = b * c;
	} else {
		tmp = 18.0 * ((x * z) * (t * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-27.0d0) * (k * j)
    if (y <= (-1.45d+105)) then
        tmp = 18.0d0 * (x * (t * (y * z)))
    else if (y <= (-1.95d+63)) then
        tmp = t_1
    else if (y <= (-1.7d-17)) then
        tmp = b * c
    else if (y <= (-8.2d-81)) then
        tmp = t_1
    else if (y <= (-4.05d-109)) then
        tmp = i * (x * (-4.0d0))
    else if (y <= (-5.7d-218)) then
        tmp = (-4.0d0) * (t * a)
    else if (y <= 6.2d+26) then
        tmp = b * c
    else
        tmp = 18.0d0 * ((x * z) * (t * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (k * j);
	double tmp;
	if (y <= -1.45e+105) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (y <= -1.95e+63) {
		tmp = t_1;
	} else if (y <= -1.7e-17) {
		tmp = b * c;
	} else if (y <= -8.2e-81) {
		tmp = t_1;
	} else if (y <= -4.05e-109) {
		tmp = i * (x * -4.0);
	} else if (y <= -5.7e-218) {
		tmp = -4.0 * (t * a);
	} else if (y <= 6.2e+26) {
		tmp = b * c;
	} else {
		tmp = 18.0 * ((x * z) * (t * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (k * j)
	tmp = 0
	if y <= -1.45e+105:
		tmp = 18.0 * (x * (t * (y * z)))
	elif y <= -1.95e+63:
		tmp = t_1
	elif y <= -1.7e-17:
		tmp = b * c
	elif y <= -8.2e-81:
		tmp = t_1
	elif y <= -4.05e-109:
		tmp = i * (x * -4.0)
	elif y <= -5.7e-218:
		tmp = -4.0 * (t * a)
	elif y <= 6.2e+26:
		tmp = b * c
	else:
		tmp = 18.0 * ((x * z) * (t * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(k * j))
	tmp = 0.0
	if (y <= -1.45e+105)
		tmp = Float64(18.0 * Float64(x * Float64(t * Float64(y * z))));
	elseif (y <= -1.95e+63)
		tmp = t_1;
	elseif (y <= -1.7e-17)
		tmp = Float64(b * c);
	elseif (y <= -8.2e-81)
		tmp = t_1;
	elseif (y <= -4.05e-109)
		tmp = Float64(i * Float64(x * -4.0));
	elseif (y <= -5.7e-218)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (y <= 6.2e+26)
		tmp = Float64(b * c);
	else
		tmp = Float64(18.0 * Float64(Float64(x * z) * Float64(t * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (k * j);
	tmp = 0.0;
	if (y <= -1.45e+105)
		tmp = 18.0 * (x * (t * (y * z)));
	elseif (y <= -1.95e+63)
		tmp = t_1;
	elseif (y <= -1.7e-17)
		tmp = b * c;
	elseif (y <= -8.2e-81)
		tmp = t_1;
	elseif (y <= -4.05e-109)
		tmp = i * (x * -4.0);
	elseif (y <= -5.7e-218)
		tmp = -4.0 * (t * a);
	elseif (y <= 6.2e+26)
		tmp = b * c;
	else
		tmp = 18.0 * ((x * z) * (t * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e+105], N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.95e+63], t$95$1, If[LessEqual[y, -1.7e-17], N[(b * c), $MachinePrecision], If[LessEqual[y, -8.2e-81], t$95$1, If[LessEqual[y, -4.05e-109], N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.7e-218], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+26], N[(b * c), $MachinePrecision], N[(18.0 * N[(N[(x * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.45000000000000005e105

   1. Initial program 75.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 75.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 75.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 75.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 75.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 77.3%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 79.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 79.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 79.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 79.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 79.7%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 75.0%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in y around inf 40.6%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.8%

         \[\leadsto 18 \cdot \left(y \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)}\right) \]

      2. associate-*r* 47.0%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(y \cdot \left(t \cdot z\right)\right) \cdot x\right)} \]

      3. *-commutative 47.0%

         \[\leadsto 18 \cdot \left(\color{blue}{\left(\left(t \cdot z\right) \cdot y\right)} \cdot x\right) \]

      4. associate-*l* 44.9%

         \[\leadsto 18 \cdot \left(\color{blue}{\left(t \cdot \left(z \cdot y\right)\right)} \cdot x\right) \]

      5. *-commutative 44.9%

         \[\leadsto 18 \cdot \left(\left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) \cdot x\right) \]

   7. Simplified 44.9%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]

   if -1.45000000000000005e105 < y < -1.95e63 or -1.6999999999999999e-17 < y < -8.19999999999999968e-81

   1. Initial program 85.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 85.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. +-commutative 85.5%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 85.5%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 85.5%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 85.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 85.5%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 85.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 85.5%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 85.5%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 85.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 85.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 85.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 41.3%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -1.95e63 < y < -1.6999999999999999e-17 or -5.6999999999999998e-218 < y < 6.1999999999999999e26

   1. Initial program 89.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 83.6%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around inf 27.6%

      \[\leadsto \color{blue}{c \cdot b} \]

   if -8.19999999999999968e-81 < y < -4.0500000000000001e-109

   1. Initial program 100.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 84.6%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in i around inf 34.3%

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

      1. *-commutative 34.3%

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      2. associate-*l* 34.3%

         \[\leadsto \color{blue}{i \cdot \left(x \cdot -4\right)} \]

   5. Simplified 34.3%

      \[\leadsto \color{blue}{i \cdot \left(x \cdot -4\right)} \]

   if -4.0500000000000001e-109 < y < -5.6999999999999998e-218

   1. Initial program 100.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 94.5%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around inf 37.2%

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

      1. *-commutative 37.2%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

   5. Simplified 37.2%

      \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

   if 6.1999999999999999e26 < y

   1. Initial program 75.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 75.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 75.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 75.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 75.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 82.1%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 82.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 82.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 82.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 82.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 82.1%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 51.9%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 43.8%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 43.8%

         \[\leadsto t \cdot \left(18 \cdot \left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      2. associate-*r* 42.2%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot z\right)}\right) \]

   7. Simplified 42.2%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(\left(y \cdot x\right) \cdot z\right)\right)} \]

   8. Taylor expanded in t around 0 45.1%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 46.6%

         \[\leadsto 18 \cdot \left(y \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)}\right) \]

      2. *-commutative 46.6%

         \[\leadsto 18 \cdot \left(y \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot x\right)\right) \]

      3. *-commutative 46.6%

         \[\leadsto 18 \cdot \left(y \cdot \color{blue}{\left(x \cdot \left(z \cdot t\right)\right)}\right) \]

      4. associate-*r* 45.3%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot \left(z \cdot t\right)\right)} \]

      5. *-commutative 45.3%

         \[\leadsto 18 \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      6. associate-*l* 42.2%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(\left(x \cdot y\right) \cdot z\right) \cdot t\right)} \]

      7. associate-*r* 43.7%

         \[\leadsto 18 \cdot \left(\color{blue}{\left(x \cdot \left(y \cdot z\right)\right)} \cdot t\right) \]

      8. *-commutative 43.7%

         \[\leadsto 18 \cdot \left(\left(x \cdot \color{blue}{\left(z \cdot y\right)}\right) \cdot t\right) \]

      9. associate-*r* 43.8%

         \[\leadsto 18 \cdot \left(\color{blue}{\left(\left(x \cdot z\right) \cdot y\right)} \cdot t\right) \]

      10. associate-*l* 46.2%

          \[\leadsto 18 \cdot \color{blue}{\left(\left(x \cdot z\right) \cdot \left(y \cdot t\right)\right)} \]

   10. Simplified 46.2%

       \[\leadsto \color{blue}{18 \cdot \left(\left(x \cdot z\right) \cdot \left(y \cdot t\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+105}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+63}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-17}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-81}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;y \leq -4.05 \cdot 10^{-109}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-218}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \end{array} \]

Alternative 11: 31.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+105}:\\ \;\;\;\;t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-17}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-108}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-217}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* k j))))
   (if (<= y -3.6e+105)
     (* t (* x (* z (* 18.0 y))))
     (if (<= y -1.85e+63)
       t_1
       (if (<= y -2.05e-17)
         (* b c)
         (if (<= y -4.5e-81)
           t_1
           (if (<= y -5.8e-108)
             (* i (* x -4.0))
             (if (<= y -1.95e-217)
               (* -4.0 (* t a))
               (if (<= y 3.2e+26) (* b c) (* 18.0 (* (* x z) (* t y))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (k * j);
	double tmp;
	if (y <= -3.6e+105) {
		tmp = t * (x * (z * (18.0 * y)));
	} else if (y <= -1.85e+63) {
		tmp = t_1;
	} else if (y <= -2.05e-17) {
		tmp = b * c;
	} else if (y <= -4.5e-81) {
		tmp = t_1;
	} else if (y <= -5.8e-108) {
		tmp = i * (x * -4.0);
	} else if (y <= -1.95e-217) {
		tmp = -4.0 * (t * a);
	} else if (y <= 3.2e+26) {
		tmp = b * c;
	} else {
		tmp = 18.0 * ((x * z) * (t * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-27.0d0) * (k * j)
    if (y <= (-3.6d+105)) then
        tmp = t * (x * (z * (18.0d0 * y)))
    else if (y <= (-1.85d+63)) then
        tmp = t_1
    else if (y <= (-2.05d-17)) then
        tmp = b * c
    else if (y <= (-4.5d-81)) then
        tmp = t_1
    else if (y <= (-5.8d-108)) then
        tmp = i * (x * (-4.0d0))
    else if (y <= (-1.95d-217)) then
        tmp = (-4.0d0) * (t * a)
    else if (y <= 3.2d+26) then
        tmp = b * c
    else
        tmp = 18.0d0 * ((x * z) * (t * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (k * j);
	double tmp;
	if (y <= -3.6e+105) {
		tmp = t * (x * (z * (18.0 * y)));
	} else if (y <= -1.85e+63) {
		tmp = t_1;
	} else if (y <= -2.05e-17) {
		tmp = b * c;
	} else if (y <= -4.5e-81) {
		tmp = t_1;
	} else if (y <= -5.8e-108) {
		tmp = i * (x * -4.0);
	} else if (y <= -1.95e-217) {
		tmp = -4.0 * (t * a);
	} else if (y <= 3.2e+26) {
		tmp = b * c;
	} else {
		tmp = 18.0 * ((x * z) * (t * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (k * j)
	tmp = 0
	if y <= -3.6e+105:
		tmp = t * (x * (z * (18.0 * y)))
	elif y <= -1.85e+63:
		tmp = t_1
	elif y <= -2.05e-17:
		tmp = b * c
	elif y <= -4.5e-81:
		tmp = t_1
	elif y <= -5.8e-108:
		tmp = i * (x * -4.0)
	elif y <= -1.95e-217:
		tmp = -4.0 * (t * a)
	elif y <= 3.2e+26:
		tmp = b * c
	else:
		tmp = 18.0 * ((x * z) * (t * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(k * j))
	tmp = 0.0
	if (y <= -3.6e+105)
		tmp = Float64(t * Float64(x * Float64(z * Float64(18.0 * y))));
	elseif (y <= -1.85e+63)
		tmp = t_1;
	elseif (y <= -2.05e-17)
		tmp = Float64(b * c);
	elseif (y <= -4.5e-81)
		tmp = t_1;
	elseif (y <= -5.8e-108)
		tmp = Float64(i * Float64(x * -4.0));
	elseif (y <= -1.95e-217)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (y <= 3.2e+26)
		tmp = Float64(b * c);
	else
		tmp = Float64(18.0 * Float64(Float64(x * z) * Float64(t * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (k * j);
	tmp = 0.0;
	if (y <= -3.6e+105)
		tmp = t * (x * (z * (18.0 * y)));
	elseif (y <= -1.85e+63)
		tmp = t_1;
	elseif (y <= -2.05e-17)
		tmp = b * c;
	elseif (y <= -4.5e-81)
		tmp = t_1;
	elseif (y <= -5.8e-108)
		tmp = i * (x * -4.0);
	elseif (y <= -1.95e-217)
		tmp = -4.0 * (t * a);
	elseif (y <= 3.2e+26)
		tmp = b * c;
	else
		tmp = 18.0 * ((x * z) * (t * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+105], N[(t * N[(x * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.85e+63], t$95$1, If[LessEqual[y, -2.05e-17], N[(b * c), $MachinePrecision], If[LessEqual[y, -4.5e-81], t$95$1, If[LessEqual[y, -5.8e-108], N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.95e-217], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+26], N[(b * c), $MachinePrecision], N[(18.0 * N[(N[(x * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -3.5999999999999999e105

   1. Initial program 75.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 75.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 75.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 75.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 75.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 77.3%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 79.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 79.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 79.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 79.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 79.7%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 54.0%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 42.7%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 42.7%

         \[\leadsto t \cdot \left(18 \cdot \left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      2. associate-*r* 42.9%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot z\right)}\right) \]

   7. Simplified 42.9%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(\left(y \cdot x\right) \cdot z\right)\right)} \]

   8. Taylor expanded in y around 0 42.7%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 42.7%

         \[\leadsto t \cdot \color{blue}{\left(\left(18 \cdot y\right) \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 42.7%

         \[\leadsto t \cdot \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(x \cdot z\right)}\right) \]

      3. associate-*l* 42.8%

         \[\leadsto t \cdot \color{blue}{\left(\left(\left(18 \cdot y\right) \cdot x\right) \cdot z\right)} \]

      4. *-commutative 42.8%

         \[\leadsto t \cdot \left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot z\right) \]

      5. associate-*l* 45.1%

         \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)} \]

   10. Simplified 45.1%

       \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)} \]

   if -3.5999999999999999e105 < y < -1.84999999999999984e63 or -2.05e-17 < y < -4.5e-81

   1. Initial program 85.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 85.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. +-commutative 85.5%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 85.5%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 85.5%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 85.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 85.5%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 85.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 85.5%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 85.5%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 85.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 85.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 85.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 41.3%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -1.84999999999999984e63 < y < -2.05e-17 or -1.95e-217 < y < 3.20000000000000029e26

   1. Initial program 89.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 83.6%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around inf 27.6%

      \[\leadsto \color{blue}{c \cdot b} \]

   if -4.5e-81 < y < -5.8000000000000002e-108

   1. Initial program 100.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 84.6%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in i around inf 34.3%

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

      1. *-commutative 34.3%

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      2. associate-*l* 34.3%

         \[\leadsto \color{blue}{i \cdot \left(x \cdot -4\right)} \]

   5. Simplified 34.3%

      \[\leadsto \color{blue}{i \cdot \left(x \cdot -4\right)} \]

   if -5.8000000000000002e-108 < y < -1.95e-217

   1. Initial program 100.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 94.5%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around inf 37.2%

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

      1. *-commutative 37.2%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

   5. Simplified 37.2%

      \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

   if 3.20000000000000029e26 < y

   1. Initial program 75.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 75.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 75.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 75.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 75.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 82.1%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 82.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 82.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 82.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 82.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 82.1%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 51.9%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 43.8%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 43.8%

         \[\leadsto t \cdot \left(18 \cdot \left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      2. associate-*r* 42.2%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot z\right)}\right) \]

   7. Simplified 42.2%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(\left(y \cdot x\right) \cdot z\right)\right)} \]

   8. Taylor expanded in t around 0 45.1%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 46.6%

         \[\leadsto 18 \cdot \left(y \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)}\right) \]

      2. *-commutative 46.6%

         \[\leadsto 18 \cdot \left(y \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot x\right)\right) \]

      3. *-commutative 46.6%

         \[\leadsto 18 \cdot \left(y \cdot \color{blue}{\left(x \cdot \left(z \cdot t\right)\right)}\right) \]

      4. associate-*r* 45.3%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot \left(z \cdot t\right)\right)} \]

      5. *-commutative 45.3%

         \[\leadsto 18 \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      6. associate-*l* 42.2%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(\left(x \cdot y\right) \cdot z\right) \cdot t\right)} \]

      7. associate-*r* 43.7%

         \[\leadsto 18 \cdot \left(\color{blue}{\left(x \cdot \left(y \cdot z\right)\right)} \cdot t\right) \]

      8. *-commutative 43.7%

         \[\leadsto 18 \cdot \left(\left(x \cdot \color{blue}{\left(z \cdot y\right)}\right) \cdot t\right) \]

      9. associate-*r* 43.8%

         \[\leadsto 18 \cdot \left(\color{blue}{\left(\left(x \cdot z\right) \cdot y\right)} \cdot t\right) \]

      10. associate-*l* 46.2%

          \[\leadsto 18 \cdot \color{blue}{\left(\left(x \cdot z\right) \cdot \left(y \cdot t\right)\right)} \]

   10. Simplified 46.2%

       \[\leadsto \color{blue}{18 \cdot \left(\left(x \cdot z\right) \cdot \left(y \cdot t\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+105}:\\ \;\;\;\;t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+63}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-17}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-81}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-108}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-217}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \end{array} \]

Alternative 12: 48.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;x \leq -4.1 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+169}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a)))) (t_2 (- (* b c) (* 27.0 (* k j)))))
   (if (<= x -4.1e+114)
     (* t (* x (* z (* 18.0 y))))
     (if (<= x -3.3e-15)
       t_2
       (if (<= x -5.2e-295)
         t_1
         (if (<= x 1.08e-277)
           t_2
           (if (<= x 2.7e-202)
             t_1
             (if (<= x 3.3e+87)
               t_2
               (if (<= x 2.15e+169)
                 (* (* 18.0 y) (* x (* t z)))
                 (- (* b c) (* 4.0 (* i x))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = (b * c) - (27.0 * (k * j));
	double tmp;
	if (x <= -4.1e+114) {
		tmp = t * (x * (z * (18.0 * y)));
	} else if (x <= -3.3e-15) {
		tmp = t_2;
	} else if (x <= -5.2e-295) {
		tmp = t_1;
	} else if (x <= 1.08e-277) {
		tmp = t_2;
	} else if (x <= 2.7e-202) {
		tmp = t_1;
	} else if (x <= 3.3e+87) {
		tmp = t_2;
	} else if (x <= 2.15e+169) {
		tmp = (18.0 * y) * (x * (t * z));
	} else {
		tmp = (b * c) - (4.0 * (i * x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    t_2 = (b * c) - (27.0d0 * (k * j))
    if (x <= (-4.1d+114)) then
        tmp = t * (x * (z * (18.0d0 * y)))
    else if (x <= (-3.3d-15)) then
        tmp = t_2
    else if (x <= (-5.2d-295)) then
        tmp = t_1
    else if (x <= 1.08d-277) then
        tmp = t_2
    else if (x <= 2.7d-202) then
        tmp = t_1
    else if (x <= 3.3d+87) then
        tmp = t_2
    else if (x <= 2.15d+169) then
        tmp = (18.0d0 * y) * (x * (t * z))
    else
        tmp = (b * c) - (4.0d0 * (i * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = (b * c) - (27.0 * (k * j));
	double tmp;
	if (x <= -4.1e+114) {
		tmp = t * (x * (z * (18.0 * y)));
	} else if (x <= -3.3e-15) {
		tmp = t_2;
	} else if (x <= -5.2e-295) {
		tmp = t_1;
	} else if (x <= 1.08e-277) {
		tmp = t_2;
	} else if (x <= 2.7e-202) {
		tmp = t_1;
	} else if (x <= 3.3e+87) {
		tmp = t_2;
	} else if (x <= 2.15e+169) {
		tmp = (18.0 * y) * (x * (t * z));
	} else {
		tmp = (b * c) - (4.0 * (i * x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	t_2 = (b * c) - (27.0 * (k * j))
	tmp = 0
	if x <= -4.1e+114:
		tmp = t * (x * (z * (18.0 * y)))
	elif x <= -3.3e-15:
		tmp = t_2
	elif x <= -5.2e-295:
		tmp = t_1
	elif x <= 1.08e-277:
		tmp = t_2
	elif x <= 2.7e-202:
		tmp = t_1
	elif x <= 3.3e+87:
		tmp = t_2
	elif x <= 2.15e+169:
		tmp = (18.0 * y) * (x * (t * z))
	else:
		tmp = (b * c) - (4.0 * (i * x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_2 = Float64(Float64(b * c) - Float64(27.0 * Float64(k * j)))
	tmp = 0.0
	if (x <= -4.1e+114)
		tmp = Float64(t * Float64(x * Float64(z * Float64(18.0 * y))));
	elseif (x <= -3.3e-15)
		tmp = t_2;
	elseif (x <= -5.2e-295)
		tmp = t_1;
	elseif (x <= 1.08e-277)
		tmp = t_2;
	elseif (x <= 2.7e-202)
		tmp = t_1;
	elseif (x <= 3.3e+87)
		tmp = t_2;
	elseif (x <= 2.15e+169)
		tmp = Float64(Float64(18.0 * y) * Float64(x * Float64(t * z)));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(i * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	t_2 = (b * c) - (27.0 * (k * j));
	tmp = 0.0;
	if (x <= -4.1e+114)
		tmp = t * (x * (z * (18.0 * y)));
	elseif (x <= -3.3e-15)
		tmp = t_2;
	elseif (x <= -5.2e-295)
		tmp = t_1;
	elseif (x <= 1.08e-277)
		tmp = t_2;
	elseif (x <= 2.7e-202)
		tmp = t_1;
	elseif (x <= 3.3e+87)
		tmp = t_2;
	elseif (x <= 2.15e+169)
		tmp = (18.0 * y) * (x * (t * z));
	else
		tmp = (b * c) - (4.0 * (i * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.1e+114], N[(t * N[(x * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.3e-15], t$95$2, If[LessEqual[x, -5.2e-295], t$95$1, If[LessEqual[x, 1.08e-277], t$95$2, If[LessEqual[x, 2.7e-202], t$95$1, If[LessEqual[x, 3.3e+87], t$95$2, If[LessEqual[x, 2.15e+169], N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.1000000000000001e114

   1. Initial program 70.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 70.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 70.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 70.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 70.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 72.6%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 77.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 77.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 77.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 77.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 77.1%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 77.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 63.8%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 52.4%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 52.4%

         \[\leadsto t \cdot \left(18 \cdot \left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      2. associate-*r* 52.4%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot z\right)}\right) \]

   7. Simplified 52.4%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(\left(y \cdot x\right) \cdot z\right)\right)} \]

   8. Taylor expanded in y around 0 52.4%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 52.4%

         \[\leadsto t \cdot \color{blue}{\left(\left(18 \cdot y\right) \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 52.4%

         \[\leadsto t \cdot \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(x \cdot z\right)}\right) \]

      3. associate-*l* 52.5%

         \[\leadsto t \cdot \color{blue}{\left(\left(\left(18 \cdot y\right) \cdot x\right) \cdot z\right)} \]

      4. *-commutative 52.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot z\right) \]

      5. associate-*l* 54.6%

         \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)} \]

   10. Simplified 54.6%

       \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)} \]

   if -4.1000000000000001e114 < x < -3.3e-15 or -5.1999999999999997e-295 < x < 1.0800000000000001e-277 or 2.6999999999999999e-202 < x < 3.3000000000000001e87

   1. Initial program 90.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 74.0%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 62.1%

      \[\leadsto \color{blue}{c \cdot b - 27 \cdot \left(k \cdot j\right)} \]

   if -3.3e-15 < x < -5.1999999999999997e-295 or 1.0800000000000001e-277 < x < 2.6999999999999999e-202

   1. Initial program 96.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 96.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 96.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 96.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 96.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 96.0%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 92.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 92.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 92.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 92.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 92.3%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 82.2%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in x around 0 72.4%

      \[\leadsto \color{blue}{c \cdot b + -4 \cdot \left(a \cdot t\right)} \]

   if 3.3000000000000001e87 < x < 2.1500000000000001e169

   1. Initial program 75.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 75.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 75.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 75.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 75.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 80.3%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 80.3%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 80.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 80.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 80.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 80.3%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 80.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 65.6%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 60.3%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.4%

         \[\leadsto \color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 60.4%

         \[\leadsto \color{blue}{\left(t \cdot \left(z \cdot x\right)\right) \cdot \left(18 \cdot y\right)} \]

      3. associate-*r* 60.4%

         \[\leadsto \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)} \cdot \left(18 \cdot y\right) \]

      4. *-commutative 60.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(t \cdot z\right)\right)} \cdot \left(18 \cdot y\right) \]

   7. Simplified 60.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(t \cdot z\right)\right) \cdot \left(18 \cdot y\right)} \]

   if 2.1500000000000001e169 < x

   1. Initial program 63.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 63.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 63.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 63.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 63.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 63.8%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 66.8%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 66.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 66.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 66.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 66.8%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 66.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 61.2%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in t around 0 55.5%

      \[\leadsto \color{blue}{c \cdot b - 4 \cdot \left(i \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-15}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-295}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-277}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-202}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+169}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \end{array} \]

Alternative 13: 49.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(k \cdot j\right)\\ t_2 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -7400000:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+170}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 27.0 (* k j)))) (t_2 (+ (* b c) (* -4.0 (* t a)))))
   (if (<= x -1.8e+121)
     (* t (* x (* z (* 18.0 y))))
     (if (<= x -7400000.0)
       (+ (* -4.0 (* i x)) (* j (* k -27.0)))
       (if (<= x -1.1e-293)
         t_2
         (if (<= x 3.8e-278)
           t_1
           (if (<= x 7.2e-203)
             t_2
             (if (<= x 1.4e+85)
               t_1
               (if (<= x 1.15e+170)
                 (* (* 18.0 y) (* x (* t z)))
                 (- (* b c) (* 4.0 (* i x))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (k * j));
	double t_2 = (b * c) + (-4.0 * (t * a));
	double tmp;
	if (x <= -1.8e+121) {
		tmp = t * (x * (z * (18.0 * y)));
	} else if (x <= -7400000.0) {
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0));
	} else if (x <= -1.1e-293) {
		tmp = t_2;
	} else if (x <= 3.8e-278) {
		tmp = t_1;
	} else if (x <= 7.2e-203) {
		tmp = t_2;
	} else if (x <= 1.4e+85) {
		tmp = t_1;
	} else if (x <= 1.15e+170) {
		tmp = (18.0 * y) * (x * (t * z));
	} else {
		tmp = (b * c) - (4.0 * (i * x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - (27.0d0 * (k * j))
    t_2 = (b * c) + ((-4.0d0) * (t * a))
    if (x <= (-1.8d+121)) then
        tmp = t * (x * (z * (18.0d0 * y)))
    else if (x <= (-7400000.0d0)) then
        tmp = ((-4.0d0) * (i * x)) + (j * (k * (-27.0d0)))
    else if (x <= (-1.1d-293)) then
        tmp = t_2
    else if (x <= 3.8d-278) then
        tmp = t_1
    else if (x <= 7.2d-203) then
        tmp = t_2
    else if (x <= 1.4d+85) then
        tmp = t_1
    else if (x <= 1.15d+170) then
        tmp = (18.0d0 * y) * (x * (t * z))
    else
        tmp = (b * c) - (4.0d0 * (i * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (k * j));
	double t_2 = (b * c) + (-4.0 * (t * a));
	double tmp;
	if (x <= -1.8e+121) {
		tmp = t * (x * (z * (18.0 * y)));
	} else if (x <= -7400000.0) {
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0));
	} else if (x <= -1.1e-293) {
		tmp = t_2;
	} else if (x <= 3.8e-278) {
		tmp = t_1;
	} else if (x <= 7.2e-203) {
		tmp = t_2;
	} else if (x <= 1.4e+85) {
		tmp = t_1;
	} else if (x <= 1.15e+170) {
		tmp = (18.0 * y) * (x * (t * z));
	} else {
		tmp = (b * c) - (4.0 * (i * x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (27.0 * (k * j))
	t_2 = (b * c) + (-4.0 * (t * a))
	tmp = 0
	if x <= -1.8e+121:
		tmp = t * (x * (z * (18.0 * y)))
	elif x <= -7400000.0:
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0))
	elif x <= -1.1e-293:
		tmp = t_2
	elif x <= 3.8e-278:
		tmp = t_1
	elif x <= 7.2e-203:
		tmp = t_2
	elif x <= 1.4e+85:
		tmp = t_1
	elif x <= 1.15e+170:
		tmp = (18.0 * y) * (x * (t * z))
	else:
		tmp = (b * c) - (4.0 * (i * x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(27.0 * Float64(k * j)))
	t_2 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (x <= -1.8e+121)
		tmp = Float64(t * Float64(x * Float64(z * Float64(18.0 * y))));
	elseif (x <= -7400000.0)
		tmp = Float64(Float64(-4.0 * Float64(i * x)) + Float64(j * Float64(k * -27.0)));
	elseif (x <= -1.1e-293)
		tmp = t_2;
	elseif (x <= 3.8e-278)
		tmp = t_1;
	elseif (x <= 7.2e-203)
		tmp = t_2;
	elseif (x <= 1.4e+85)
		tmp = t_1;
	elseif (x <= 1.15e+170)
		tmp = Float64(Float64(18.0 * y) * Float64(x * Float64(t * z)));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(i * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (27.0 * (k * j));
	t_2 = (b * c) + (-4.0 * (t * a));
	tmp = 0.0;
	if (x <= -1.8e+121)
		tmp = t * (x * (z * (18.0 * y)));
	elseif (x <= -7400000.0)
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0));
	elseif (x <= -1.1e-293)
		tmp = t_2;
	elseif (x <= 3.8e-278)
		tmp = t_1;
	elseif (x <= 7.2e-203)
		tmp = t_2;
	elseif (x <= 1.4e+85)
		tmp = t_1;
	elseif (x <= 1.15e+170)
		tmp = (18.0 * y) * (x * (t * z));
	else
		tmp = (b * c) - (4.0 * (i * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.8e+121], N[(t * N[(x * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7400000.0], N[(N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.1e-293], t$95$2, If[LessEqual[x, 3.8e-278], t$95$1, If[LessEqual[x, 7.2e-203], t$95$2, If[LessEqual[x, 1.4e+85], t$95$1, If[LessEqual[x, 1.15e+170], N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.79999999999999991e121

   1. Initial program 68.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 68.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 68.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 68.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 68.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 71.3%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 75.9%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 75.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 75.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 75.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 75.9%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 75.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 52.4%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 52.4%

         \[\leadsto t \cdot \left(18 \cdot \left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      2. associate-*r* 52.4%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot z\right)}\right) \]

   7. Simplified 52.4%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(\left(y \cdot x\right) \cdot z\right)\right)} \]

   8. Taylor expanded in y around 0 52.4%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 52.4%

         \[\leadsto t \cdot \color{blue}{\left(\left(18 \cdot y\right) \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 52.4%

         \[\leadsto t \cdot \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(x \cdot z\right)}\right) \]

      3. associate-*l* 52.5%

         \[\leadsto t \cdot \color{blue}{\left(\left(\left(18 \cdot y\right) \cdot x\right) \cdot z\right)} \]

      4. *-commutative 52.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot z\right) \]

      5. associate-*l* 54.8%

         \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)} \]

   10. Simplified 54.8%

       \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)} \]

   if -1.79999999999999991e121 < x < -7.4e6

   1. Initial program 86.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 73.1%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around 0 60.0%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 60.0%

         \[\leadsto \color{blue}{-\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]

      2. *-commutative 60.0%

         \[\leadsto -\left(4 \cdot \color{blue}{\left(x \cdot i\right)} + 27 \cdot \left(k \cdot j\right)\right) \]

      3. distribute-neg-in 60.0%

         \[\leadsto \color{blue}{\left(-4 \cdot \left(x \cdot i\right)\right) + \left(-27 \cdot \left(k \cdot j\right)\right)} \]

      4. distribute-lft-neg-in 60.0%

         \[\leadsto \color{blue}{\left(-4\right) \cdot \left(x \cdot i\right)} + \left(-27 \cdot \left(k \cdot j\right)\right) \]

      5. metadata-eval 60.0%

         \[\leadsto \color{blue}{-4} \cdot \left(x \cdot i\right) + \left(-27 \cdot \left(k \cdot j\right)\right) \]

      6. distribute-lft-neg-in 60.0%

         \[\leadsto -4 \cdot \left(x \cdot i\right) + \color{blue}{\left(-27\right) \cdot \left(k \cdot j\right)} \]

      7. metadata-eval 60.0%

         \[\leadsto -4 \cdot \left(x \cdot i\right) + \color{blue}{-27} \cdot \left(k \cdot j\right) \]

      8. associate-*r* 60.0%

         \[\leadsto -4 \cdot \left(x \cdot i\right) + \color{blue}{\left(-27 \cdot k\right) \cdot j} \]

   5. Simplified 60.0%

      \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right) + \left(-27 \cdot k\right) \cdot j} \]

   if -7.4e6 < x < -1.1e-293 or 3.7999999999999999e-278 < x < 7.19999999999999958e-203

   1. Initial program 94.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 94.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 94.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 94.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 94.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 95.2%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 91.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 91.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 91.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 91.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 91.7%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 81.1%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in x around 0 70.9%

      \[\leadsto \color{blue}{c \cdot b + -4 \cdot \left(a \cdot t\right)} \]

   if -1.1e-293 < x < 3.7999999999999999e-278 or 7.19999999999999958e-203 < x < 1.4e85

   1. Initial program 94.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 81.9%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 68.0%

      \[\leadsto \color{blue}{c \cdot b - 27 \cdot \left(k \cdot j\right)} \]

   if 1.4e85 < x < 1.15e170

   1. Initial program 75.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 75.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 75.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 75.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 75.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 80.3%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 80.3%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 80.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 80.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 80.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 80.3%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 80.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 65.6%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 60.3%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.4%

         \[\leadsto \color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 60.4%

         \[\leadsto \color{blue}{\left(t \cdot \left(z \cdot x\right)\right) \cdot \left(18 \cdot y\right)} \]

      3. associate-*r* 60.4%

         \[\leadsto \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)} \cdot \left(18 \cdot y\right) \]

      4. *-commutative 60.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(t \cdot z\right)\right)} \cdot \left(18 \cdot y\right) \]

   7. Simplified 60.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(t \cdot z\right)\right) \cdot \left(18 \cdot y\right)} \]

   if 1.15e170 < x

   1. Initial program 63.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 63.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 63.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 63.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 63.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 63.8%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 66.8%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 66.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 66.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 66.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 66.8%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 66.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 61.2%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in t around 0 55.5%

      \[\leadsto \color{blue}{c \cdot b - 4 \cdot \left(i \cdot x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -7400000:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-293}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-278}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-203}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+85}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+170}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \end{array} \]

Alternative 14: 49.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 27 \cdot \left(k \cdot j\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := b \cdot c + t_2\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -2000000:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-126}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-278}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-202}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+85}:\\ \;\;\;\;b \cdot c - t_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+169}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 27.0 (* k j))) (t_2 (* -4.0 (* t a))) (t_3 (+ (* b c) t_2)))
   (if (<= x -1.2e+121)
     (* t (* x (* z (* 18.0 y))))
     (if (<= x -2000000.0)
       (+ (* -4.0 (* i x)) (* j (* k -27.0)))
       (if (<= x -1.65e-126)
         t_3
         (if (<= x 9.6e-278)
           (- t_2 t_1)
           (if (<= x 3.5e-202)
             t_3
             (if (<= x 1.8e+85)
               (- (* b c) t_1)
               (if (<= x 6e+169)
                 (* (* 18.0 y) (* x (* t z)))
                 (- (* b c) (* 4.0 (* i x))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (k * j);
	double t_2 = -4.0 * (t * a);
	double t_3 = (b * c) + t_2;
	double tmp;
	if (x <= -1.2e+121) {
		tmp = t * (x * (z * (18.0 * y)));
	} else if (x <= -2000000.0) {
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0));
	} else if (x <= -1.65e-126) {
		tmp = t_3;
	} else if (x <= 9.6e-278) {
		tmp = t_2 - t_1;
	} else if (x <= 3.5e-202) {
		tmp = t_3;
	} else if (x <= 1.8e+85) {
		tmp = (b * c) - t_1;
	} else if (x <= 6e+169) {
		tmp = (18.0 * y) * (x * (t * z));
	} else {
		tmp = (b * c) - (4.0 * (i * x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 27.0d0 * (k * j)
    t_2 = (-4.0d0) * (t * a)
    t_3 = (b * c) + t_2
    if (x <= (-1.2d+121)) then
        tmp = t * (x * (z * (18.0d0 * y)))
    else if (x <= (-2000000.0d0)) then
        tmp = ((-4.0d0) * (i * x)) + (j * (k * (-27.0d0)))
    else if (x <= (-1.65d-126)) then
        tmp = t_3
    else if (x <= 9.6d-278) then
        tmp = t_2 - t_1
    else if (x <= 3.5d-202) then
        tmp = t_3
    else if (x <= 1.8d+85) then
        tmp = (b * c) - t_1
    else if (x <= 6d+169) then
        tmp = (18.0d0 * y) * (x * (t * z))
    else
        tmp = (b * c) - (4.0d0 * (i * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (k * j);
	double t_2 = -4.0 * (t * a);
	double t_3 = (b * c) + t_2;
	double tmp;
	if (x <= -1.2e+121) {
		tmp = t * (x * (z * (18.0 * y)));
	} else if (x <= -2000000.0) {
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0));
	} else if (x <= -1.65e-126) {
		tmp = t_3;
	} else if (x <= 9.6e-278) {
		tmp = t_2 - t_1;
	} else if (x <= 3.5e-202) {
		tmp = t_3;
	} else if (x <= 1.8e+85) {
		tmp = (b * c) - t_1;
	} else if (x <= 6e+169) {
		tmp = (18.0 * y) * (x * (t * z));
	} else {
		tmp = (b * c) - (4.0 * (i * x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (k * j)
	t_2 = -4.0 * (t * a)
	t_3 = (b * c) + t_2
	tmp = 0
	if x <= -1.2e+121:
		tmp = t * (x * (z * (18.0 * y)))
	elif x <= -2000000.0:
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0))
	elif x <= -1.65e-126:
		tmp = t_3
	elif x <= 9.6e-278:
		tmp = t_2 - t_1
	elif x <= 3.5e-202:
		tmp = t_3
	elif x <= 1.8e+85:
		tmp = (b * c) - t_1
	elif x <= 6e+169:
		tmp = (18.0 * y) * (x * (t * z))
	else:
		tmp = (b * c) - (4.0 * (i * x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(k * j))
	t_2 = Float64(-4.0 * Float64(t * a))
	t_3 = Float64(Float64(b * c) + t_2)
	tmp = 0.0
	if (x <= -1.2e+121)
		tmp = Float64(t * Float64(x * Float64(z * Float64(18.0 * y))));
	elseif (x <= -2000000.0)
		tmp = Float64(Float64(-4.0 * Float64(i * x)) + Float64(j * Float64(k * -27.0)));
	elseif (x <= -1.65e-126)
		tmp = t_3;
	elseif (x <= 9.6e-278)
		tmp = Float64(t_2 - t_1);
	elseif (x <= 3.5e-202)
		tmp = t_3;
	elseif (x <= 1.8e+85)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (x <= 6e+169)
		tmp = Float64(Float64(18.0 * y) * Float64(x * Float64(t * z)));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(i * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 27.0 * (k * j);
	t_2 = -4.0 * (t * a);
	t_3 = (b * c) + t_2;
	tmp = 0.0;
	if (x <= -1.2e+121)
		tmp = t * (x * (z * (18.0 * y)));
	elseif (x <= -2000000.0)
		tmp = (-4.0 * (i * x)) + (j * (k * -27.0));
	elseif (x <= -1.65e-126)
		tmp = t_3;
	elseif (x <= 9.6e-278)
		tmp = t_2 - t_1;
	elseif (x <= 3.5e-202)
		tmp = t_3;
	elseif (x <= 1.8e+85)
		tmp = (b * c) - t_1;
	elseif (x <= 6e+169)
		tmp = (18.0 * y) * (x * (t * z));
	else
		tmp = (b * c) - (4.0 * (i * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[x, -1.2e+121], N[(t * N[(x * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2000000.0], N[(N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.65e-126], t$95$3, If[LessEqual[x, 9.6e-278], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[x, 3.5e-202], t$95$3, If[LessEqual[x, 1.8e+85], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 6e+169], N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -1.2e121

   1. Initial program 68.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 68.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 68.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 68.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 68.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 71.3%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 75.9%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 75.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 75.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 75.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 75.9%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 75.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 52.4%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 52.4%

         \[\leadsto t \cdot \left(18 \cdot \left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      2. associate-*r* 52.4%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot z\right)}\right) \]

   7. Simplified 52.4%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(\left(y \cdot x\right) \cdot z\right)\right)} \]

   8. Taylor expanded in y around 0 52.4%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 52.4%

         \[\leadsto t \cdot \color{blue}{\left(\left(18 \cdot y\right) \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 52.4%

         \[\leadsto t \cdot \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(x \cdot z\right)}\right) \]

      3. associate-*l* 52.5%

         \[\leadsto t \cdot \color{blue}{\left(\left(\left(18 \cdot y\right) \cdot x\right) \cdot z\right)} \]

      4. *-commutative 52.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot z\right) \]

      5. associate-*l* 54.8%

         \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)} \]

   10. Simplified 54.8%

       \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)} \]

   if -1.2e121 < x < -2e6

   1. Initial program 86.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 73.1%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around 0 60.0%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 60.0%

         \[\leadsto \color{blue}{-\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]

      2. *-commutative 60.0%

         \[\leadsto -\left(4 \cdot \color{blue}{\left(x \cdot i\right)} + 27 \cdot \left(k \cdot j\right)\right) \]

      3. distribute-neg-in 60.0%

         \[\leadsto \color{blue}{\left(-4 \cdot \left(x \cdot i\right)\right) + \left(-27 \cdot \left(k \cdot j\right)\right)} \]

      4. distribute-lft-neg-in 60.0%

         \[\leadsto \color{blue}{\left(-4\right) \cdot \left(x \cdot i\right)} + \left(-27 \cdot \left(k \cdot j\right)\right) \]

      5. metadata-eval 60.0%

         \[\leadsto \color{blue}{-4} \cdot \left(x \cdot i\right) + \left(-27 \cdot \left(k \cdot j\right)\right) \]

      6. distribute-lft-neg-in 60.0%

         \[\leadsto -4 \cdot \left(x \cdot i\right) + \color{blue}{\left(-27\right) \cdot \left(k \cdot j\right)} \]

      7. metadata-eval 60.0%

         \[\leadsto -4 \cdot \left(x \cdot i\right) + \color{blue}{-27} \cdot \left(k \cdot j\right) \]

      8. associate-*r* 60.0%

         \[\leadsto -4 \cdot \left(x \cdot i\right) + \color{blue}{\left(-27 \cdot k\right) \cdot j} \]

   5. Simplified 60.0%

      \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right) + \left(-27 \cdot k\right) \cdot j} \]

   if -2e6 < x < -1.65e-126 or 9.5999999999999999e-278 < x < 3.4999999999999999e-202

   1. Initial program 95.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 95.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 95.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 95.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 95.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 98.0%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 96.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 96.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 96.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 96.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 96.1%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 96.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 87.5%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in x around 0 74.3%

      \[\leadsto \color{blue}{c \cdot b + -4 \cdot \left(a \cdot t\right)} \]

   if -1.65e-126 < x < 9.5999999999999999e-278

   1. Initial program 92.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around -inf 74.5%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(-18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - -4 \cdot a\right) \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in y around 0 70.6%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) - 27 \cdot \left(k \cdot j\right)} \]

   if 3.4999999999999999e-202 < x < 1.7999999999999999e85

   1. Initial program 93.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 81.2%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 65.4%

      \[\leadsto \color{blue}{c \cdot b - 27 \cdot \left(k \cdot j\right)} \]

   if 1.7999999999999999e85 < x < 5.9999999999999999e169

   1. Initial program 75.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 75.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 75.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 75.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 75.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 80.3%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 80.3%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 80.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 80.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 80.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 80.3%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 80.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 65.6%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 60.3%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.4%

         \[\leadsto \color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 60.4%

         \[\leadsto \color{blue}{\left(t \cdot \left(z \cdot x\right)\right) \cdot \left(18 \cdot y\right)} \]

      3. associate-*r* 60.4%

         \[\leadsto \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)} \cdot \left(18 \cdot y\right) \]

      4. *-commutative 60.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(t \cdot z\right)\right)} \cdot \left(18 \cdot y\right) \]

   7. Simplified 60.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(t \cdot z\right)\right) \cdot \left(18 \cdot y\right)} \]

   if 5.9999999999999999e169 < x

   1. Initial program 63.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 63.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 63.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 63.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 63.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 63.8%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 66.8%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 66.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 66.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 66.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 66.8%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 66.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 61.2%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in t around 0 55.5%

      \[\leadsto \color{blue}{c \cdot b - 4 \cdot \left(i \cdot x\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -2000000:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-126}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-278}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-202}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+85}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+169}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \end{array} \]

Alternative 15: 73.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+21}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - t_1\\ \mathbf{elif}\;x \leq -0.0145:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+83}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0)))
        (t_2 (* x (- (* 18.0 (* y (* t z))) (* i 4.0)))))
   (if (<= x -8.5e+117)
     t_2
     (if (<= x -4.2e+21)
       (- (- (* b c) (* 4.0 (* i x))) t_1)
       (if (<= x -0.0145)
         (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))
         (if (<= x 3.5e+83) (- (- (* b c) (* 4.0 (* t a))) t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	double tmp;
	if (x <= -8.5e+117) {
		tmp = t_2;
	} else if (x <= -4.2e+21) {
		tmp = ((b * c) - (4.0 * (i * x))) - t_1;
	} else if (x <= -0.0145) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (x <= 3.5e+83) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    t_2 = x * ((18.0d0 * (y * (t * z))) - (i * 4.0d0))
    if (x <= (-8.5d+117)) then
        tmp = t_2
    else if (x <= (-4.2d+21)) then
        tmp = ((b * c) - (4.0d0 * (i * x))) - t_1
    else if (x <= (-0.0145d0)) then
        tmp = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    else if (x <= 3.5d+83) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	double tmp;
	if (x <= -8.5e+117) {
		tmp = t_2;
	} else if (x <= -4.2e+21) {
		tmp = ((b * c) - (4.0 * (i * x))) - t_1;
	} else if (x <= -0.0145) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (x <= 3.5e+83) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	t_2 = x * ((18.0 * (y * (t * z))) - (i * 4.0))
	tmp = 0
	if x <= -8.5e+117:
		tmp = t_2
	elif x <= -4.2e+21:
		tmp = ((b * c) - (4.0 * (i * x))) - t_1
	elif x <= -0.0145:
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	elif x <= 3.5e+83:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	t_2 = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -8.5e+117)
		tmp = t_2;
	elseif (x <= -4.2e+21)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(i * x))) - t_1);
	elseif (x <= -0.0145)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	elseif (x <= 3.5e+83)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	t_2 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	tmp = 0.0;
	if (x <= -8.5e+117)
		tmp = t_2;
	elseif (x <= -4.2e+21)
		tmp = ((b * c) - (4.0 * (i * x))) - t_1;
	elseif (x <= -0.0145)
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	elseif (x <= 3.5e+83)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e+117], t$95$2, If[LessEqual[x, -4.2e+21], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, -0.0145], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e+83], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.49999999999999966e117 or 3.49999999999999977e83 < x

   1. Initial program 68.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 68.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 68.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 68.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 68.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 70.6%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 73.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 73.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 73.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 73.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 73.7%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 73.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 72.9%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

   if -8.49999999999999966e117 < x < -4.2e21

   1. Initial program 89.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 84.2%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if -4.2e21 < x < -0.0145000000000000007

   1. Initial program 57.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 57.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 57.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 57.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 57.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 86.3%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 86.3%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 86.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 86.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 86.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 86.3%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 72.7%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   if -0.0145000000000000007 < x < 3.49999999999999977e83

   1. Initial program 95.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 84.3%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+21}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq -0.0145:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+83}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]

Alternative 16: 73.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+19}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - t_1\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-54}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+85}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0)))
        (t_2 (* x (- (* 18.0 (* y (* t z))) (* i 4.0)))))
   (if (<= x -1.55e+121)
     t_2
     (if (<= x -2.3e+19)
       (- (- (* b c) (* 4.0 (* i x))) t_1)
       (if (<= x -1.25e-54)
         (+ (* b c) (* t (- (* 18.0 (* y (* x z))) (* a 4.0))))
         (if (<= x 9.5e+85) (- (- (* b c) (* 4.0 (* t a))) t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	double tmp;
	if (x <= -1.55e+121) {
		tmp = t_2;
	} else if (x <= -2.3e+19) {
		tmp = ((b * c) - (4.0 * (i * x))) - t_1;
	} else if (x <= -1.25e-54) {
		tmp = (b * c) + (t * ((18.0 * (y * (x * z))) - (a * 4.0)));
	} else if (x <= 9.5e+85) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    t_2 = x * ((18.0d0 * (y * (t * z))) - (i * 4.0d0))
    if (x <= (-1.55d+121)) then
        tmp = t_2
    else if (x <= (-2.3d+19)) then
        tmp = ((b * c) - (4.0d0 * (i * x))) - t_1
    else if (x <= (-1.25d-54)) then
        tmp = (b * c) + (t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0)))
    else if (x <= 9.5d+85) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	double tmp;
	if (x <= -1.55e+121) {
		tmp = t_2;
	} else if (x <= -2.3e+19) {
		tmp = ((b * c) - (4.0 * (i * x))) - t_1;
	} else if (x <= -1.25e-54) {
		tmp = (b * c) + (t * ((18.0 * (y * (x * z))) - (a * 4.0)));
	} else if (x <= 9.5e+85) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	t_2 = x * ((18.0 * (y * (t * z))) - (i * 4.0))
	tmp = 0
	if x <= -1.55e+121:
		tmp = t_2
	elif x <= -2.3e+19:
		tmp = ((b * c) - (4.0 * (i * x))) - t_1
	elif x <= -1.25e-54:
		tmp = (b * c) + (t * ((18.0 * (y * (x * z))) - (a * 4.0)))
	elif x <= 9.5e+85:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	t_2 = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -1.55e+121)
		tmp = t_2;
	elseif (x <= -2.3e+19)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(i * x))) - t_1);
	elseif (x <= -1.25e-54)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0))));
	elseif (x <= 9.5e+85)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	t_2 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	tmp = 0.0;
	if (x <= -1.55e+121)
		tmp = t_2;
	elseif (x <= -2.3e+19)
		tmp = ((b * c) - (4.0 * (i * x))) - t_1;
	elseif (x <= -1.25e-54)
		tmp = (b * c) + (t * ((18.0 * (y * (x * z))) - (a * 4.0)));
	elseif (x <= 9.5e+85)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.55e+121], t$95$2, If[LessEqual[x, -2.3e+19], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, -1.25e-54], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e+85], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.55000000000000004e121 or 9.49999999999999945e85 < x

   1. Initial program 68.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 68.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 68.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 68.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 68.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 70.6%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 73.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 73.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 73.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 73.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 73.7%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 73.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 72.9%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

   if -1.55000000000000004e121 < x < -2.3e19

   1. Initial program 89.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 84.2%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if -2.3e19 < x < -1.25000000000000004e-54

   1. Initial program 82.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 82.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 82.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 82.6%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 82.6%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 94.4%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 94.4%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 94.4%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 94.4%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 94.4%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 94.4%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 94.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 88.8%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in i around 0 77.5%

      \[\leadsto \color{blue}{c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   if -1.25000000000000004e-54 < x < 9.49999999999999945e85

   1. Initial program 95.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 86.1%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+19}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-54}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+85}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]

Alternative 17: 78.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(-4 \cdot a - -18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(t \cdot a\right)\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))))
   (if (<= t -3.4e-21)
     (- (* t (- (* -4.0 a) (* -18.0 (* y (* x z))))) t_1)
     (- (- (* b c) (+ (* 4.0 (* i x)) (* 4.0 (* t a)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t <= -3.4e-21) {
		tmp = (t * ((-4.0 * a) - (-18.0 * (y * (x * z))))) - t_1;
	} else {
		tmp = ((b * c) - ((4.0 * (i * x)) + (4.0 * (t * a)))) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    if (t <= (-3.4d-21)) then
        tmp = (t * (((-4.0d0) * a) - ((-18.0d0) * (y * (x * z))))) - t_1
    else
        tmp = ((b * c) - ((4.0d0 * (i * x)) + (4.0d0 * (t * a)))) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t <= -3.4e-21) {
		tmp = (t * ((-4.0 * a) - (-18.0 * (y * (x * z))))) - t_1;
	} else {
		tmp = ((b * c) - ((4.0 * (i * x)) + (4.0 * (t * a)))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if t <= -3.4e-21:
		tmp = (t * ((-4.0 * a) - (-18.0 * (y * (x * z))))) - t_1
	else:
		tmp = ((b * c) - ((4.0 * (i * x)) + (4.0 * (t * a)))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t <= -3.4e-21)
		tmp = Float64(Float64(t * Float64(Float64(-4.0 * a) - Float64(-18.0 * Float64(y * Float64(x * z))))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(i * x)) + Float64(4.0 * Float64(t * a)))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if (t <= -3.4e-21)
		tmp = (t * ((-4.0 * a) - (-18.0 * (y * (x * z))))) - t_1;
	else
		tmp = ((b * c) - ((4.0 * (i * x)) + (4.0 * (t * a)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e-21], N[(N[(t * N[(N[(-4.0 * a), $MachinePrecision] - N[(-18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4e-21

   1. Initial program 77.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around -inf 79.8%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(-18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - -4 \cdot a\right) \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]

   if -3.4e-21 < t

   1. Initial program 86.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 83.0%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(-4 \cdot a - -18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(t \cdot a\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 18: 51.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 4 \cdot \left(i \cdot x\right)\\ t_2 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-164}:\\ \;\;\;\;27 \cdot \left(k \cdot \left(-j\right)\right) - t_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-131}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+82}:\\ \;\;\;\;b \cdot c - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* i x))) (t_2 (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))))
   (if (<= a -1e-16)
     t_2
     (if (<= a -2.9e-164)
       (- (* 27.0 (* k (- j))) t_1)
       (if (<= a 5.8e-131)
         (- (* b c) (* 27.0 (* k j)))
         (if (<= a 1.95e+82) (- (* b c) t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (i * x);
	double t_2 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double tmp;
	if (a <= -1e-16) {
		tmp = t_2;
	} else if (a <= -2.9e-164) {
		tmp = (27.0 * (k * -j)) - t_1;
	} else if (a <= 5.8e-131) {
		tmp = (b * c) - (27.0 * (k * j));
	} else if (a <= 1.95e+82) {
		tmp = (b * c) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 4.0d0 * (i * x)
    t_2 = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    if (a <= (-1d-16)) then
        tmp = t_2
    else if (a <= (-2.9d-164)) then
        tmp = (27.0d0 * (k * -j)) - t_1
    else if (a <= 5.8d-131) then
        tmp = (b * c) - (27.0d0 * (k * j))
    else if (a <= 1.95d+82) then
        tmp = (b * c) - t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (i * x);
	double t_2 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double tmp;
	if (a <= -1e-16) {
		tmp = t_2;
	} else if (a <= -2.9e-164) {
		tmp = (27.0 * (k * -j)) - t_1;
	} else if (a <= 5.8e-131) {
		tmp = (b * c) - (27.0 * (k * j));
	} else if (a <= 1.95e+82) {
		tmp = (b * c) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (i * x)
	t_2 = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	tmp = 0
	if a <= -1e-16:
		tmp = t_2
	elif a <= -2.9e-164:
		tmp = (27.0 * (k * -j)) - t_1
	elif a <= 5.8e-131:
		tmp = (b * c) - (27.0 * (k * j))
	elif a <= 1.95e+82:
		tmp = (b * c) - t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(i * x))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (a <= -1e-16)
		tmp = t_2;
	elseif (a <= -2.9e-164)
		tmp = Float64(Float64(27.0 * Float64(k * Float64(-j))) - t_1);
	elseif (a <= 5.8e-131)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(k * j)));
	elseif (a <= 1.95e+82)
		tmp = Float64(Float64(b * c) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (i * x);
	t_2 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	tmp = 0.0;
	if (a <= -1e-16)
		tmp = t_2;
	elseif (a <= -2.9e-164)
		tmp = (27.0 * (k * -j)) - t_1;
	elseif (a <= 5.8e-131)
		tmp = (b * c) - (27.0 * (k * j));
	elseif (a <= 1.95e+82)
		tmp = (b * c) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e-16], t$95$2, If[LessEqual[a, -2.9e-164], N[(N[(27.0 * N[(k * (-j)), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[a, 5.8e-131], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.95e+82], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.9999999999999998e-17 or 1.94999999999999988e82 < a

   1. Initial program 79.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 79.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 79.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 79.6%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 79.6%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 84.7%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 84.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 84.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 84.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 84.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 84.8%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 84.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 63.2%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   if -9.9999999999999998e-17 < a < -2.9e-164

   1. Initial program 91.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 68.5%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around 0 60.0%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]

   if -2.9e-164 < a < 5.8000000000000004e-131

   1. Initial program 89.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 63.4%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 60.8%

      \[\leadsto \color{blue}{c \cdot b - 27 \cdot \left(k \cdot j\right)} \]

   if 5.8000000000000004e-131 < a < 1.94999999999999988e82

   1. Initial program 81.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 81.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 81.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 81.6%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 81.6%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 81.6%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 84.4%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 84.4%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 84.4%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 84.4%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 84.4%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 84.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 81.6%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in t around 0 61.0%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-164}:\\ \;\;\;\;27 \cdot \left(k \cdot \left(-j\right)\right) - 4 \cdot \left(i \cdot x\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-131}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+82}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 19: 45.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+22}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;x \leq -9200000:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+170}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -3.7e+112)
   (* t (* x (* z (* 18.0 y))))
   (if (<= x -2.9e+22)
     (* -27.0 (* k j))
     (if (<= x -9200000.0)
       (* 18.0 (* y (* t (* x z))))
       (if (<= x 7.4e+86)
         (+ (* b c) (* -4.0 (* t a)))
         (if (<= x 3.7e+170)
           (* (* 18.0 y) (* x (* t z)))
           (* i (* x -4.0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -3.7e+112) {
		tmp = t * (x * (z * (18.0 * y)));
	} else if (x <= -2.9e+22) {
		tmp = -27.0 * (k * j);
	} else if (x <= -9200000.0) {
		tmp = 18.0 * (y * (t * (x * z)));
	} else if (x <= 7.4e+86) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 3.7e+170) {
		tmp = (18.0 * y) * (x * (t * z));
	} else {
		tmp = i * (x * -4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-3.7d+112)) then
        tmp = t * (x * (z * (18.0d0 * y)))
    else if (x <= (-2.9d+22)) then
        tmp = (-27.0d0) * (k * j)
    else if (x <= (-9200000.0d0)) then
        tmp = 18.0d0 * (y * (t * (x * z)))
    else if (x <= 7.4d+86) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (x <= 3.7d+170) then
        tmp = (18.0d0 * y) * (x * (t * z))
    else
        tmp = i * (x * (-4.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -3.7e+112) {
		tmp = t * (x * (z * (18.0 * y)));
	} else if (x <= -2.9e+22) {
		tmp = -27.0 * (k * j);
	} else if (x <= -9200000.0) {
		tmp = 18.0 * (y * (t * (x * z)));
	} else if (x <= 7.4e+86) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 3.7e+170) {
		tmp = (18.0 * y) * (x * (t * z));
	} else {
		tmp = i * (x * -4.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -3.7e+112:
		tmp = t * (x * (z * (18.0 * y)))
	elif x <= -2.9e+22:
		tmp = -27.0 * (k * j)
	elif x <= -9200000.0:
		tmp = 18.0 * (y * (t * (x * z)))
	elif x <= 7.4e+86:
		tmp = (b * c) + (-4.0 * (t * a))
	elif x <= 3.7e+170:
		tmp = (18.0 * y) * (x * (t * z))
	else:
		tmp = i * (x * -4.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -3.7e+112)
		tmp = Float64(t * Float64(x * Float64(z * Float64(18.0 * y))));
	elseif (x <= -2.9e+22)
		tmp = Float64(-27.0 * Float64(k * j));
	elseif (x <= -9200000.0)
		tmp = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))));
	elseif (x <= 7.4e+86)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 3.7e+170)
		tmp = Float64(Float64(18.0 * y) * Float64(x * Float64(t * z)));
	else
		tmp = Float64(i * Float64(x * -4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -3.7e+112)
		tmp = t * (x * (z * (18.0 * y)));
	elseif (x <= -2.9e+22)
		tmp = -27.0 * (k * j);
	elseif (x <= -9200000.0)
		tmp = 18.0 * (y * (t * (x * z)));
	elseif (x <= 7.4e+86)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (x <= 3.7e+170)
		tmp = (18.0 * y) * (x * (t * z));
	else
		tmp = i * (x * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -3.7e+112], N[(t * N[(x * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.9e+22], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9200000.0], N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e+86], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e+170], N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -3.70000000000000004e112

   1. Initial program 70.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 70.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 70.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 70.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 70.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 72.6%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 77.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 77.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 77.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 77.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 77.1%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 77.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 63.8%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 52.4%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 52.4%

         \[\leadsto t \cdot \left(18 \cdot \left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      2. associate-*r* 52.4%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot z\right)}\right) \]

   7. Simplified 52.4%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(\left(y \cdot x\right) \cdot z\right)\right)} \]

   8. Taylor expanded in y around 0 52.4%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 52.4%

         \[\leadsto t \cdot \color{blue}{\left(\left(18 \cdot y\right) \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 52.4%

         \[\leadsto t \cdot \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(x \cdot z\right)}\right) \]

      3. associate-*l* 52.5%

         \[\leadsto t \cdot \color{blue}{\left(\left(\left(18 \cdot y\right) \cdot x\right) \cdot z\right)} \]

      4. *-commutative 52.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot z\right) \]

      5. associate-*l* 54.6%

         \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)} \]

   10. Simplified 54.6%

       \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)} \]

   if -3.70000000000000004e112 < x < -2.9e22

   1. Initial program 88.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 88.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. +-commutative 88.1%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 88.2%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 88.2%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 88.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 88.2%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 88.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 88.2%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 88.2%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 88.2%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 88.2%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 88.2%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 94.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 39.2%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -2.9e22 < x < -9.2e6

   1. Initial program 66.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 66.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 66.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 66.7%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 66.7%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 100.0%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 100.0%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 100.0%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 100.0%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 100.0%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 100.0%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 100.0%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]

   if -9.2e6 < x < 7.39999999999999983e86

   1. Initial program 94.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 94.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 94.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 94.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 94.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 95.7%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 92.9%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 92.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 92.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 92.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 93.0%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 93.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 75.3%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in x around 0 61.0%

      \[\leadsto \color{blue}{c \cdot b + -4 \cdot \left(a \cdot t\right)} \]

   if 7.39999999999999983e86 < x < 3.69999999999999987e170

   1. Initial program 75.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 75.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 75.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 75.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 75.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 80.3%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 80.3%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 80.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 80.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 80.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 80.3%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 80.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 65.6%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 60.3%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.4%

         \[\leadsto \color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 60.4%

         \[\leadsto \color{blue}{\left(t \cdot \left(z \cdot x\right)\right) \cdot \left(18 \cdot y\right)} \]

      3. associate-*r* 60.4%

         \[\leadsto \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)} \cdot \left(18 \cdot y\right) \]

      4. *-commutative 60.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(t \cdot z\right)\right)} \cdot \left(18 \cdot y\right) \]

   7. Simplified 60.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(t \cdot z\right)\right) \cdot \left(18 \cdot y\right)} \]

   if 3.69999999999999987e170 < x

   1. Initial program 63.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 65.6%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in i around inf 46.7%

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

      1. *-commutative 46.7%

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      2. associate-*l* 49.5%

         \[\leadsto \color{blue}{i \cdot \left(x \cdot -4\right)} \]

   5. Simplified 49.5%

      \[\leadsto \color{blue}{i \cdot \left(x \cdot -4\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+22}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;x \leq -9200000:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+170}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \end{array} \]

Alternative 20: 48.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+120}:\\ \;\;\;\;t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -34000000:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+170}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (* i x)))))
   (if (<= x -1.15e+120)
     (* t (* x (* z (* 18.0 y))))
     (if (<= x -3.2e+27)
       t_1
       (if (<= x -34000000.0)
         (* 18.0 (* y (* t (* x z))))
         (if (<= x 4.9e+86)
           (+ (* b c) (* -4.0 (* t a)))
           (if (<= x 9.5e+170) (* (* 18.0 y) (* x (* t z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (i * x));
	double tmp;
	if (x <= -1.15e+120) {
		tmp = t * (x * (z * (18.0 * y)));
	} else if (x <= -3.2e+27) {
		tmp = t_1;
	} else if (x <= -34000000.0) {
		tmp = 18.0 * (y * (t * (x * z)));
	} else if (x <= 4.9e+86) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 9.5e+170) {
		tmp = (18.0 * y) * (x * (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * (i * x))
    if (x <= (-1.15d+120)) then
        tmp = t * (x * (z * (18.0d0 * y)))
    else if (x <= (-3.2d+27)) then
        tmp = t_1
    else if (x <= (-34000000.0d0)) then
        tmp = 18.0d0 * (y * (t * (x * z)))
    else if (x <= 4.9d+86) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (x <= 9.5d+170) then
        tmp = (18.0d0 * y) * (x * (t * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (i * x));
	double tmp;
	if (x <= -1.15e+120) {
		tmp = t * (x * (z * (18.0 * y)));
	} else if (x <= -3.2e+27) {
		tmp = t_1;
	} else if (x <= -34000000.0) {
		tmp = 18.0 * (y * (t * (x * z)));
	} else if (x <= 4.9e+86) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 9.5e+170) {
		tmp = (18.0 * y) * (x * (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (i * x))
	tmp = 0
	if x <= -1.15e+120:
		tmp = t * (x * (z * (18.0 * y)))
	elif x <= -3.2e+27:
		tmp = t_1
	elif x <= -34000000.0:
		tmp = 18.0 * (y * (t * (x * z)))
	elif x <= 4.9e+86:
		tmp = (b * c) + (-4.0 * (t * a))
	elif x <= 9.5e+170:
		tmp = (18.0 * y) * (x * (t * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(i * x)))
	tmp = 0.0
	if (x <= -1.15e+120)
		tmp = Float64(t * Float64(x * Float64(z * Float64(18.0 * y))));
	elseif (x <= -3.2e+27)
		tmp = t_1;
	elseif (x <= -34000000.0)
		tmp = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))));
	elseif (x <= 4.9e+86)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 9.5e+170)
		tmp = Float64(Float64(18.0 * y) * Float64(x * Float64(t * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (i * x));
	tmp = 0.0;
	if (x <= -1.15e+120)
		tmp = t * (x * (z * (18.0 * y)));
	elseif (x <= -3.2e+27)
		tmp = t_1;
	elseif (x <= -34000000.0)
		tmp = 18.0 * (y * (t * (x * z)));
	elseif (x <= 4.9e+86)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (x <= 9.5e+170)
		tmp = (18.0 * y) * (x * (t * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+120], N[(t * N[(x * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.2e+27], t$95$1, If[LessEqual[x, -34000000.0], N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.9e+86], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e+170], N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.14999999999999996e120

   1. Initial program 68.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 68.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 68.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 68.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 68.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 71.3%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 75.9%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 75.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 75.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 75.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 75.9%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 75.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 52.4%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 52.4%

         \[\leadsto t \cdot \left(18 \cdot \left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      2. associate-*r* 52.4%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot z\right)}\right) \]

   7. Simplified 52.4%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(\left(y \cdot x\right) \cdot z\right)\right)} \]

   8. Taylor expanded in y around 0 52.4%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 52.4%

         \[\leadsto t \cdot \color{blue}{\left(\left(18 \cdot y\right) \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 52.4%

         \[\leadsto t \cdot \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(x \cdot z\right)}\right) \]

      3. associate-*l* 52.5%

         \[\leadsto t \cdot \color{blue}{\left(\left(\left(18 \cdot y\right) \cdot x\right) \cdot z\right)} \]

      4. *-commutative 52.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot z\right) \]

      5. associate-*l* 54.8%

         \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)} \]

   10. Simplified 54.8%

       \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)} \]

   if -1.14999999999999996e120 < x < -3.20000000000000015e27 or 9.5000000000000005e170 < x

   1. Initial program 72.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 72.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 72.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 72.1%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 72.1%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 74.1%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 76.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 76.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 76.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 76.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 76.1%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 76.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 64.6%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in t around 0 55.0%

      \[\leadsto \color{blue}{c \cdot b - 4 \cdot \left(i \cdot x\right)} \]

   if -3.20000000000000015e27 < x < -3.4e7

   1. Initial program 79.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 79.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 79.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 79.7%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 79.7%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 99.7%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 99.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 99.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 99.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 99.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 100.0%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 60.8%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 61.0%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]

   if -3.4e7 < x < 4.8999999999999999e86

   1. Initial program 94.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 94.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 94.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 94.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 94.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 95.7%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 92.9%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 92.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 92.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 92.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 93.0%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 93.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 75.3%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in x around 0 61.0%

      \[\leadsto \color{blue}{c \cdot b + -4 \cdot \left(a \cdot t\right)} \]

   if 4.8999999999999999e86 < x < 9.5000000000000005e170

   1. Initial program 75.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 75.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 75.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 75.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 75.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 80.3%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 80.3%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 80.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 80.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 80.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 80.3%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 80.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 65.6%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 60.3%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.4%

         \[\leadsto \color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 60.4%

         \[\leadsto \color{blue}{\left(t \cdot \left(z \cdot x\right)\right) \cdot \left(18 \cdot y\right)} \]

      3. associate-*r* 60.4%

         \[\leadsto \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)} \cdot \left(18 \cdot y\right) \]

      4. *-commutative 60.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(t \cdot z\right)\right)} \cdot \left(18 \cdot y\right) \]

   7. Simplified 60.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(t \cdot z\right)\right) \cdot \left(18 \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+120}:\\ \;\;\;\;t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+27}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \mathbf{elif}\;x \leq -34000000:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+170}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \end{array} \]

Alternative 21: 32.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(x \cdot -4\right)\\ t_2 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;k \leq -7 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -6 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3.25 \cdot 10^{-133}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 6 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* i (* x -4.0))) (t_2 (* -27.0 (* k j))))
   (if (<= k -7e-8)
     t_2
     (if (<= k -6e-148)
       t_1
       (if (<= k 3.25e-133) (* b c) (if (<= k 6e+144) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = i * (x * -4.0);
	double t_2 = -27.0 * (k * j);
	double tmp;
	if (k <= -7e-8) {
		tmp = t_2;
	} else if (k <= -6e-148) {
		tmp = t_1;
	} else if (k <= 3.25e-133) {
		tmp = b * c;
	} else if (k <= 6e+144) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (x * (-4.0d0))
    t_2 = (-27.0d0) * (k * j)
    if (k <= (-7d-8)) then
        tmp = t_2
    else if (k <= (-6d-148)) then
        tmp = t_1
    else if (k <= 3.25d-133) then
        tmp = b * c
    else if (k <= 6d+144) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = i * (x * -4.0);
	double t_2 = -27.0 * (k * j);
	double tmp;
	if (k <= -7e-8) {
		tmp = t_2;
	} else if (k <= -6e-148) {
		tmp = t_1;
	} else if (k <= 3.25e-133) {
		tmp = b * c;
	} else if (k <= 6e+144) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = i * (x * -4.0)
	t_2 = -27.0 * (k * j)
	tmp = 0
	if k <= -7e-8:
		tmp = t_2
	elif k <= -6e-148:
		tmp = t_1
	elif k <= 3.25e-133:
		tmp = b * c
	elif k <= 6e+144:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(i * Float64(x * -4.0))
	t_2 = Float64(-27.0 * Float64(k * j))
	tmp = 0.0
	if (k <= -7e-8)
		tmp = t_2;
	elseif (k <= -6e-148)
		tmp = t_1;
	elseif (k <= 3.25e-133)
		tmp = Float64(b * c);
	elseif (k <= 6e+144)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = i * (x * -4.0);
	t_2 = -27.0 * (k * j);
	tmp = 0.0;
	if (k <= -7e-8)
		tmp = t_2;
	elseif (k <= -6e-148)
		tmp = t_1;
	elseif (k <= 3.25e-133)
		tmp = b * c;
	elseif (k <= 6e+144)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -7e-8], t$95$2, If[LessEqual[k, -6e-148], t$95$1, If[LessEqual[k, 3.25e-133], N[(b * c), $MachinePrecision], If[LessEqual[k, 6e+144], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if k < -7.00000000000000048e-8 or 5.9999999999999998e144 < k

   1. Initial program 80.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 80.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. +-commutative 80.8%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 80.8%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 80.8%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 85.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 85.3%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 85.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 85.3%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 85.3%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 85.3%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 85.3%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 85.3%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 49.5%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -7.00000000000000048e-8 < k < -5.99999999999999996e-148 or 3.2500000000000001e-133 < k < 5.9999999999999998e144

   1. Initial program 85.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 80.0%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in i around inf 31.3%

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

      1. *-commutative 31.3%

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      2. associate-*l* 31.3%

         \[\leadsto \color{blue}{i \cdot \left(x \cdot -4\right)} \]

   5. Simplified 31.3%

      \[\leadsto \color{blue}{i \cdot \left(x \cdot -4\right)} \]

   if -5.99999999999999996e-148 < k < 3.2500000000000001e-133

   1. Initial program 86.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 73.1%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around inf 33.1%

      \[\leadsto \color{blue}{c \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -7 \cdot 10^{-8}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;k \leq -6 \cdot 10^{-148}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;k \leq 3.25 \cdot 10^{-133}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 6 \cdot 10^{+144}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \]

Alternative 22: 33.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{+22}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-235}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t a))))
   (if (<= b -1.9e+22)
     (* b c)
     (if (<= b -2.2e-130)
       t_1
       (if (<= b 3.5e-235) (* k (* j -27.0)) (if (<= b 7e+95) t_1 (* b c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double tmp;
	if (b <= -1.9e+22) {
		tmp = b * c;
	} else if (b <= -2.2e-130) {
		tmp = t_1;
	} else if (b <= 3.5e-235) {
		tmp = k * (j * -27.0);
	} else if (b <= 7e+95) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * a)
    if (b <= (-1.9d+22)) then
        tmp = b * c
    else if (b <= (-2.2d-130)) then
        tmp = t_1
    else if (b <= 3.5d-235) then
        tmp = k * (j * (-27.0d0))
    else if (b <= 7d+95) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double tmp;
	if (b <= -1.9e+22) {
		tmp = b * c;
	} else if (b <= -2.2e-130) {
		tmp = t_1;
	} else if (b <= 3.5e-235) {
		tmp = k * (j * -27.0);
	} else if (b <= 7e+95) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (t * a)
	tmp = 0
	if b <= -1.9e+22:
		tmp = b * c
	elif b <= -2.2e-130:
		tmp = t_1
	elif b <= 3.5e-235:
		tmp = k * (j * -27.0)
	elif b <= 7e+95:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(t * a))
	tmp = 0.0
	if (b <= -1.9e+22)
		tmp = Float64(b * c);
	elseif (b <= -2.2e-130)
		tmp = t_1;
	elseif (b <= 3.5e-235)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (b <= 7e+95)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (t * a);
	tmp = 0.0;
	if (b <= -1.9e+22)
		tmp = b * c;
	elseif (b <= -2.2e-130)
		tmp = t_1;
	elseif (b <= 3.5e-235)
		tmp = k * (j * -27.0);
	elseif (b <= 7e+95)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.9e+22], N[(b * c), $MachinePrecision], If[LessEqual[b, -2.2e-130], t$95$1, If[LessEqual[b, 3.5e-235], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e+95], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.9000000000000002e22 or 6.99999999999999999e95 < b

   1. Initial program 82.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 78.3%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around inf 40.2%

      \[\leadsto \color{blue}{c \cdot b} \]

   if -1.9000000000000002e22 < b < -2.1999999999999999e-130 or 3.4999999999999999e-235 < b < 6.99999999999999999e95

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 71.9%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around inf 31.8%

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

      1. *-commutative 31.8%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

   5. Simplified 31.8%

      \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

   if -2.1999999999999999e-130 < b < 3.4999999999999999e-235

   1. Initial program 84.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 78.0%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in j around inf 30.0%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-commutative 30.0%

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative 30.0%

         \[\leadsto \color{blue}{\left(j \cdot k\right) \cdot -27} \]

      3. *-commutative 30.0%

         \[\leadsto \color{blue}{\left(k \cdot j\right)} \cdot -27 \]

      4. associate-*r* 30.1%

         \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   5. Simplified 30.1%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+22}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-130}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-235}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+95}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 23: 33.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -9.5 \cdot 10^{-26} \lor \neg \left(k \leq 1.5 \cdot 10^{+74}\right):\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= k -9.5e-26) (not (<= k 1.5e+74))) (* -27.0 (* k j)) (* b c)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((k <= -9.5e-26) || !(k <= 1.5e+74)) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((k <= (-9.5d-26)) .or. (.not. (k <= 1.5d+74))) then
        tmp = (-27.0d0) * (k * j)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((k <= -9.5e-26) || !(k <= 1.5e+74)) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (k <= -9.5e-26) or not (k <= 1.5e+74):
		tmp = -27.0 * (k * j)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((k <= -9.5e-26) || !(k <= 1.5e+74))
		tmp = Float64(-27.0 * Float64(k * j));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((k <= -9.5e-26) || ~((k <= 1.5e+74)))
		tmp = -27.0 * (k * j);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[k, -9.5e-26], N[Not[LessEqual[k, 1.5e+74]], $MachinePrecision]], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -9.4999999999999995e-26 or 1.5e74 < k

   1. Initial program 79.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 79.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. +-commutative 79.1%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 79.1%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 79.1%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 83.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 83.9%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 83.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 83.9%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 83.9%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 83.9%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 83.9%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 83.9%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 88.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 46.2%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -9.4999999999999995e-26 < k < 1.5e74

   1. Initial program 87.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 74.8%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around inf 28.4%

      \[\leadsto \color{blue}{c \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -9.5 \cdot 10^{-26} \lor \neg \left(k \leq 1.5 \cdot 10^{+74}\right):\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 24: 23.7% accurate, 10.3× speedup

Math

\[\begin{array}{l} \\ b \cdot c \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    code = b * c
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(b * c), $MachinePrecision]

Derivation

1. Initial program 84.1%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

2. Taylor expanded in y around 0 75.9%

   \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

3. Taylor expanded in c around inf 23.8%

   \[\leadsto \color{blue}{c \cdot b} \]

4. Final simplification 23.8%

   \[\leadsto b \cdot c \]

Developer target: 89.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023240 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))