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

Percentage Accurate: 85.1% → 90.3%

Time: 20.4s

Alternatives: 15

Speedup: 0.5×

• 51.2% 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: 85.1% 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: 90.3% 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 81.7%

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

   1. sub-neg 81.7%

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

   2. +-commutative 81.7%

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

   3. associate-*l* 82.5%

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

   4. distribute-rgt-neg-in 82.5%

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

   5. fma-def 84.1%

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

   6. *-commutative 84.1%

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

   7. distribute-rgt-neg-in 84.1%

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

   8. metadata-eval 84.1%

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

   9. sub-neg 84.1%

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

   10. +-commutative 84.1%

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

   11. associate-*l* 84.1%

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

   12. distribute-rgt-neg-in 84.1%

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

3. Simplified 91.5%

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

4. Final simplification 91.5%

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

Alternative 2: 89.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<=
      (-
       (-
        (+ (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))) (* b c))
        (* i (* x 4.0)))
       (* k (* j 27.0)))
      INFINITY)
   (-
    (+ (* t (- (* (* y z) (* x 18.0)) (* a 4.0))) (* b c))
    (+ (* x (* i 4.0)) (* j (* k 27.0))))
   (* t (- (* 18.0 (* y (* x z))) (* a 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 ((((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0))) <= ((double) INFINITY)) {
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (b * c)) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 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 tmp;
	if ((((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0))) <= Double.POSITIVE_INFINITY) {
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (b * c)) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (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))) <= Inf)
		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(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 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 ((((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0))) <= Inf)
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (b * c)) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	else
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[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], Infinity], 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[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 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 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-- 94.3%

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

      6. associate-*l* 95.1%

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

      7. distribute-lft-neg-in 95.1%

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

      8. cancel-sign-sub 95.1%

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

      9. associate-*l* 95.1%

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

      10. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   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-- 20.6%

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

      6. associate-*l* 23.5%

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

      7. distribute-lft-neg-in 23.5%

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

      8. cancel-sign-sub 23.5%

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

      9. associate-*l* 23.5%

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

      10. associate-*l* 23.5%

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

   3. Simplified 23.5%

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

   4. Taylor expanded in t around inf 56.1%

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

4. Final simplification 90.7%

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

Alternative 3: 52.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(-4 \cdot t\right) - j \cdot \left(k \cdot 27\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-159}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-281}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-38}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+141}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* a (* -4.0 t)) (* j (* k 27.0))))
        (t_2 (* k (* j 27.0)))
        (t_3 (+ (* b c) (* -4.0 (* t a)))))
   (if (<= t_2 -5e+16)
     t_1
     (if (<= t_2 -5e-159)
       t_3
       (if (<= t_2 -5e-281)
         (* x (- (* 18.0 (* y (* t z))) (* i 4.0)))
         (if (<= t_2 5e-38)
           t_3
           (if (<= t_2 2e+44)
             t_1
             (if (<= t_2 5e+141)
               (- (* b c) (* x (* i 4.0)))
               (- (* 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 = (a * (-4.0 * t)) - (j * (k * 27.0));
	double t_2 = k * (j * 27.0);
	double t_3 = (b * c) + (-4.0 * (t * a));
	double tmp;
	if (t_2 <= -5e+16) {
		tmp = t_1;
	} else if (t_2 <= -5e-159) {
		tmp = t_3;
	} else if (t_2 <= -5e-281) {
		tmp = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	} else if (t_2 <= 5e-38) {
		tmp = t_3;
	} else if (t_2 <= 2e+44) {
		tmp = t_1;
	} else if (t_2 <= 5e+141) {
		tmp = (b * c) - (x * (i * 4.0));
	} else {
		tmp = (b * c) - 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 = (a * ((-4.0d0) * t)) - (j * (k * 27.0d0))
    t_2 = k * (j * 27.0d0)
    t_3 = (b * c) + ((-4.0d0) * (t * a))
    if (t_2 <= (-5d+16)) then
        tmp = t_1
    else if (t_2 <= (-5d-159)) then
        tmp = t_3
    else if (t_2 <= (-5d-281)) then
        tmp = x * ((18.0d0 * (y * (t * z))) - (i * 4.0d0))
    else if (t_2 <= 5d-38) then
        tmp = t_3
    else if (t_2 <= 2d+44) then
        tmp = t_1
    else if (t_2 <= 5d+141) then
        tmp = (b * c) - (x * (i * 4.0d0))
    else
        tmp = (b * c) - 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 * (-4.0 * t)) - (j * (k * 27.0));
	double t_2 = k * (j * 27.0);
	double t_3 = (b * c) + (-4.0 * (t * a));
	double tmp;
	if (t_2 <= -5e+16) {
		tmp = t_1;
	} else if (t_2 <= -5e-159) {
		tmp = t_3;
	} else if (t_2 <= -5e-281) {
		tmp = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	} else if (t_2 <= 5e-38) {
		tmp = t_3;
	} else if (t_2 <= 2e+44) {
		tmp = t_1;
	} else if (t_2 <= 5e+141) {
		tmp = (b * c) - (x * (i * 4.0));
	} else {
		tmp = (b * c) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (a * (-4.0 * t)) - (j * (k * 27.0))
	t_2 = k * (j * 27.0)
	t_3 = (b * c) + (-4.0 * (t * a))
	tmp = 0
	if t_2 <= -5e+16:
		tmp = t_1
	elif t_2 <= -5e-159:
		tmp = t_3
	elif t_2 <= -5e-281:
		tmp = x * ((18.0 * (y * (t * z))) - (i * 4.0))
	elif t_2 <= 5e-38:
		tmp = t_3
	elif t_2 <= 2e+44:
		tmp = t_1
	elif t_2 <= 5e+141:
		tmp = (b * c) - (x * (i * 4.0))
	else:
		tmp = (b * c) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(a * Float64(-4.0 * t)) - Float64(j * Float64(k * 27.0)))
	t_2 = Float64(k * Float64(j * 27.0))
	t_3 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (t_2 <= -5e+16)
		tmp = t_1;
	elseif (t_2 <= -5e-159)
		tmp = t_3;
	elseif (t_2 <= -5e-281)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(i * 4.0)));
	elseif (t_2 <= 5e-38)
		tmp = t_3;
	elseif (t_2 <= 2e+44)
		tmp = t_1;
	elseif (t_2 <= 5e+141)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(i * 4.0)));
	else
		tmp = Float64(Float64(b * c) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (a * (-4.0 * t)) - (j * (k * 27.0));
	t_2 = k * (j * 27.0);
	t_3 = (b * c) + (-4.0 * (t * a));
	tmp = 0.0;
	if (t_2 <= -5e+16)
		tmp = t_1;
	elseif (t_2 <= -5e-159)
		tmp = t_3;
	elseif (t_2 <= -5e-281)
		tmp = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	elseif (t_2 <= 5e-38)
		tmp = t_3;
	elseif (t_2 <= 2e+44)
		tmp = t_1;
	elseif (t_2 <= 5e+141)
		tmp = (b * c) - (x * (i * 4.0));
	else
		tmp = (b * c) - 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[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+16], t$95$1, If[LessEqual[t$95$2, -5e-159], t$95$3, If[LessEqual[t$95$2, -5e-281], N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e-38], t$95$3, If[LessEqual[t$95$2, 2e+44], t$95$1, If[LessEqual[t$95$2, 5e+141], N[(N[(b * c), $MachinePrecision] - N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 j 27) k) < -5e16 or 5.00000000000000033e-38 < (*.f64 (*.f64 j 27) k) < 2.0000000000000002e44

   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. distribute-rgt-out-- 84.6%

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

      2. associate-*r* 84.6%

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

      3. add-cube-cbrt 84.4%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied egg-rr 84.4%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in a around inf 66.0%

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

      1. *-commutative 66.0%

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

      2. associate-*l* 66.0%

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

   6. Simplified 66.0%

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

   7. Taylor expanded in j around 0 67.4%

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

      1. associate-*r* 67.4%

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

   9. Simplified 67.4%

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

   if -5e16 < (*.f64 (*.f64 j 27) k) < -5.00000000000000032e-159 or -4.9999999999999998e-281 < (*.f64 (*.f64 j 27) k) < 5.00000000000000033e-38

   1. Initial program 83.1%

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

   2. Taylor expanded in y around 0 77.4%

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

   3. Taylor expanded in i around 0 64.8%

      \[\leadsto \color{blue}{c \cdot b - \left(27 \cdot \left(k \cdot j\right) + 4 \cdot \left(a \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. fma-neg 65.8%

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

      2. +-commutative 65.8%

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

      3. *-commutative 65.8%

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

      4. *-commutative 65.8%

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

      5. associate-*r* 65.8%

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

      6. distribute-neg-in 65.8%

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

      7. distribute-lft-neg-in 65.8%

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

      8. metadata-eval 65.8%

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

      9. *-commutative 65.8%

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

      10. *-commutative 65.8%

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

      11. associate-*l* 65.8%

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

      12. associate-*r* 65.8%

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

      13. distribute-rgt-neg-in 65.8%

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

      14. metadata-eval 65.8%

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

      15. *-commutative 65.8%

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

      16. associate-*l* 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in j around 0 62.9%

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

   if -5.00000000000000032e-159 < (*.f64 (*.f64 j 27) k) < -4.9999999999999998e-281

   1. Initial program 85.6%

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

      1. sub-neg 85.6%

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

      2. associate-+l- 85.6%

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

      3. sub-neg 85.6%

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

      4. sub-neg 85.6%

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

      5. distribute-rgt-out-- 85.6%

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

      6. associate-*l* 90.5%

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

      7. distribute-lft-neg-in 90.5%

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

      8. cancel-sign-sub 90.5%

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

      9. associate-*l* 90.5%

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

      10. associate-*l* 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in x around inf 71.5%

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

   if 2.0000000000000002e44 < (*.f64 (*.f64 j 27) k) < 5.00000000000000025e141

   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. Step-by-step derivation

      1. sub-neg 84.6%

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

      2. associate-+l- 84.6%

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

      3. sub-neg 84.6%

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

      4. sub-neg 84.6%

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

      5. distribute-rgt-out-- 92.3%

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

      6. associate-*l* 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 0 86.0%

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

   5. Taylor expanded in i around inf 86.0%

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

      1. associate-*r* 86.0%

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

      2. *-commutative 86.0%

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

   7. Simplified 86.0%

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

   if 5.00000000000000025e141 < (*.f64 (*.f64 j 27) k)

   1. Initial program 80.7%

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

      1. distribute-rgt-out-- 82.6%

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

      2. associate-*r* 86.5%

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

      3. add-cube-cbrt 86.5%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied egg-rr 86.5%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in b around inf 82.1%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{-159}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{-281}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{-38}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+141}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 4: 52.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(-4 \cdot t\right) - j \cdot \left(k \cdot 27\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-38}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+141}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* a (* -4.0 t)) (* j (* k 27.0)))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -5e+16)
     t_1
     (if (<= t_2 5e-38)
       (+ (* b c) (* -4.0 (* t a)))
       (if (<= t_2 2e+44)
         t_1
         (if (<= t_2 5e+141) (- (* b c) (* x (* i 4.0))) (- (* 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 = (a * (-4.0 * t)) - (j * (k * 27.0));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -5e+16) {
		tmp = t_1;
	} else if (t_2 <= 5e-38) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (t_2 <= 2e+44) {
		tmp = t_1;
	} else if (t_2 <= 5e+141) {
		tmp = (b * c) - (x * (i * 4.0));
	} else {
		tmp = (b * c) - 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 * ((-4.0d0) * t)) - (j * (k * 27.0d0))
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-5d+16)) then
        tmp = t_1
    else if (t_2 <= 5d-38) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (t_2 <= 2d+44) then
        tmp = t_1
    else if (t_2 <= 5d+141) then
        tmp = (b * c) - (x * (i * 4.0d0))
    else
        tmp = (b * c) - 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 * (-4.0 * t)) - (j * (k * 27.0));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -5e+16) {
		tmp = t_1;
	} else if (t_2 <= 5e-38) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (t_2 <= 2e+44) {
		tmp = t_1;
	} else if (t_2 <= 5e+141) {
		tmp = (b * c) - (x * (i * 4.0));
	} else {
		tmp = (b * c) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (a * (-4.0 * t)) - (j * (k * 27.0))
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -5e+16:
		tmp = t_1
	elif t_2 <= 5e-38:
		tmp = (b * c) + (-4.0 * (t * a))
	elif t_2 <= 2e+44:
		tmp = t_1
	elif t_2 <= 5e+141:
		tmp = (b * c) - (x * (i * 4.0))
	else:
		tmp = (b * c) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(a * Float64(-4.0 * t)) - Float64(j * Float64(k * 27.0)))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -5e+16)
		tmp = t_1;
	elseif (t_2 <= 5e-38)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (t_2 <= 2e+44)
		tmp = t_1;
	elseif (t_2 <= 5e+141)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(i * 4.0)));
	else
		tmp = Float64(Float64(b * c) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (a * (-4.0 * t)) - (j * (k * 27.0));
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -5e+16)
		tmp = t_1;
	elseif (t_2 <= 5e-38)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (t_2 <= 2e+44)
		tmp = t_1;
	elseif (t_2 <= 5e+141)
		tmp = (b * c) - (x * (i * 4.0));
	else
		tmp = (b * c) - 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[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+16], t$95$1, If[LessEqual[t$95$2, 5e-38], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+44], t$95$1, If[LessEqual[t$95$2, 5e+141], N[(N[(b * c), $MachinePrecision] - N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j 27) k) < -5e16 or 5.00000000000000033e-38 < (*.f64 (*.f64 j 27) k) < 2.0000000000000002e44

   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. distribute-rgt-out-- 84.6%

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

      2. associate-*r* 84.6%

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

      3. add-cube-cbrt 84.4%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied egg-rr 84.4%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in a around inf 66.0%

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

      1. *-commutative 66.0%

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

      2. associate-*l* 66.0%

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

   6. Simplified 66.0%

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

   7. Taylor expanded in j around 0 67.4%

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

      1. associate-*r* 67.4%

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

   9. Simplified 67.4%

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

   if -5e16 < (*.f64 (*.f64 j 27) k) < 5.00000000000000033e-38

   1. Initial program 83.5%

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

   2. Taylor expanded in y around 0 75.7%

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

   3. Taylor expanded in i around 0 60.2%

      \[\leadsto \color{blue}{c \cdot b - \left(27 \cdot \left(k \cdot j\right) + 4 \cdot \left(a \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. fma-neg 61.0%

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

      2. +-commutative 61.0%

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

      3. *-commutative 61.0%

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

      4. *-commutative 61.0%

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

      5. associate-*r* 61.0%

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

      6. distribute-neg-in 61.0%

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

      7. distribute-lft-neg-in 61.0%

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

      8. metadata-eval 61.0%

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

      9. *-commutative 61.0%

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

      10. *-commutative 61.0%

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

      11. associate-*l* 61.0%

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

      12. associate-*r* 61.0%

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

      13. distribute-rgt-neg-in 61.0%

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

      14. metadata-eval 61.0%

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

      15. *-commutative 61.0%

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

      16. associate-*l* 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in j around 0 58.6%

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

   if 2.0000000000000002e44 < (*.f64 (*.f64 j 27) k) < 5.00000000000000025e141

   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. Step-by-step derivation

      1. sub-neg 84.6%

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

      2. associate-+l- 84.6%

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

      3. sub-neg 84.6%

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

      4. sub-neg 84.6%

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

      5. distribute-rgt-out-- 92.3%

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

      6. associate-*l* 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 0 86.0%

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

   5. Taylor expanded in i around inf 86.0%

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

      1. associate-*r* 86.0%

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

      2. *-commutative 86.0%

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

   7. Simplified 86.0%

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

   if 5.00000000000000025e141 < (*.f64 (*.f64 j 27) k)

   1. Initial program 80.7%

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

      1. distribute-rgt-out-- 82.6%

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

      2. associate-*r* 86.5%

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

      3. add-cube-cbrt 86.5%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied egg-rr 86.5%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in b around inf 82.1%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{-38}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+141}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 5: 54.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := b \cdot c - t_1\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+44}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+141}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))) (t_2 (- (* b c) t_1)))
   (if (<= t_1 -5e+32)
     t_2
     (if (<= t_1 2e+44)
       (+ (* b c) (* -4.0 (* t a)))
       (if (<= t_1 5e+141) (- (* b c) (* x (* i 4.0))) 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 = k * (j * 27.0);
	double t_2 = (b * c) - t_1;
	double tmp;
	if (t_1 <= -5e+32) {
		tmp = t_2;
	} else if (t_1 <= 2e+44) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (t_1 <= 5e+141) {
		tmp = (b * c) - (x * (i * 4.0));
	} 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 = k * (j * 27.0d0)
    t_2 = (b * c) - t_1
    if (t_1 <= (-5d+32)) then
        tmp = t_2
    else if (t_1 <= 2d+44) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (t_1 <= 5d+141) then
        tmp = (b * c) - (x * (i * 4.0d0))
    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 = k * (j * 27.0);
	double t_2 = (b * c) - t_1;
	double tmp;
	if (t_1 <= -5e+32) {
		tmp = t_2;
	} else if (t_1 <= 2e+44) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (t_1 <= 5e+141) {
		tmp = (b * c) - (x * (i * 4.0));
	} 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 = (b * c) - t_1
	tmp = 0
	if t_1 <= -5e+32:
		tmp = t_2
	elif t_1 <= 2e+44:
		tmp = (b * c) + (-4.0 * (t * a))
	elif t_1 <= 5e+141:
		tmp = (b * c) - (x * (i * 4.0))
	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(Float64(b * c) - t_1)
	tmp = 0.0
	if (t_1 <= -5e+32)
		tmp = t_2;
	elseif (t_1 <= 2e+44)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (t_1 <= 5e+141)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(i * 4.0)));
	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 = k * (j * 27.0);
	t_2 = (b * c) - t_1;
	tmp = 0.0;
	if (t_1 <= -5e+32)
		tmp = t_2;
	elseif (t_1 <= 2e+44)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (t_1 <= 5e+141)
		tmp = (b * c) - (x * (i * 4.0));
	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[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+32], t$95$2, If[LessEqual[t$95$1, 2e+44], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+141], N[(N[(b * c), $MachinePrecision] - N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -4.9999999999999997e32 or 5.00000000000000025e141 < (*.f64 (*.f64 j 27) k)

   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. distribute-rgt-out-- 81.6%

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

      2. associate-*r* 83.5%

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

      3. add-cube-cbrt 83.5%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied egg-rr 83.5%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in b around inf 70.9%

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

   if -4.9999999999999997e32 < (*.f64 (*.f64 j 27) k) < 2.0000000000000002e44

   1. Initial program 84.5%

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

   2. Taylor expanded in y around 0 77.8%

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

   3. Taylor expanded in i around 0 61.0%

      \[\leadsto \color{blue}{c \cdot b - \left(27 \cdot \left(k \cdot j\right) + 4 \cdot \left(a \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. fma-neg 61.7%

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

      2. +-commutative 61.7%

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

      3. *-commutative 61.7%

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

      4. *-commutative 61.7%

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

      5. associate-*r* 61.7%

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

      6. distribute-neg-in 61.7%

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

      7. distribute-lft-neg-in 61.7%

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

      8. metadata-eval 61.7%

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

      9. *-commutative 61.7%

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

      10. *-commutative 61.7%

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

      11. associate-*l* 61.7%

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

      12. associate-*r* 61.7%

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

      13. distribute-rgt-neg-in 61.7%

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

      14. metadata-eval 61.7%

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

      15. *-commutative 61.7%

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

      16. associate-*l* 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in j around 0 55.5%

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

   if 2.0000000000000002e44 < (*.f64 (*.f64 j 27) k) < 5.00000000000000025e141

   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. Step-by-step derivation

      1. sub-neg 84.6%

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

      2. associate-+l- 84.6%

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

      3. sub-neg 84.6%

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

      4. sub-neg 84.6%

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

      5. distribute-rgt-out-- 92.3%

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

      6. associate-*l* 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 0 86.0%

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

   5. Taylor expanded in i around inf 86.0%

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

      1. associate-*r* 86.0%

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

      2. *-commutative 86.0%

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

   7. Simplified 86.0%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{+32}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+44}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+141}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 6: 67.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+132}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+141}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))))
   (if (<= t_1 -2e+132)
     (- (* a (* -4.0 t)) (* j (* k 27.0)))
     (if (<= t_1 5e+141)
       (- (* b c) (+ (* 4.0 (* x i)) (* 4.0 (* t a))))
       (- (* b c) 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_1 <= -2e+132) {
		tmp = (a * (-4.0 * t)) - (j * (k * 27.0));
	} else if (t_1 <= 5e+141) {
		tmp = (b * c) - ((4.0 * (x * i)) + (4.0 * (t * a)));
	} else {
		tmp = (b * c) - 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_1 <= (-2d+132)) then
        tmp = (a * ((-4.0d0) * t)) - (j * (k * 27.0d0))
    else if (t_1 <= 5d+141) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + (4.0d0 * (t * a)))
    else
        tmp = (b * c) - 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_1 <= -2e+132) {
		tmp = (a * (-4.0 * t)) - (j * (k * 27.0));
	} else if (t_1 <= 5e+141) {
		tmp = (b * c) - ((4.0 * (x * i)) + (4.0 * (t * a)));
	} else {
		tmp = (b * c) - 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_1 <= -2e+132:
		tmp = (a * (-4.0 * t)) - (j * (k * 27.0))
	elif t_1 <= 5e+141:
		tmp = (b * c) - ((4.0 * (x * i)) + (4.0 * (t * a)))
	else:
		tmp = (b * c) - 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_1 <= -2e+132)
		tmp = Float64(Float64(a * Float64(-4.0 * t)) - Float64(j * Float64(k * 27.0)));
	elseif (t_1 <= 5e+141)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(4.0 * Float64(t * a))));
	else
		tmp = Float64(Float64(b * c) - 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_1 <= -2e+132)
		tmp = (a * (-4.0 * t)) - (j * (k * 27.0));
	elseif (t_1 <= 5e+141)
		tmp = (b * c) - ((4.0 * (x * i)) + (4.0 * (t * a)));
	else
		tmp = (b * c) - 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$95$1, -2e+132], N[(N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+141], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -1.99999999999999998e132

   1. Initial program 70.6%

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

      1. distribute-rgt-out-- 77.9%

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

      2. associate-*r* 77.9%

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

      3. add-cube-cbrt 77.9%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied egg-rr 77.9%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in a around inf 73.4%

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

      1. *-commutative 73.4%

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

      2. associate-*l* 73.4%

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

   6. Simplified 73.4%

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

   7. Taylor expanded in j around 0 75.8%

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

      1. associate-*r* 75.9%

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

   9. Simplified 75.9%

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

   if -1.99999999999999998e132 < (*.f64 (*.f64 j 27) k) < 5.00000000000000025e141

   1. Initial program 84.9%

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

   2. Taylor expanded in y around 0 78.1%

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

   3. Taylor expanded in j around 0 71.9%

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

   if 5.00000000000000025e141 < (*.f64 (*.f64 j 27) k)

   1. Initial program 80.7%

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

      1. distribute-rgt-out-- 82.6%

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

      2. associate-*r* 86.5%

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

      3. add-cube-cbrt 86.5%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied egg-rr 86.5%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in b around inf 82.1%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -2 \cdot 10^{+132}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+141}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 7: 69.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+132}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+36}:\\ \;\;\;\;b \cdot c - \left(t_1 + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(t_1 + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -2e+132)
     (- (* a (* -4.0 t)) (* j (* k 27.0)))
     (if (<= t_2 5e+36)
       (- (* b c) (+ t_1 (* 4.0 (* t a))))
       (- (* b c) (+ t_1 (* 27.0 (* j k))))))))

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 * (x * i);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -2e+132) {
		tmp = (a * (-4.0 * t)) - (j * (k * 27.0));
	} else if (t_2 <= 5e+36) {
		tmp = (b * c) - (t_1 + (4.0 * (t * a)));
	} else {
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	}
	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 * (x * i)
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-2d+132)) then
        tmp = (a * ((-4.0d0) * t)) - (j * (k * 27.0d0))
    else if (t_2 <= 5d+36) then
        tmp = (b * c) - (t_1 + (4.0d0 * (t * a)))
    else
        tmp = (b * c) - (t_1 + (27.0d0 * (j * k)))
    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 * (x * i);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -2e+132) {
		tmp = (a * (-4.0 * t)) - (j * (k * 27.0));
	} else if (t_2 <= 5e+36) {
		tmp = (b * c) - (t_1 + (4.0 * (t * a)));
	} else {
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -2e+132:
		tmp = (a * (-4.0 * t)) - (j * (k * 27.0))
	elif t_2 <= 5e+36:
		tmp = (b * c) - (t_1 + (4.0 * (t * a)))
	else:
		tmp = (b * c) - (t_1 + (27.0 * (j * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -2e+132)
		tmp = Float64(Float64(a * Float64(-4.0 * t)) - Float64(j * Float64(k * 27.0)));
	elseif (t_2 <= 5e+36)
		tmp = Float64(Float64(b * c) - Float64(t_1 + Float64(4.0 * Float64(t * a))));
	else
		tmp = Float64(Float64(b * c) - Float64(t_1 + Float64(27.0 * Float64(j * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -2e+132)
		tmp = (a * (-4.0 * t)) - (j * (k * 27.0));
	elseif (t_2 <= 5e+36)
		tmp = (b * c) - (t_1 + (4.0 * (t * a)));
	else
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	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[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+132], N[(N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+36], N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -1.99999999999999998e132

   1. Initial program 70.6%

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

      1. distribute-rgt-out-- 77.9%

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

      2. associate-*r* 77.9%

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

      3. add-cube-cbrt 77.9%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied egg-rr 77.9%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in a around inf 73.4%

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

      1. *-commutative 73.4%

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

      2. associate-*l* 73.4%

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

   6. Simplified 73.4%

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

   7. Taylor expanded in j around 0 75.8%

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

      1. associate-*r* 75.9%

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

   9. Simplified 75.9%

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

   if -1.99999999999999998e132 < (*.f64 (*.f64 j 27) k) < 4.99999999999999977e36

   1. Initial program 85.2%

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

   2. Taylor expanded in y around 0 77.0%

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

   3. Taylor expanded in j around 0 71.5%

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

   if 4.99999999999999977e36 < (*.f64 (*.f64 j 27) k)

   1. Initial program 80.9%

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

      1. sub-neg 80.9%

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

      2. associate-+l- 80.9%

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

      3. sub-neg 80.9%

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

      4. sub-neg 80.9%

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

      5. distribute-rgt-out-- 83.8%

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

      6. associate-*l* 89.6%

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

      7. distribute-lft-neg-in 89.6%

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

      8. cancel-sign-sub 89.6%

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

      9. associate-*l* 89.6%

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

      10. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in t around 0 84.2%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -2 \cdot 10^{+132}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+36}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]

Alternative 8: 79.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+133} \lor \neg \left(x \leq 1.6 \cdot 10^{+174}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(18 \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -1.3e+133) (not (<= x 1.6e+174)))
   (* x (- (* y (* 18.0 (* t z))) (* i 4.0)))
   (- (- (* b c) (+ (* 4.0 (* x i)) (* 4.0 (* t a)))) (* k (* j 27.0)))))

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 <= -1.3e+133) || !(x <= 1.6e+174)) {
		tmp = x * ((y * (18.0 * (t * z))) - (i * 4.0));
	} else {
		tmp = ((b * c) - ((4.0 * (x * i)) + (4.0 * (t * a)))) - (k * (j * 27.0));
	}
	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 <= (-1.3d+133)) .or. (.not. (x <= 1.6d+174))) then
        tmp = x * ((y * (18.0d0 * (t * z))) - (i * 4.0d0))
    else
        tmp = ((b * c) - ((4.0d0 * (x * i)) + (4.0d0 * (t * a)))) - (k * (j * 27.0d0))
    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 <= -1.3e+133) || !(x <= 1.6e+174)) {
		tmp = x * ((y * (18.0 * (t * z))) - (i * 4.0));
	} else {
		tmp = ((b * c) - ((4.0 * (x * i)) + (4.0 * (t * a)))) - (k * (j * 27.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -1.3e+133) or not (x <= 1.6e+174):
		tmp = x * ((y * (18.0 * (t * z))) - (i * 4.0))
	else:
		tmp = ((b * c) - ((4.0 * (x * i)) + (4.0 * (t * a)))) - (k * (j * 27.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -1.3e+133) || !(x <= 1.6e+174))
		tmp = Float64(x * Float64(Float64(y * Float64(18.0 * Float64(t * z))) - Float64(i * 4.0)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(4.0 * Float64(t * a)))) - Float64(k * Float64(j * 27.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -1.3e+133) || ~((x <= 1.6e+174)))
		tmp = x * ((y * (18.0 * (t * z))) - (i * 4.0));
	else
		tmp = ((b * c) - ((4.0 * (x * i)) + (4.0 * (t * a)))) - (k * (j * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -1.3e+133], N[Not[LessEqual[x, 1.6e+174]], $MachinePrecision]], N[(x * N[(N[(y * N[(18.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2999999999999999e133 or 1.6e174 < x

   1. Initial program 66.0%

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

      1. sub-neg 66.0%

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

      2. associate-+l- 66.0%

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

      3. sub-neg 66.0%

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

      4. sub-neg 66.0%

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

      5. distribute-rgt-out-- 70.7%

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

      6. associate-*l* 78.2%

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

      7. distribute-lft-neg-in 78.2%

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

      8. cancel-sign-sub 78.2%

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

      9. associate-*l* 78.2%

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

      10. associate-*l* 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in x around inf 81.6%

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

      1. pow1 81.6%

         \[\leadsto \left(\color{blue}{{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}^{1}} - 4 \cdot i\right) \cdot x \]

   6. Applied egg-rr 81.6%

      \[\leadsto \left(\color{blue}{{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}^{1}} - 4 \cdot i\right) \cdot x \]
   7. Step-by-step derivation

      1. unpow1 81.6%

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

      2. *-commutative 81.6%

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

      3. *-commutative 81.6%

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

      4. associate-*l* 81.7%

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

   8. Simplified 81.7%

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

   9. Taylor expanded in t around 0 81.6%

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

       1. *-commutative 81.6%

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

       2. associate-*l* 81.7%

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

   11. Simplified 81.7%

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

   if -1.2999999999999999e133 < x < 1.6e174

   1. Initial program 87.0%

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

   2. Taylor expanded in y around 0 87.3%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+133} \lor \neg \left(x \leq 1.6 \cdot 10^{+174}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(18 \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 9: 31.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-4 \cdot a\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -2.4 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -3.9 \cdot 10^{-231}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.25 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-57}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.65 \cdot 10^{+70}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 8 \cdot 10^{+119}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.85 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* -4.0 a))) (t_2 (* -27.0 (* j k))))
   (if (<= k -2.4e-93)
     t_2
     (if (<= k -3.9e-231)
       (* b c)
       (if (<= k 1.25e-132)
         t_1
         (if (<= k 6e-57)
           (* b c)
           (if (<= k 1.65e+70)
             (* 18.0 (* y (* t (* x z))))
             (if (<= k 8e+119)
               (* k (* j -27.0))
               (if (<= k 1.85e+143) 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 = t * (-4.0 * a);
	double t_2 = -27.0 * (j * k);
	double tmp;
	if (k <= -2.4e-93) {
		tmp = t_2;
	} else if (k <= -3.9e-231) {
		tmp = b * c;
	} else if (k <= 1.25e-132) {
		tmp = t_1;
	} else if (k <= 6e-57) {
		tmp = b * c;
	} else if (k <= 1.65e+70) {
		tmp = 18.0 * (y * (t * (x * z)));
	} else if (k <= 8e+119) {
		tmp = k * (j * -27.0);
	} else if (k <= 1.85e+143) {
		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 = t * ((-4.0d0) * a)
    t_2 = (-27.0d0) * (j * k)
    if (k <= (-2.4d-93)) then
        tmp = t_2
    else if (k <= (-3.9d-231)) then
        tmp = b * c
    else if (k <= 1.25d-132) then
        tmp = t_1
    else if (k <= 6d-57) then
        tmp = b * c
    else if (k <= 1.65d+70) then
        tmp = 18.0d0 * (y * (t * (x * z)))
    else if (k <= 8d+119) then
        tmp = k * (j * (-27.0d0))
    else if (k <= 1.85d+143) 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 = t * (-4.0 * a);
	double t_2 = -27.0 * (j * k);
	double tmp;
	if (k <= -2.4e-93) {
		tmp = t_2;
	} else if (k <= -3.9e-231) {
		tmp = b * c;
	} else if (k <= 1.25e-132) {
		tmp = t_1;
	} else if (k <= 6e-57) {
		tmp = b * c;
	} else if (k <= 1.65e+70) {
		tmp = 18.0 * (y * (t * (x * z)));
	} else if (k <= 8e+119) {
		tmp = k * (j * -27.0);
	} else if (k <= 1.85e+143) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (-4.0 * a)
	t_2 = -27.0 * (j * k)
	tmp = 0
	if k <= -2.4e-93:
		tmp = t_2
	elif k <= -3.9e-231:
		tmp = b * c
	elif k <= 1.25e-132:
		tmp = t_1
	elif k <= 6e-57:
		tmp = b * c
	elif k <= 1.65e+70:
		tmp = 18.0 * (y * (t * (x * z)))
	elif k <= 8e+119:
		tmp = k * (j * -27.0)
	elif k <= 1.85e+143:
		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(t * Float64(-4.0 * a))
	t_2 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (k <= -2.4e-93)
		tmp = t_2;
	elseif (k <= -3.9e-231)
		tmp = Float64(b * c);
	elseif (k <= 1.25e-132)
		tmp = t_1;
	elseif (k <= 6e-57)
		tmp = Float64(b * c);
	elseif (k <= 1.65e+70)
		tmp = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))));
	elseif (k <= 8e+119)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (k <= 1.85e+143)
		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 = t * (-4.0 * a);
	t_2 = -27.0 * (j * k);
	tmp = 0.0;
	if (k <= -2.4e-93)
		tmp = t_2;
	elseif (k <= -3.9e-231)
		tmp = b * c;
	elseif (k <= 1.25e-132)
		tmp = t_1;
	elseif (k <= 6e-57)
		tmp = b * c;
	elseif (k <= 1.65e+70)
		tmp = 18.0 * (y * (t * (x * z)));
	elseif (k <= 8e+119)
		tmp = k * (j * -27.0);
	elseif (k <= 1.85e+143)
		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[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2.4e-93], t$95$2, If[LessEqual[k, -3.9e-231], N[(b * c), $MachinePrecision], If[LessEqual[k, 1.25e-132], t$95$1, If[LessEqual[k, 6e-57], N[(b * c), $MachinePrecision], If[LessEqual[k, 1.65e+70], N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8e+119], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.85e+143], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -2.4000000000000001e-93 or 1.8500000000000001e143 < k

   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. +-commutative 80.3%

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

      3. associate-*l* 80.4%

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

      4. distribute-rgt-neg-in 80.4%

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

      5. fma-def 83.5%

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

      6. *-commutative 83.5%

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

      7. distribute-rgt-neg-in 83.5%

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

      8. metadata-eval 83.5%

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

      9. sub-neg 83.5%

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

      10. +-commutative 83.5%

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

      11. associate-*l* 83.5%

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

      12. distribute-rgt-neg-in 83.5%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in j around inf 48.8%

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

   if -2.4000000000000001e-93 < k < -3.8999999999999998e-231 or 1.25e-132 < k < 6.00000000000000001e-57

   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. Step-by-step derivation

      1. distribute-rgt-out-- 87.9%

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

      2. associate-*r* 90.5%

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

      3. add-cube-cbrt 90.4%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied egg-rr 90.4%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in i around 0 77.1%

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

   5. Taylor expanded in c around inf 40.8%

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

   if -3.8999999999999998e-231 < k < 1.25e-132 or 7.99999999999999955e119 < k < 1.8500000000000001e143

   1. Initial program 81.7%

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

      1. sub-neg 81.7%

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

      2. associate-+l- 81.7%

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

      3. sub-neg 81.7%

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

      4. sub-neg 81.7%

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

      5. distribute-rgt-out-- 81.7%

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

      6. associate-*l* 81.7%

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

      7. distribute-lft-neg-in 81.7%

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

      8. cancel-sign-sub 81.7%

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

      9. associate-*l* 81.7%

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

      10. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in t around inf 52.5%

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

   5. Taylor expanded in y around 0 41.9%

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

   if 6.00000000000000001e-57 < k < 1.65000000000000008e70

   1. Initial program 82.0%

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

      1. sub-neg 82.0%

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

      2. associate-+l- 82.0%

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

      3. sub-neg 82.0%

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

      4. sub-neg 82.0%

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

      5. distribute-rgt-out-- 82.0%

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

      6. associate-*l* 81.8%

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

      7. distribute-lft-neg-in 81.8%

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

      8. cancel-sign-sub 81.8%

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

      9. associate-*l* 81.8%

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

      10. associate-*l* 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in t around inf 41.4%

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

   5. Taylor expanded in y around inf 25.5%

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

   if 1.65000000000000008e70 < k < 7.99999999999999955e119

   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. distribute-rgt-out-- 85.5%

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

      2. associate-*r* 85.5%

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

      3. add-cube-cbrt 85.5%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied egg-rr 85.5%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in i around 0 57.4%

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

   5. Taylor expanded in j around inf 58.7%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 58.7%

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

      2. associate-*r* 58.7%

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

   7. Simplified 58.7%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.4 \cdot 10^{-93}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq -3.9 \cdot 10^{-231}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.25 \cdot 10^{-132}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-57}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.65 \cdot 10^{+70}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 8 \cdot 10^{+119}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.85 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 10: 44.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{if}\;j \leq -1.26 \cdot 10^{+159}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -5.6 \cdot 10^{-226}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{-173}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* x (* i 4.0)))))
   (if (<= j -1.26e+159)
     (* -27.0 (* j k))
     (if (<= j -5.6e-226)
       (+ (* b c) (* -4.0 (* t a)))
       (if (<= j 1.3e-256)
         t_1
         (if (<= j 5.4e-173)
           (* t (* -4.0 a))
           (if (<= j 9.5e+45) t_1 (* j (* k -27.0)))))))))

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 = (b * c) - (x * (i * 4.0));
	double tmp;
	if (j <= -1.26e+159) {
		tmp = -27.0 * (j * k);
	} else if (j <= -5.6e-226) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (j <= 1.3e-256) {
		tmp = t_1;
	} else if (j <= 5.4e-173) {
		tmp = t * (-4.0 * a);
	} else if (j <= 9.5e+45) {
		tmp = t_1;
	} else {
		tmp = j * (k * -27.0);
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (b * c) - (x * (i * 4.0d0))
    if (j <= (-1.26d+159)) then
        tmp = (-27.0d0) * (j * k)
    else if (j <= (-5.6d-226)) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (j <= 1.3d-256) then
        tmp = t_1
    else if (j <= 5.4d-173) then
        tmp = t * ((-4.0d0) * a)
    else if (j <= 9.5d+45) then
        tmp = t_1
    else
        tmp = j * (k * (-27.0d0))
    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 t_1 = (b * c) - (x * (i * 4.0));
	double tmp;
	if (j <= -1.26e+159) {
		tmp = -27.0 * (j * k);
	} else if (j <= -5.6e-226) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (j <= 1.3e-256) {
		tmp = t_1;
	} else if (j <= 5.4e-173) {
		tmp = t * (-4.0 * a);
	} else if (j <= 9.5e+45) {
		tmp = t_1;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (x * (i * 4.0))
	tmp = 0
	if j <= -1.26e+159:
		tmp = -27.0 * (j * k)
	elif j <= -5.6e-226:
		tmp = (b * c) + (-4.0 * (t * a))
	elif j <= 1.3e-256:
		tmp = t_1
	elif j <= 5.4e-173:
		tmp = t * (-4.0 * a)
	elif j <= 9.5e+45:
		tmp = t_1
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(x * Float64(i * 4.0)))
	tmp = 0.0
	if (j <= -1.26e+159)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (j <= -5.6e-226)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (j <= 1.3e-256)
		tmp = t_1;
	elseif (j <= 5.4e-173)
		tmp = Float64(t * Float64(-4.0 * a));
	elseif (j <= 9.5e+45)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (x * (i * 4.0));
	tmp = 0.0;
	if (j <= -1.26e+159)
		tmp = -27.0 * (j * k);
	elseif (j <= -5.6e-226)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (j <= 1.3e-256)
		tmp = t_1;
	elseif (j <= 5.4e-173)
		tmp = t * (-4.0 * a);
	elseif (j <= 9.5e+45)
		tmp = t_1;
	else
		tmp = j * (k * -27.0);
	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[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.26e+159], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.6e-226], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.3e-256], t$95$1, If[LessEqual[j, 5.4e-173], N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.5e+45], t$95$1, N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.2599999999999999e159

   1. Initial program 75.9%

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

      1. sub-neg 75.9%

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

      2. +-commutative 75.9%

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

      3. associate-*l* 79.0%

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

      4. distribute-rgt-neg-in 79.0%

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

      5. fma-def 82.0%

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

      6. *-commutative 82.0%

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

      7. distribute-rgt-neg-in 82.0%

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

      8. metadata-eval 82.0%

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

      9. sub-neg 82.0%

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

      10. +-commutative 82.0%

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

      11. associate-*l* 82.0%

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

      12. distribute-rgt-neg-in 82.0%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in j around inf 52.6%

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

   if -1.2599999999999999e159 < j < -5.60000000000000016e-226

   1. Initial program 90.1%

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

   2. Taylor expanded in y around 0 81.3%

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

   3. Taylor expanded in i around 0 72.8%

      \[\leadsto \color{blue}{c \cdot b - \left(27 \cdot \left(k \cdot j\right) + 4 \cdot \left(a \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. fma-neg 72.8%

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

      2. +-commutative 72.8%

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

      3. *-commutative 72.8%

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

      4. *-commutative 72.8%

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

      5. associate-*r* 72.8%

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

      6. distribute-neg-in 72.8%

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

      7. distribute-lft-neg-in 72.8%

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

      8. metadata-eval 72.8%

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

      9. *-commutative 72.8%

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

      10. *-commutative 72.8%

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

      11. associate-*l* 72.8%

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

      12. associate-*r* 72.8%

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

      13. distribute-rgt-neg-in 72.8%

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

      14. metadata-eval 72.8%

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

      15. *-commutative 72.8%

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

      16. associate-*l* 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in j around 0 49.5%

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

   if -5.60000000000000016e-226 < j < 1.3e-256 or 5.3999999999999999e-173 < j < 9.4999999999999998e45

   1. Initial program 81.8%

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

      1. sub-neg 81.8%

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

      2. associate-+l- 81.8%

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

      3. sub-neg 81.8%

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

      4. sub-neg 81.8%

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

      5. distribute-rgt-out-- 83.2%

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

      6. associate-*l* 83.0%

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

      7. distribute-lft-neg-in 83.0%

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

      8. cancel-sign-sub 83.0%

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

      9. associate-*l* 83.0%

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

      10. associate-*l* 83.0%

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

   3. Simplified 83.0%

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

   4. Taylor expanded in t around 0 68.6%

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

   5. Taylor expanded in i around inf 55.4%

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

      1. associate-*r* 55.4%

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

      2. *-commutative 55.4%

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

   7. Simplified 55.4%

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

   if 1.3e-256 < j < 5.3999999999999999e-173

   1. Initial program 82.3%

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

      1. sub-neg 82.3%

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

      2. associate-+l- 82.3%

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

      3. sub-neg 82.3%

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

      4. sub-neg 82.3%

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

      5. distribute-rgt-out-- 88.2%

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

      6. associate-*l* 87.9%

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

      7. distribute-lft-neg-in 87.9%

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

      8. cancel-sign-sub 87.9%

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

      9. associate-*l* 87.9%

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

      10. associate-*l* 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in t around inf 59.6%

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

   5. Taylor expanded in y around 0 42.7%

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

   if 9.4999999999999998e45 < j

   1. Initial program 75.2%

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

   2. Taylor expanded in y around 0 78.2%

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

   3. Taylor expanded in j around inf 47.9%

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

      1. *-commutative 47.9%

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

      2. *-commutative 47.9%

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

      3. associate-*l* 47.9%

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

   5. Simplified 47.9%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.26 \cdot 10^{+159}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -5.6 \cdot 10^{-226}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{-256}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{-173}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+45}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 11: 71.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(y \cdot \left(18 \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+87}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -9.5e+132)
   (* x (- (* y (* 18.0 (* t z))) (* i 4.0)))
   (if (<= x 1.95e+87)
     (- (- (* b c) (* 4.0 (* t a))) (* k (* j 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 <= -9.5e+132) {
		tmp = x * ((y * (18.0 * (t * z))) - (i * 4.0));
	} else if (x <= 1.95e+87) {
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 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 <= (-9.5d+132)) then
        tmp = x * ((y * (18.0d0 * (t * z))) - (i * 4.0d0))
    else if (x <= 1.95d+87) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - (k * (j * 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 <= -9.5e+132) {
		tmp = x * ((y * (18.0 * (t * z))) - (i * 4.0));
	} else if (x <= 1.95e+87) {
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 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 <= -9.5e+132:
		tmp = x * ((y * (18.0 * (t * z))) - (i * 4.0))
	elif x <= 1.95e+87:
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 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 <= -9.5e+132)
		tmp = Float64(x * Float64(Float64(y * Float64(18.0 * Float64(t * z))) - Float64(i * 4.0)));
	elseif (x <= 1.95e+87)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(k * Float64(j * 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 <= -9.5e+132)
		tmp = x * ((y * (18.0 * (t * z))) - (i * 4.0));
	elseif (x <= 1.95e+87)
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 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, -9.5e+132], N[(x * N[(N[(y * N[(18.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e+87], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $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 3 regimes

2. if x < -9.5000000000000005e132

   1. Initial program 70.1%

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

      1. sub-neg 70.1%

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

      2. associate-+l- 70.1%

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

      3. sub-neg 70.1%

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

      4. sub-neg 70.1%

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

      5. distribute-rgt-out-- 73.1%

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

      6. associate-*l* 82.0%

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

      7. distribute-lft-neg-in 82.0%

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

      8. cancel-sign-sub 82.0%

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

      9. associate-*l* 82.0%

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

      10. associate-*l* 82.0%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in x around inf 79.3%

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

      1. pow1 79.3%

         \[\leadsto \left(\color{blue}{{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}^{1}} - 4 \cdot i\right) \cdot x \]

   6. Applied egg-rr 79.3%

      \[\leadsto \left(\color{blue}{{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}^{1}} - 4 \cdot i\right) \cdot x \]
   7. Step-by-step derivation

      1. unpow1 79.3%

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

      2. *-commutative 79.3%

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

      3. *-commutative 79.3%

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

      4. associate-*l* 79.3%

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

   8. Simplified 79.3%

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

   9. Taylor expanded in t around 0 79.3%

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

       1. *-commutative 79.3%

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

       2. associate-*l* 79.4%

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

   11. Simplified 79.4%

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

   if -9.5000000000000005e132 < x < 1.9500000000000001e87

   1. Initial program 88.5%

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

   2. Taylor expanded in x around 0 81.5%

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

   if 1.9500000000000001e87 < x

   1. Initial program 65.7%

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

      1. sub-neg 65.7%

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

      2. associate-+l- 65.7%

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

      3. sub-neg 65.7%

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

      4. sub-neg 65.7%

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

      5. distribute-rgt-out-- 69.7%

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

      6. associate-*l* 77.5%

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

      7. distribute-lft-neg-in 77.5%

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

      8. cancel-sign-sub 77.5%

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

      9. associate-*l* 77.5%

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

      10. associate-*l* 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in x around inf 76.3%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(y \cdot \left(18 \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+87}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]

Alternative 12: 30.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-4 \cdot a\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -2.1 \cdot 10^{-98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -1.45 \cdot 10^{-230}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 4 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{-54}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{+120}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 2 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* -4.0 a))) (t_2 (* -27.0 (* j k))))
   (if (<= k -2.1e-98)
     t_2
     (if (<= k -1.45e-230)
       (* b c)
       (if (<= k 4e-135)
         t_1
         (if (<= k 1.22e-54)
           (* b c)
           (if (<= k 3.2e+120)
             (* k (* j -27.0))
             (if (<= k 2e+143) 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 = t * (-4.0 * a);
	double t_2 = -27.0 * (j * k);
	double tmp;
	if (k <= -2.1e-98) {
		tmp = t_2;
	} else if (k <= -1.45e-230) {
		tmp = b * c;
	} else if (k <= 4e-135) {
		tmp = t_1;
	} else if (k <= 1.22e-54) {
		tmp = b * c;
	} else if (k <= 3.2e+120) {
		tmp = k * (j * -27.0);
	} else if (k <= 2e+143) {
		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 = t * ((-4.0d0) * a)
    t_2 = (-27.0d0) * (j * k)
    if (k <= (-2.1d-98)) then
        tmp = t_2
    else if (k <= (-1.45d-230)) then
        tmp = b * c
    else if (k <= 4d-135) then
        tmp = t_1
    else if (k <= 1.22d-54) then
        tmp = b * c
    else if (k <= 3.2d+120) then
        tmp = k * (j * (-27.0d0))
    else if (k <= 2d+143) 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 = t * (-4.0 * a);
	double t_2 = -27.0 * (j * k);
	double tmp;
	if (k <= -2.1e-98) {
		tmp = t_2;
	} else if (k <= -1.45e-230) {
		tmp = b * c;
	} else if (k <= 4e-135) {
		tmp = t_1;
	} else if (k <= 1.22e-54) {
		tmp = b * c;
	} else if (k <= 3.2e+120) {
		tmp = k * (j * -27.0);
	} else if (k <= 2e+143) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (-4.0 * a)
	t_2 = -27.0 * (j * k)
	tmp = 0
	if k <= -2.1e-98:
		tmp = t_2
	elif k <= -1.45e-230:
		tmp = b * c
	elif k <= 4e-135:
		tmp = t_1
	elif k <= 1.22e-54:
		tmp = b * c
	elif k <= 3.2e+120:
		tmp = k * (j * -27.0)
	elif k <= 2e+143:
		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(t * Float64(-4.0 * a))
	t_2 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (k <= -2.1e-98)
		tmp = t_2;
	elseif (k <= -1.45e-230)
		tmp = Float64(b * c);
	elseif (k <= 4e-135)
		tmp = t_1;
	elseif (k <= 1.22e-54)
		tmp = Float64(b * c);
	elseif (k <= 3.2e+120)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (k <= 2e+143)
		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 = t * (-4.0 * a);
	t_2 = -27.0 * (j * k);
	tmp = 0.0;
	if (k <= -2.1e-98)
		tmp = t_2;
	elseif (k <= -1.45e-230)
		tmp = b * c;
	elseif (k <= 4e-135)
		tmp = t_1;
	elseif (k <= 1.22e-54)
		tmp = b * c;
	elseif (k <= 3.2e+120)
		tmp = k * (j * -27.0);
	elseif (k <= 2e+143)
		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[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2.1e-98], t$95$2, If[LessEqual[k, -1.45e-230], N[(b * c), $MachinePrecision], If[LessEqual[k, 4e-135], t$95$1, If[LessEqual[k, 1.22e-54], N[(b * c), $MachinePrecision], If[LessEqual[k, 3.2e+120], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2e+143], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -2.09999999999999992e-98 or 2e143 < k

   1. Initial program 79.9%

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

      1. sub-neg 79.9%

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

      2. +-commutative 79.9%

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

      3. associate-*l* 80.0%

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

      4. distribute-rgt-neg-in 80.0%

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

      5. fma-def 83.1%

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

      6. *-commutative 83.1%

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

      7. distribute-rgt-neg-in 83.1%

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

      8. metadata-eval 83.1%

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

      9. sub-neg 83.1%

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

      10. +-commutative 83.1%

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

      11. associate-*l* 83.1%

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

      12. distribute-rgt-neg-in 83.1%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in j around inf 48.0%

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

   if -2.09999999999999992e-98 < k < -1.45000000000000003e-230 or 4.0000000000000002e-135 < k < 1.22e-54

   1. Initial program 85.1%

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

      1. distribute-rgt-out-- 87.6%

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

      2. associate-*r* 90.3%

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

      3. add-cube-cbrt 90.2%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied egg-rr 90.2%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in i around 0 76.5%

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

   5. Taylor expanded in c around inf 41.8%

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

   if -1.45000000000000003e-230 < k < 4.0000000000000002e-135 or 3.19999999999999982e120 < k < 2e143

   1. Initial program 81.7%

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

      1. sub-neg 81.7%

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

      2. associate-+l- 81.7%

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

      3. sub-neg 81.7%

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

      4. sub-neg 81.7%

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

      5. distribute-rgt-out-- 81.7%

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

      6. associate-*l* 81.7%

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

      7. distribute-lft-neg-in 81.7%

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

      8. cancel-sign-sub 81.7%

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

      9. associate-*l* 81.7%

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

      10. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in t around inf 52.5%

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

   5. Taylor expanded in y around 0 41.9%

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

   if 1.22e-54 < k < 3.19999999999999982e120

   1. Initial program 85.7%

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

      1. distribute-rgt-out-- 85.7%

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

      2. associate-*r* 85.5%

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

      3. add-cube-cbrt 85.2%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied egg-rr 85.2%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in i around 0 68.7%

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

   5. Taylor expanded in j around inf 23.7%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 23.7%

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

      2. associate-*r* 23.7%

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

   7. Simplified 23.7%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.1 \cdot 10^{-98}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq -1.45 \cdot 10^{-230}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 4 \cdot 10^{-135}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{-54}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{+120}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 2 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 13: 46.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -5.1 \cdot 10^{+154}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{+60}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= j -5.1e+154)
   (* -27.0 (* j k))
   (if (<= j 1.16e+60) (+ (* b c) (* -4.0 (* t a))) (* j (* k -27.0)))))

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 (j <= -5.1e+154) {
		tmp = -27.0 * (j * k);
	} else if (j <= 1.16e+60) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = j * (k * -27.0);
	}
	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 (j <= (-5.1d+154)) then
        tmp = (-27.0d0) * (j * k)
    else if (j <= 1.16d+60) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else
        tmp = j * (k * (-27.0d0))
    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 (j <= -5.1e+154) {
		tmp = -27.0 * (j * k);
	} else if (j <= 1.16e+60) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if j <= -5.1e+154:
		tmp = -27.0 * (j * k)
	elif j <= 1.16e+60:
		tmp = (b * c) + (-4.0 * (t * a))
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (j <= -5.1e+154)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (j <= 1.16e+60)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (j <= -5.1e+154)
		tmp = -27.0 * (j * k);
	elseif (j <= 1.16e+60)
		tmp = (b * c) + (-4.0 * (t * a));
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[j, -5.1e+154], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.16e+60], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -5.0999999999999999e154

   1. Initial program 76.6%

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

      1. sub-neg 76.6%

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

      2. +-commutative 76.6%

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

      3. associate-*l* 79.6%

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

      4. distribute-rgt-neg-in 79.6%

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

      5. fma-def 82.5%

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

      6. *-commutative 82.5%

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

      7. distribute-rgt-neg-in 82.5%

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

      8. metadata-eval 82.5%

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

      9. sub-neg 82.5%

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

      10. +-commutative 82.5%

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

      11. associate-*l* 82.5%

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

      12. distribute-rgt-neg-in 82.5%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in j around inf 54.0%

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

   if -5.0999999999999999e154 < j < 1.15999999999999996e60

   1. Initial program 85.7%

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

   2. Taylor expanded in y around 0 81.2%

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

   3. Taylor expanded in i around 0 66.4%

      \[\leadsto \color{blue}{c \cdot b - \left(27 \cdot \left(k \cdot j\right) + 4 \cdot \left(a \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. fma-neg 66.4%

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

      2. +-commutative 66.4%

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

      3. *-commutative 66.4%

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

      4. *-commutative 66.4%

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

      5. associate-*r* 66.4%

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

      6. distribute-neg-in 66.4%

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

      7. distribute-lft-neg-in 66.4%

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

      8. metadata-eval 66.4%

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

      9. *-commutative 66.4%

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

      10. *-commutative 66.4%

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

      11. associate-*l* 66.4%

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

      12. associate-*r* 66.4%

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

      13. distribute-rgt-neg-in 66.4%

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

      14. metadata-eval 66.4%

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

      15. *-commutative 66.4%

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

      16. associate-*l* 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in j around 0 50.1%

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

   if 1.15999999999999996e60 < j

   1. Initial program 74.4%

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

   2. Taylor expanded in y around 0 77.7%

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

   3. Taylor expanded in j around inf 49.4%

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

      1. *-commutative 49.4%

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

      2. *-commutative 49.4%

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

      3. associate-*l* 49.4%

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

   5. Simplified 49.4%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.1 \cdot 10^{+154}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{+60}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 14: 31.7% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -4.25 \cdot 10^{-98} \lor \neg \left(k \leq 1.35 \cdot 10^{-55}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= k -4.25e-98) (not (<= k 1.35e-55))) (* -27.0 (* j k)) (* 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 <= -4.25e-98) || !(k <= 1.35e-55)) {
		tmp = -27.0 * (j * k);
	} 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 <= (-4.25d-98)) .or. (.not. (k <= 1.35d-55))) then
        tmp = (-27.0d0) * (j * k)
    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 <= -4.25e-98) || !(k <= 1.35e-55)) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (k <= -4.25e-98) or not (k <= 1.35e-55):
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((k <= -4.25e-98) || !(k <= 1.35e-55))
		tmp = Float64(-27.0 * Float64(j * k));
	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 <= -4.25e-98) || ~((k <= 1.35e-55)))
		tmp = -27.0 * (j * k);
	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, -4.25e-98], N[Not[LessEqual[k, 1.35e-55]], $MachinePrecision]], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -4.2499999999999999e-98 or 1.35000000000000002e-55 < k

   1. Initial program 80.0%

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

      1. sub-neg 80.0%

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

      2. +-commutative 80.0%

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

      3. associate-*l* 80.1%

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

      4. distribute-rgt-neg-in 80.1%

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

      5. fma-def 82.5%

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

      6. *-commutative 82.5%

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

      7. distribute-rgt-neg-in 82.5%

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

      8. metadata-eval 82.5%

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

      9. sub-neg 82.5%

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

      10. +-commutative 82.5%

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

      11. associate-*l* 82.5%

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

      12. distribute-rgt-neg-in 82.5%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in j around inf 42.6%

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

   if -4.2499999999999999e-98 < k < 1.35000000000000002e-55

   1. Initial program 84.9%

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

      1. distribute-rgt-out-- 86.0%

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

      2. associate-*r* 87.1%

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

      3. add-cube-cbrt 86.8%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied egg-rr 86.8%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in i around 0 68.1%

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

   5. Taylor expanded in c around inf 28.2%

      \[\leadsto \color{blue}{c \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -4.25 \cdot 10^{-98} \lor \neg \left(k \leq 1.35 \cdot 10^{-55}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 15: 23.0% 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 81.7%

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

   1. distribute-rgt-out-- 84.5%

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

   2. associate-*r* 85.6%

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

   3. add-cube-cbrt 85.4%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

3. Applied egg-rr 85.4%

   \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)} \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}\right) \cdot \sqrt[3]{t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)}} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

4. Taylor expanded in i around 0 75.9%

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

5. Taylor expanded in c around inf 22.5%

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

6. Final simplification 22.5%

   \[\leadsto b \cdot c \]

Developer target: 88.9% 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 2023200 
(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)))