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

Percentage Accurate: 84.7% → 91.4%

Time: 26.1s

Alternatives: 21

Speedup: 1.0×

• 49.8% 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: 84.7% 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: 91.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.7%

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

   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%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in x around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. cancel-sign-sub-inv 77.8%

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

      3. metadata-eval 77.8%

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

      4. associate-*r* 78.0%

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

      5. *-commutative 78.0%

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

   6. Simplified 78.0%

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

4. Final simplification 95.4%

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

Alternative 2: 87.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+171}:\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -7.8e+171)
   (-
    (- (+ (* b c) (* 18.0 (* y (* t (* x z))))) (* 4.0 (* t a)))
    (* (* j 27.0) k))
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* 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) {
	double tmp;
	if (y <= -7.8e+171) {
		tmp = (((b * c) + (18.0 * (y * (t * (x * z))))) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * 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) :: tmp
    if (y <= (-7.8d+171)) then
        tmp = (((b * c) + (18.0d0 * (y * (t * (x * z))))) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    else
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * 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 tmp;
	if (y <= -7.8e+171) {
		tmp = (((b * c) + (18.0 * (y * (t * (x * z))))) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if y <= -7.8e+171:
		tmp = (((b * c) + (18.0 * (y * (t * (x * z))))) - (4.0 * (t * a))) - ((j * 27.0) * k)
	else:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -7.8e+171)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(y * Float64(t * Float64(x * z))))) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (y <= -7.8e+171)
		tmp = (((b * c) + (18.0 * (y * (t * (x * z))))) - (4.0 * (t * a))) - ((j * 27.0) * k);
	else
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -7.8e+171], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.8e171

   1. Initial program 74.5%

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

   2. Taylor expanded in i around 0 90.2%

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

   if -7.8e171 < y

   1. Initial program 92.0%

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

   3. Simplified 93.3%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+171}:\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]

Alternative 3: 83.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-91} \lor \neg \left(t \leq 6.8 \cdot 10^{-76}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.8e-91) (not (<= t 6.8e-76)))
   (- (+ (* b c) (* t (+ (* 18.0 (* y (* x z))) (* a -4.0)))) (* 27.0 (* j k)))
   (-
    (+ (* b c) (* 18.0 (* y (* t (* x z)))))
    (+ (* 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) {
	double tmp;
	if ((t <= -1.8e-91) || !(t <= 6.8e-76)) {
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - (27.0 * (j * k));
	} else {
		tmp = ((b * c) + (18.0 * (y * (t * (x * z))))) - ((x * (4.0 * i)) + (j * (27.0 * 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) :: tmp
    if ((t <= (-1.8d-91)) .or. (.not. (t <= 6.8d-76))) then
        tmp = ((b * c) + (t * ((18.0d0 * (y * (x * z))) + (a * (-4.0d0))))) - (27.0d0 * (j * k))
    else
        tmp = ((b * c) + (18.0d0 * (y * (t * (x * z))))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * 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 tmp;
	if ((t <= -1.8e-91) || !(t <= 6.8e-76)) {
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - (27.0 * (j * k));
	} else {
		tmp = ((b * c) + (18.0 * (y * (t * (x * z))))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.8e-91) or not (t <= 6.8e-76):
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - (27.0 * (j * k))
	else:
		tmp = ((b * c) + (18.0 * (y * (t * (x * z))))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.8e-91) || !(t <= 6.8e-76))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) + Float64(a * -4.0)))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(y * Float64(t * Float64(x * z))))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -1.8e-91) || ~((t <= 6.8e-76)))
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - (27.0 * (j * k));
	else
		tmp = ((b * c) + (18.0 * (y * (t * (x * z))))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.8e-91], N[Not[LessEqual[t, 6.8e-76]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8e-91 or 6.7999999999999998e-76 < t

   1. Initial program 92.3%

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

      1. associate--l- 92.3%

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

      2. associate-+l- 92.3%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in i around 0 89.9%

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

   if -1.8e-91 < t < 6.7999999999999998e-76

   1. Initial program 86.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in a around 0 87.2%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-91} \lor \neg \left(t \leq 6.8 \cdot 10^{-76}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]

Alternative 4: 74.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := \left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_2\\ t_4 := b \cdot c + t_1\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{-5}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-94}:\\ \;\;\;\;\left(18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - t_2\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-61}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-26}:\\ \;\;\;\;t_1 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+103}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (+ (* 18.0 (* y (* x z))) (* a -4.0))))
        (t_2 (* (* j 27.0) k))
        (t_3 (- (- (* b c) (* 4.0 (* x i))) t_2))
        (t_4 (+ (* b c) t_1)))
   (if (<= t -2.9e-5)
     t_4
     (if (<= t -8.4e-94)
       (- (- (* 18.0 (* y (* t (* x z)))) (* 4.0 (* t a))) t_2)
       (if (<= t 1.5e-61)
         t_3
         (if (<= t 4.9e-26)
           (- t_1 (* 27.0 (* j k)))
           (if (<= t 1.15e+103) t_3 t_4)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	double t_2 = (j * 27.0) * k;
	double t_3 = ((b * c) - (4.0 * (x * i))) - t_2;
	double t_4 = (b * c) + t_1;
	double tmp;
	if (t <= -2.9e-5) {
		tmp = t_4;
	} else if (t <= -8.4e-94) {
		tmp = ((18.0 * (y * (t * (x * z)))) - (4.0 * (t * a))) - t_2;
	} else if (t <= 1.5e-61) {
		tmp = t_3;
	} else if (t <= 4.9e-26) {
		tmp = t_1 - (27.0 * (j * k));
	} else if (t <= 1.15e+103) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = t * ((18.0d0 * (y * (x * z))) + (a * (-4.0d0)))
    t_2 = (j * 27.0d0) * k
    t_3 = ((b * c) - (4.0d0 * (x * i))) - t_2
    t_4 = (b * c) + t_1
    if (t <= (-2.9d-5)) then
        tmp = t_4
    else if (t <= (-8.4d-94)) then
        tmp = ((18.0d0 * (y * (t * (x * z)))) - (4.0d0 * (t * a))) - t_2
    else if (t <= 1.5d-61) then
        tmp = t_3
    else if (t <= 4.9d-26) then
        tmp = t_1 - (27.0d0 * (j * k))
    else if (t <= 1.15d+103) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	double t_2 = (j * 27.0) * k;
	double t_3 = ((b * c) - (4.0 * (x * i))) - t_2;
	double t_4 = (b * c) + t_1;
	double tmp;
	if (t <= -2.9e-5) {
		tmp = t_4;
	} else if (t <= -8.4e-94) {
		tmp = ((18.0 * (y * (t * (x * z)))) - (4.0 * (t * a))) - t_2;
	} else if (t <= 1.5e-61) {
		tmp = t_3;
	} else if (t <= 4.9e-26) {
		tmp = t_1 - (27.0 * (j * k));
	} else if (t <= 1.15e+103) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((18.0 * (y * (x * z))) + (a * -4.0))
	t_2 = (j * 27.0) * k
	t_3 = ((b * c) - (4.0 * (x * i))) - t_2
	t_4 = (b * c) + t_1
	tmp = 0
	if t <= -2.9e-5:
		tmp = t_4
	elif t <= -8.4e-94:
		tmp = ((18.0 * (y * (t * (x * z)))) - (4.0 * (t * a))) - t_2
	elif t <= 1.5e-61:
		tmp = t_3
	elif t <= 4.9e-26:
		tmp = t_1 - (27.0 * (j * k))
	elif t <= 1.15e+103:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) + Float64(a * -4.0)))
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_2)
	t_4 = Float64(Float64(b * c) + t_1)
	tmp = 0.0
	if (t <= -2.9e-5)
		tmp = t_4;
	elseif (t <= -8.4e-94)
		tmp = Float64(Float64(Float64(18.0 * Float64(y * Float64(t * Float64(x * z)))) - Float64(4.0 * Float64(t * a))) - t_2);
	elseif (t <= 1.5e-61)
		tmp = t_3;
	elseif (t <= 4.9e-26)
		tmp = Float64(t_1 - Float64(27.0 * Float64(j * k)));
	elseif (t <= 1.15e+103)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	t_2 = (j * 27.0) * k;
	t_3 = ((b * c) - (4.0 * (x * i))) - t_2;
	t_4 = (b * c) + t_1;
	tmp = 0.0;
	if (t <= -2.9e-5)
		tmp = t_4;
	elseif (t <= -8.4e-94)
		tmp = ((18.0 * (y * (t * (x * z)))) - (4.0 * (t * a))) - t_2;
	elseif (t <= 1.5e-61)
		tmp = t_3;
	elseif (t <= 4.9e-26)
		tmp = t_1 - (27.0 * (j * k));
	elseif (t <= 1.15e+103)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t, -2.9e-5], t$95$4, If[LessEqual[t, -8.4e-94], N[(N[(N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t, 1.5e-61], t$95$3, If[LessEqual[t, 4.9e-26], N[(t$95$1 - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+103], t$95$3, t$95$4]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.9e-5 or 1.15000000000000004e103 < t

   1. Initial program 90.7%

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

      1. associate--l- 90.7%

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

      2. associate-+l- 90.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in i around 0 92.0%

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

   5. Taylor expanded in k around 0 86.0%

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

   if -2.9e-5 < t < -8.4000000000000004e-94

   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 i around 0 84.9%

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

   3. Taylor expanded in c around 0 84.7%

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

   if -8.4000000000000004e-94 < t < 1.50000000000000006e-61 or 4.8999999999999999e-26 < t < 1.15000000000000004e103

   1. Initial program 89.2%

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

   2. Taylor expanded in t around 0 85.6%

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

   if 1.50000000000000006e-61 < t < 4.8999999999999999e-26

   1. Initial program 100.0%

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

      1. associate--l- 100.0%

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

      2. associate-+l- 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in i around 0 100.0%

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

   5. Taylor expanded in c around 0 99.1%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) + -4 \cdot a\right) \cdot t - 27 \cdot \left(k \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-5}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-94}:\\ \;\;\;\;\left(18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-61}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+103}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 5: 82.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-95} \lor \neg \left(t \leq 6 \cdot 10^{-76}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -7.8e-95) (not (<= t 6e-76)))
   (- (+ (* b c) (* t (+ (* 18.0 (* y (* x z))) (* a -4.0)))) (* 27.0 (* j k)))
   (- (- (* b c) (* 4.0 (* x 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) {
	double tmp;
	if ((t <= -7.8e-95) || !(t <= 6e-76)) {
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - (27.0 * (j * k));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * 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) :: tmp
    if ((t <= (-7.8d-95)) .or. (.not. (t <= 6d-76))) then
        tmp = ((b * c) + (t * ((18.0d0 * (y * (x * z))) + (a * (-4.0d0))))) - (27.0d0 * (j * k))
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - ((j * 27.0d0) * 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 tmp;
	if ((t <= -7.8e-95) || !(t <= 6e-76)) {
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - (27.0 * (j * k));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -7.8e-95) or not (t <= 6e-76):
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - (27.0 * (j * k))
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -7.8e-95) || !(t <= 6e-76))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) + Float64(a * -4.0)))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -7.8e-95) || ~((t <= 6e-76)))
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - (27.0 * (j * k));
	else
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -7.8e-95], N[Not[LessEqual[t, 6e-76]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.8e-95 or 6.00000000000000048e-76 < t

   1. Initial program 92.3%

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

      1. associate--l- 92.3%

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

      2. associate-+l- 92.3%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in i around 0 89.9%

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

   if -7.8e-95 < t < 6.00000000000000048e-76

   1. Initial program 86.2%

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

   2. Taylor expanded in t around 0 86.3%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-95} \lor \neg \left(t \leq 6 \cdot 10^{-76}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 6: 69.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{+89}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+55}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+128} \lor \neg \left(x \leq 10^{+194}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))))
   (if (<= x -4.5e+208)
     t_1
     (if (<= x -4.9e+89)
       (- (* 18.0 (* y (* t (* x z)))) (* 27.0 (* j k)))
       (if (<= x -5.5e+45)
         t_1
         (if (<= x 8.5e+55)
           (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))
           (if (or (<= x 4.5e+128) (not (<= x 1e+194)))
             t_1
             (+ (* k (* j -27.0)) (* -4.0 (* x i))))))))))

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 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -4.5e+208) {
		tmp = t_1;
	} else if (x <= -4.9e+89) {
		tmp = (18.0 * (y * (t * (x * z)))) - (27.0 * (j * k));
	} else if (x <= -5.5e+45) {
		tmp = t_1;
	} else if (x <= 8.5e+55) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if ((x <= 4.5e+128) || !(x <= 1e+194)) {
		tmp = t_1;
	} else {
		tmp = (k * (j * -27.0)) + (-4.0 * (x * i));
	}
	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 = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    if (x <= (-4.5d+208)) then
        tmp = t_1
    else if (x <= (-4.9d+89)) then
        tmp = (18.0d0 * (y * (t * (x * z)))) - (27.0d0 * (j * k))
    else if (x <= (-5.5d+45)) then
        tmp = t_1
    else if (x <= 8.5d+55) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    else if ((x <= 4.5d+128) .or. (.not. (x <= 1d+194))) then
        tmp = t_1
    else
        tmp = (k * (j * (-27.0d0))) + ((-4.0d0) * (x * i))
    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 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -4.5e+208) {
		tmp = t_1;
	} else if (x <= -4.9e+89) {
		tmp = (18.0 * (y * (t * (x * z)))) - (27.0 * (j * k));
	} else if (x <= -5.5e+45) {
		tmp = t_1;
	} else if (x <= 8.5e+55) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if ((x <= 4.5e+128) || !(x <= 1e+194)) {
		tmp = t_1;
	} else {
		tmp = (k * (j * -27.0)) + (-4.0 * (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	tmp = 0
	if x <= -4.5e+208:
		tmp = t_1
	elif x <= -4.9e+89:
		tmp = (18.0 * (y * (t * (x * z)))) - (27.0 * (j * k))
	elif x <= -5.5e+45:
		tmp = t_1
	elif x <= 8.5e+55:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	elif (x <= 4.5e+128) or not (x <= 1e+194):
		tmp = t_1
	else:
		tmp = (k * (j * -27.0)) + (-4.0 * (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)))
	tmp = 0.0
	if (x <= -4.5e+208)
		tmp = t_1;
	elseif (x <= -4.9e+89)
		tmp = Float64(Float64(18.0 * Float64(y * Float64(t * Float64(x * z)))) - Float64(27.0 * Float64(j * k)));
	elseif (x <= -5.5e+45)
		tmp = t_1;
	elseif (x <= 8.5e+55)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	elseif ((x <= 4.5e+128) || !(x <= 1e+194))
		tmp = t_1;
	else
		tmp = Float64(Float64(k * Float64(j * -27.0)) + Float64(-4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	tmp = 0.0;
	if (x <= -4.5e+208)
		tmp = t_1;
	elseif (x <= -4.9e+89)
		tmp = (18.0 * (y * (t * (x * z)))) - (27.0 * (j * k));
	elseif (x <= -5.5e+45)
		tmp = t_1;
	elseif (x <= 8.5e+55)
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	elseif ((x <= 4.5e+128) || ~((x <= 1e+194)))
		tmp = t_1;
	else
		tmp = (k * (j * -27.0)) + (-4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+208], t$95$1, If[LessEqual[x, -4.9e+89], N[(N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.5e+45], t$95$1, If[LessEqual[x, 8.5e+55], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 4.5e+128], N[Not[LessEqual[x, 1e+194]], $MachinePrecision]], t$95$1, N[(N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.50000000000000015e208 or -4.89999999999999996e89 < x < -5.5000000000000001e45 or 8.50000000000000002e55 < x < 4.5000000000000001e128 or 9.99999999999999945e193 < x

   1. Initial program 74.4%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in x around inf 80.7%

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

      1. *-commutative 80.7%

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

      2. cancel-sign-sub-inv 80.7%

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

      3. metadata-eval 80.7%

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

      4. associate-*r* 78.0%

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

      5. *-commutative 78.0%

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

   6. Simplified 78.0%

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

   if -4.50000000000000015e208 < x < -4.89999999999999996e89

   1. Initial program 89.0%

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

      1. associate--l- 89.0%

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

      2. associate-+l- 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in i around 0 82.3%

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

   5. Taylor expanded in c around 0 78.6%

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

   6. Taylor expanded in a around 0 71.6%

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

   if -5.5000000000000001e45 < x < 8.50000000000000002e55

   1. Initial program 96.6%

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

   2. Taylor expanded in x around 0 79.6%

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

   if 4.5000000000000001e128 < x < 9.99999999999999945e193

   1. Initial program 94.4%

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

   2. Taylor expanded in t around 0 89.3%

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

   3. Taylor expanded in c around 0 73.0%

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

      1. distribute-lft-in 73.0%

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

      2. *-commutative 73.0%

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

      3. neg-mul-1 73.0%

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

      4. neg-mul-1 73.0%

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

      5. distribute-lft-neg-in 73.0%

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

      6. metadata-eval 73.0%

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

      7. distribute-lft-neg-in 73.0%

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

      8. metadata-eval 73.0%

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

      9. *-commutative 73.0%

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

      10. associate-*r* 73.0%

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

   5. Simplified 73.0%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+208}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{+89}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+55}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+128} \lor \neg \left(x \leq 10^{+194}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 7: 68.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \mathbf{if}\;x \leq -7 \cdot 10^{+177}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+71}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq -5.8:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 0.0115:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+237}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)) (t_2 (- (- (* b c) (* 4.0 (* x i))) t_1)))
   (if (<= x -7e+177)
     t_2
     (if (<= x -1.05e+71)
       (- (* 18.0 (* y (* t (* x z)))) (* 27.0 (* j k)))
       (if (<= x -5.8)
         t_2
         (if (<= x 0.0115)
           (- (- (* b c) (* 4.0 (* t a))) t_1)
           (if (<= x 3.15e+237)
             t_2
             (* x (+ (* 18.0 (* z (* y t))) (* i -4.0))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = ((b * c) - (4.0 * (x * i))) - t_1;
	double tmp;
	if (x <= -7e+177) {
		tmp = t_2;
	} else if (x <= -1.05e+71) {
		tmp = (18.0 * (y * (t * (x * z)))) - (27.0 * (j * k));
	} else if (x <= -5.8) {
		tmp = t_2;
	} else if (x <= 0.0115) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 3.15e+237) {
		tmp = t_2;
	} else {
		tmp = x * ((18.0 * (z * (y * t))) + (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = ((b * c) - (4.0d0 * (x * i))) - t_1
    if (x <= (-7d+177)) then
        tmp = t_2
    else if (x <= (-1.05d+71)) then
        tmp = (18.0d0 * (y * (t * (x * z)))) - (27.0d0 * (j * k))
    else if (x <= (-5.8d0)) then
        tmp = t_2
    else if (x <= 0.0115d0) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if (x <= 3.15d+237) then
        tmp = t_2
    else
        tmp = x * ((18.0d0 * (z * (y * t))) + (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 t_1 = (j * 27.0) * k;
	double t_2 = ((b * c) - (4.0 * (x * i))) - t_1;
	double tmp;
	if (x <= -7e+177) {
		tmp = t_2;
	} else if (x <= -1.05e+71) {
		tmp = (18.0 * (y * (t * (x * z)))) - (27.0 * (j * k));
	} else if (x <= -5.8) {
		tmp = t_2;
	} else if (x <= 0.0115) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 3.15e+237) {
		tmp = t_2;
	} else {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = ((b * c) - (4.0 * (x * i))) - t_1
	tmp = 0
	if x <= -7e+177:
		tmp = t_2
	elif x <= -1.05e+71:
		tmp = (18.0 * (y * (t * (x * z)))) - (27.0 * (j * k))
	elif x <= -5.8:
		tmp = t_2
	elif x <= 0.0115:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif x <= 3.15e+237:
		tmp = t_2
	else:
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1)
	tmp = 0.0
	if (x <= -7e+177)
		tmp = t_2;
	elseif (x <= -1.05e+71)
		tmp = Float64(Float64(18.0 * Float64(y * Float64(t * Float64(x * z)))) - Float64(27.0 * Float64(j * k)));
	elseif (x <= -5.8)
		tmp = t_2;
	elseif (x <= 0.0115)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (x <= 3.15e+237)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = ((b * c) - (4.0 * (x * i))) - t_1;
	tmp = 0.0;
	if (x <= -7e+177)
		tmp = t_2;
	elseif (x <= -1.05e+71)
		tmp = (18.0 * (y * (t * (x * z)))) - (27.0 * (j * k));
	elseif (x <= -5.8)
		tmp = t_2;
	elseif (x <= 0.0115)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif (x <= 3.15e+237)
		tmp = t_2;
	else
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[x, -7e+177], t$95$2, If[LessEqual[x, -1.05e+71], N[(N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.8], t$95$2, If[LessEqual[x, 0.0115], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 3.15e+237], t$95$2, N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.99999999999999983e177 or -1.04999999999999995e71 < x < -5.79999999999999982 or 0.0115 < x < 3.15000000000000004e237

   1. Initial program 88.3%

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

   2. Taylor expanded in t around 0 74.8%

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

   if -6.99999999999999983e177 < x < -1.04999999999999995e71

   1. Initial program 85.9%

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

      1. associate--l- 85.9%

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

      2. associate-+l- 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in i around 0 86.8%

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

   5. Taylor expanded in c around 0 91.3%

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

   6. Taylor expanded in a around 0 91.0%

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

   if -5.79999999999999982 < x < 0.0115

   1. Initial program 96.9%

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

   2. Taylor expanded in x around 0 82.7%

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

   if 3.15000000000000004e237 < x

   1. Initial program 50.0%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in x around inf 93.8%

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

      1. *-commutative 93.8%

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

      2. cancel-sign-sub-inv 93.8%

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

      3. metadata-eval 93.8%

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

      4. associate-*r* 94.0%

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

      5. *-commutative 94.0%

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

   6. Simplified 94.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+177}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+71}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq -5.8:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 0.0115:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+237}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \]

Alternative 8: 68.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \mathbf{if}\;x \leq -2.45 \cdot 10^{+178}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+70}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;x \leq -1.6:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 0.01:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+237}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)) (t_2 (- (- (* b c) (* 4.0 (* x i))) t_1)))
   (if (<= x -2.45e+178)
     t_2
     (if (<= x -8e+70)
       (- (* 18.0 (* y (* t (* x z)))) (* j (* 27.0 k)))
       (if (<= x -1.6)
         t_2
         (if (<= x 0.01)
           (- (- (* b c) (* 4.0 (* t a))) t_1)
           (if (<= x 3.6e+237)
             t_2
             (* x (+ (* 18.0 (* z (* y t))) (* i -4.0))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = ((b * c) - (4.0 * (x * i))) - t_1;
	double tmp;
	if (x <= -2.45e+178) {
		tmp = t_2;
	} else if (x <= -8e+70) {
		tmp = (18.0 * (y * (t * (x * z)))) - (j * (27.0 * k));
	} else if (x <= -1.6) {
		tmp = t_2;
	} else if (x <= 0.01) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 3.6e+237) {
		tmp = t_2;
	} else {
		tmp = x * ((18.0 * (z * (y * t))) + (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = ((b * c) - (4.0d0 * (x * i))) - t_1
    if (x <= (-2.45d+178)) then
        tmp = t_2
    else if (x <= (-8d+70)) then
        tmp = (18.0d0 * (y * (t * (x * z)))) - (j * (27.0d0 * k))
    else if (x <= (-1.6d0)) then
        tmp = t_2
    else if (x <= 0.01d0) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if (x <= 3.6d+237) then
        tmp = t_2
    else
        tmp = x * ((18.0d0 * (z * (y * t))) + (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 t_1 = (j * 27.0) * k;
	double t_2 = ((b * c) - (4.0 * (x * i))) - t_1;
	double tmp;
	if (x <= -2.45e+178) {
		tmp = t_2;
	} else if (x <= -8e+70) {
		tmp = (18.0 * (y * (t * (x * z)))) - (j * (27.0 * k));
	} else if (x <= -1.6) {
		tmp = t_2;
	} else if (x <= 0.01) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 3.6e+237) {
		tmp = t_2;
	} else {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = ((b * c) - (4.0 * (x * i))) - t_1
	tmp = 0
	if x <= -2.45e+178:
		tmp = t_2
	elif x <= -8e+70:
		tmp = (18.0 * (y * (t * (x * z)))) - (j * (27.0 * k))
	elif x <= -1.6:
		tmp = t_2
	elif x <= 0.01:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif x <= 3.6e+237:
		tmp = t_2
	else:
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1)
	tmp = 0.0
	if (x <= -2.45e+178)
		tmp = t_2;
	elseif (x <= -8e+70)
		tmp = Float64(Float64(18.0 * Float64(y * Float64(t * Float64(x * z)))) - Float64(j * Float64(27.0 * k)));
	elseif (x <= -1.6)
		tmp = t_2;
	elseif (x <= 0.01)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (x <= 3.6e+237)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = ((b * c) - (4.0 * (x * i))) - t_1;
	tmp = 0.0;
	if (x <= -2.45e+178)
		tmp = t_2;
	elseif (x <= -8e+70)
		tmp = (18.0 * (y * (t * (x * z)))) - (j * (27.0 * k));
	elseif (x <= -1.6)
		tmp = t_2;
	elseif (x <= 0.01)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif (x <= 3.6e+237)
		tmp = t_2;
	else
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[x, -2.45e+178], t$95$2, If[LessEqual[x, -8e+70], N[(N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.6], t$95$2, If[LessEqual[x, 0.01], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 3.6e+237], t$95$2, N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.4500000000000001e178 or -8.00000000000000058e70 < x < -1.6000000000000001 or 0.0100000000000000002 < x < 3.60000000000000015e237

   1. Initial program 88.3%

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

   2. Taylor expanded in t around 0 74.8%

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

   if -2.4500000000000001e178 < x < -8.00000000000000058e70

   1. Initial program 85.9%

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

      1. associate--l- 85.9%

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

      2. associate-+l- 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in i around 0 86.8%

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

   5. Taylor expanded in c around 0 91.3%

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

   6. Taylor expanded in a around 0 91.0%

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

      1. sub-neg 91.0%

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

      2. associate-*r* 91.0%

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

      3. *-commutative 91.0%

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

   8. Applied egg-rr 91.0%

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

   if -1.6000000000000001 < x < 0.0100000000000000002

   1. Initial program 96.9%

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

   2. Taylor expanded in x around 0 82.7%

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

   if 3.60000000000000015e237 < x

   1. Initial program 50.0%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in x around inf 93.8%

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

      1. *-commutative 93.8%

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

      2. cancel-sign-sub-inv 93.8%

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

      3. metadata-eval 93.8%

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

      4. associate-*r* 94.0%

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

      5. *-commutative 94.0%

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

   6. Simplified 94.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+178}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+70}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;x \leq -1.6:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 0.01:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+237}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \]

Alternative 9: 75.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ t_3 := b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{-7}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-25}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (- (- (* b c) (* 4.0 (* x i))) t_1))
        (t_3 (+ (* b c) (* t (+ (* 18.0 (* y (* x z))) (* a -4.0))))))
   (if (<= t -3.2e-7)
     t_3
     (if (<= t 6.8e-76)
       t_2
       (if (<= t 1.1e-25)
         (- (- (* b c) (* 4.0 (* t a))) t_1)
         (if (<= t 1.85e+102) t_2 t_3))))))

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 = (j * 27.0) * k;
	double t_2 = ((b * c) - (4.0 * (x * i))) - t_1;
	double t_3 = (b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)));
	double tmp;
	if (t <= -3.2e-7) {
		tmp = t_3;
	} else if (t <= 6.8e-76) {
		tmp = t_2;
	} else if (t <= 1.1e-25) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (t <= 1.85e+102) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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 = (j * 27.0d0) * k
    t_2 = ((b * c) - (4.0d0 * (x * i))) - t_1
    t_3 = (b * c) + (t * ((18.0d0 * (y * (x * z))) + (a * (-4.0d0))))
    if (t <= (-3.2d-7)) then
        tmp = t_3
    else if (t <= 6.8d-76) then
        tmp = t_2
    else if (t <= 1.1d-25) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if (t <= 1.85d+102) then
        tmp = t_2
    else
        tmp = t_3
    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 = (j * 27.0) * k;
	double t_2 = ((b * c) - (4.0 * (x * i))) - t_1;
	double t_3 = (b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)));
	double tmp;
	if (t <= -3.2e-7) {
		tmp = t_3;
	} else if (t <= 6.8e-76) {
		tmp = t_2;
	} else if (t <= 1.1e-25) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (t <= 1.85e+102) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = ((b * c) - (4.0 * (x * i))) - t_1
	t_3 = (b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))
	tmp = 0
	if t <= -3.2e-7:
		tmp = t_3
	elif t <= 6.8e-76:
		tmp = t_2
	elif t <= 1.1e-25:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif t <= 1.85e+102:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1)
	t_3 = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) + Float64(a * -4.0))))
	tmp = 0.0
	if (t <= -3.2e-7)
		tmp = t_3;
	elseif (t <= 6.8e-76)
		tmp = t_2;
	elseif (t <= 1.1e-25)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (t <= 1.85e+102)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = ((b * c) - (4.0 * (x * i))) - t_1;
	t_3 = (b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)));
	tmp = 0.0;
	if (t <= -3.2e-7)
		tmp = t_3;
	elseif (t <= 6.8e-76)
		tmp = t_2;
	elseif (t <= 1.1e-25)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif (t <= 1.85e+102)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e-7], t$95$3, If[LessEqual[t, 6.8e-76], t$95$2, If[LessEqual[t, 1.1e-25], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 1.85e+102], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.2000000000000001e-7 or 1.85000000000000011e102 < t

   1. Initial program 90.9%

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

      1. associate--l- 90.9%

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

      2. associate-+l- 90.9%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in i around 0 92.2%

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

   5. Taylor expanded in k around 0 86.3%

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

   if -3.2000000000000001e-7 < t < 6.7999999999999998e-76 or 1.1000000000000001e-25 < t < 1.85000000000000011e102

   1. Initial program 88.3%

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

   2. Taylor expanded in t around 0 81.8%

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

   if 6.7999999999999998e-76 < t < 1.1000000000000001e-25

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 85.0%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-7}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-76}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-25}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+102}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 10: 75.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ t_2 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_3 := b \cdot c + t_2\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{-7}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-21}:\\ \;\;\;\;t_2 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (- (* b c) (* 4.0 (* x i))) (* (* j 27.0) k)))
        (t_2 (* t (+ (* 18.0 (* y (* x z))) (* a -4.0))))
        (t_3 (+ (* b c) t_2)))
   (if (<= t -2.4e-7)
     t_3
     (if (<= t 1.46e-61)
       t_1
       (if (<= t 4.8e-21)
         (- t_2 (* 27.0 (* j k)))
         (if (<= t 1.85e+102) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	double t_2 = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	double t_3 = (b * c) + t_2;
	double tmp;
	if (t <= -2.4e-7) {
		tmp = t_3;
	} else if (t <= 1.46e-61) {
		tmp = t_1;
	} else if (t <= 4.8e-21) {
		tmp = t_2 - (27.0 * (j * k));
	} else if (t <= 1.85e+102) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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 = ((b * c) - (4.0d0 * (x * i))) - ((j * 27.0d0) * k)
    t_2 = t * ((18.0d0 * (y * (x * z))) + (a * (-4.0d0)))
    t_3 = (b * c) + t_2
    if (t <= (-2.4d-7)) then
        tmp = t_3
    else if (t <= 1.46d-61) then
        tmp = t_1
    else if (t <= 4.8d-21) then
        tmp = t_2 - (27.0d0 * (j * k))
    else if (t <= 1.85d+102) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	double t_2 = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	double t_3 = (b * c) + t_2;
	double tmp;
	if (t <= -2.4e-7) {
		tmp = t_3;
	} else if (t <= 1.46e-61) {
		tmp = t_1;
	} else if (t <= 4.8e-21) {
		tmp = t_2 - (27.0 * (j * k));
	} else if (t <= 1.85e+102) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k)
	t_2 = t * ((18.0 * (y * (x * z))) + (a * -4.0))
	t_3 = (b * c) + t_2
	tmp = 0
	if t <= -2.4e-7:
		tmp = t_3
	elif t <= 1.46e-61:
		tmp = t_1
	elif t <= 4.8e-21:
		tmp = t_2 - (27.0 * (j * k))
	elif t <= 1.85e+102:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(Float64(j * 27.0) * k))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) + Float64(a * -4.0)))
	t_3 = Float64(Float64(b * c) + t_2)
	tmp = 0.0
	if (t <= -2.4e-7)
		tmp = t_3;
	elseif (t <= 1.46e-61)
		tmp = t_1;
	elseif (t <= 4.8e-21)
		tmp = Float64(t_2 - Float64(27.0 * Float64(j * k)));
	elseif (t <= 1.85e+102)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	t_2 = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	t_3 = (b * c) + t_2;
	tmp = 0.0;
	if (t <= -2.4e-7)
		tmp = t_3;
	elseif (t <= 1.46e-61)
		tmp = t_1;
	elseif (t <= 4.8e-21)
		tmp = t_2 - (27.0 * (j * k));
	elseif (t <= 1.85e+102)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t, -2.4e-7], t$95$3, If[LessEqual[t, 1.46e-61], t$95$1, If[LessEqual[t, 4.8e-21], N[(t$95$2 - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e+102], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.39999999999999979e-7 or 1.85000000000000011e102 < t

   1. Initial program 90.9%

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

      1. associate--l- 90.9%

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

      2. associate-+l- 90.9%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in i around 0 92.2%

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

   5. Taylor expanded in k around 0 86.3%

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

   if -2.39999999999999979e-7 < t < 1.46e-61 or 4.7999999999999999e-21 < t < 1.85000000000000011e102

   1. Initial program 88.6%

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

   2. Taylor expanded in t around 0 82.2%

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

   if 1.46e-61 < t < 4.7999999999999999e-21

   1. Initial program 100.0%

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

      1. associate--l- 100.0%

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

      2. associate-+l- 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in i around 0 100.0%

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

   5. Taylor expanded in c around 0 99.1%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) + -4 \cdot a\right) \cdot t - 27 \cdot \left(k \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-7}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{-61}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+102}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 11: 32.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-118}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-212}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-167}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+114}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (* 18.0 (* y (* t (* x z))))))
   (if (<= z -4.2e+59)
     t_2
     (if (<= z -3.5e-118)
       (* k (* j -27.0))
       (if (<= z -2.25e-212)
         t_2
         (if (<= z 2.6e-299)
           t_1
           (if (<= z 1.56e-167)
             (* t (* a -4.0))
             (if (<= z 2.9e-64)
               t_1
               (if (<= z 9.2e+114)
                 (* b c)
                 (* (* 18.0 y) (* x (* z t))))))))))))

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 = j * (k * -27.0);
	double t_2 = 18.0 * (y * (t * (x * z)));
	double tmp;
	if (z <= -4.2e+59) {
		tmp = t_2;
	} else if (z <= -3.5e-118) {
		tmp = k * (j * -27.0);
	} else if (z <= -2.25e-212) {
		tmp = t_2;
	} else if (z <= 2.6e-299) {
		tmp = t_1;
	} else if (z <= 1.56e-167) {
		tmp = t * (a * -4.0);
	} else if (z <= 2.9e-64) {
		tmp = t_1;
	} else if (z <= 9.2e+114) {
		tmp = b * c;
	} else {
		tmp = (18.0 * y) * (x * (z * t));
	}
	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 = j * (k * (-27.0d0))
    t_2 = 18.0d0 * (y * (t * (x * z)))
    if (z <= (-4.2d+59)) then
        tmp = t_2
    else if (z <= (-3.5d-118)) then
        tmp = k * (j * (-27.0d0))
    else if (z <= (-2.25d-212)) then
        tmp = t_2
    else if (z <= 2.6d-299) then
        tmp = t_1
    else if (z <= 1.56d-167) then
        tmp = t * (a * (-4.0d0))
    else if (z <= 2.9d-64) then
        tmp = t_1
    else if (z <= 9.2d+114) then
        tmp = b * c
    else
        tmp = (18.0d0 * y) * (x * (z * t))
    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 = j * (k * -27.0);
	double t_2 = 18.0 * (y * (t * (x * z)));
	double tmp;
	if (z <= -4.2e+59) {
		tmp = t_2;
	} else if (z <= -3.5e-118) {
		tmp = k * (j * -27.0);
	} else if (z <= -2.25e-212) {
		tmp = t_2;
	} else if (z <= 2.6e-299) {
		tmp = t_1;
	} else if (z <= 1.56e-167) {
		tmp = t * (a * -4.0);
	} else if (z <= 2.9e-64) {
		tmp = t_1;
	} else if (z <= 9.2e+114) {
		tmp = b * c;
	} else {
		tmp = (18.0 * y) * (x * (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = 18.0 * (y * (t * (x * z)))
	tmp = 0
	if z <= -4.2e+59:
		tmp = t_2
	elif z <= -3.5e-118:
		tmp = k * (j * -27.0)
	elif z <= -2.25e-212:
		tmp = t_2
	elif z <= 2.6e-299:
		tmp = t_1
	elif z <= 1.56e-167:
		tmp = t * (a * -4.0)
	elif z <= 2.9e-64:
		tmp = t_1
	elif z <= 9.2e+114:
		tmp = b * c
	else:
		tmp = (18.0 * y) * (x * (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))))
	tmp = 0.0
	if (z <= -4.2e+59)
		tmp = t_2;
	elseif (z <= -3.5e-118)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (z <= -2.25e-212)
		tmp = t_2;
	elseif (z <= 2.6e-299)
		tmp = t_1;
	elseif (z <= 1.56e-167)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (z <= 2.9e-64)
		tmp = t_1;
	elseif (z <= 9.2e+114)
		tmp = Float64(b * c);
	else
		tmp = Float64(Float64(18.0 * y) * Float64(x * Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = 18.0 * (y * (t * (x * z)));
	tmp = 0.0;
	if (z <= -4.2e+59)
		tmp = t_2;
	elseif (z <= -3.5e-118)
		tmp = k * (j * -27.0);
	elseif (z <= -2.25e-212)
		tmp = t_2;
	elseif (z <= 2.6e-299)
		tmp = t_1;
	elseif (z <= 1.56e-167)
		tmp = t * (a * -4.0);
	elseif (z <= 2.9e-64)
		tmp = t_1;
	elseif (z <= 9.2e+114)
		tmp = b * c;
	else
		tmp = (18.0 * y) * (x * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+59], t$95$2, If[LessEqual[z, -3.5e-118], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.25e-212], t$95$2, If[LessEqual[z, 2.6e-299], t$95$1, If[LessEqual[z, 1.56e-167], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-64], t$95$1, If[LessEqual[z, 9.2e+114], N[(b * c), $MachinePrecision], N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -4.19999999999999968e59 or -3.5e-118 < z < -2.2499999999999999e-212

   1. Initial program 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in y around inf 40.5%

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

   if -4.19999999999999968e59 < z < -3.5e-118

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in j around inf 36.5%

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

      1. *-commutative 36.5%

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

      2. associate-*l* 36.5%

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

   6. Simplified 36.5%

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

   if -2.2499999999999999e-212 < z < 2.5999999999999999e-299 or 1.56000000000000005e-167 < z < 2.8999999999999999e-64

   1. Initial program 95.7%

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

   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 j around inf 28.8%

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

      1. *-commutative 28.8%

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

      2. *-commutative 28.8%

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

      3. associate-*l* 28.8%

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

   6. Simplified 28.8%

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

   if 2.5999999999999999e-299 < z < 1.56000000000000005e-167

   1. Initial program 86.0%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 33.2%

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

      1. *-commutative 33.2%

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

      2. *-commutative 33.2%

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

      3. associate-*r* 33.2%

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

   6. Simplified 33.2%

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

   if 2.8999999999999999e-64 < z < 9.2000000000000001e114

   1. Initial program 93.1%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in b around inf 25.3%

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

   if 9.2000000000000001e114 < z

   1. Initial program 79.4%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in a around 0 63.1%

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

   5. Taylor expanded in y around inf 53.3%

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

      1. associate-*r* 53.4%

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

      2. associate-*r* 58.3%

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

   7. Simplified 58.3%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+59}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-118}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-212}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-299}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-167}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-64}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+114}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 12: 50.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;i \leq -4.8 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-76}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;i \leq 540000000000:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* k (* j -27.0)) (* -4.0 (* x i)))))
   (if (<= i -4.8e+69)
     t_1
     (if (<= i 1.7e-76)
       (- (* b c) (* 27.0 (* j k)))
       (if (<= i 1.7e-42)
         (* t (* a -4.0))
         (if (<= i 540000000000.0) (* (* 18.0 y) (* x (* z t))) 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)) + (-4.0 * (x * i));
	double tmp;
	if (i <= -4.8e+69) {
		tmp = t_1;
	} else if (i <= 1.7e-76) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (i <= 1.7e-42) {
		tmp = t * (a * -4.0);
	} else if (i <= 540000000000.0) {
		tmp = (18.0 * y) * (x * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (k * (j * (-27.0d0))) + ((-4.0d0) * (x * i))
    if (i <= (-4.8d+69)) then
        tmp = t_1
    else if (i <= 1.7d-76) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (i <= 1.7d-42) then
        tmp = t * (a * (-4.0d0))
    else if (i <= 540000000000.0d0) then
        tmp = (18.0d0 * y) * (x * (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (k * (j * -27.0)) + (-4.0 * (x * i));
	double tmp;
	if (i <= -4.8e+69) {
		tmp = t_1;
	} else if (i <= 1.7e-76) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (i <= 1.7e-42) {
		tmp = t * (a * -4.0);
	} else if (i <= 540000000000.0) {
		tmp = (18.0 * y) * (x * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (k * (j * -27.0)) + (-4.0 * (x * i))
	tmp = 0
	if i <= -4.8e+69:
		tmp = t_1
	elif i <= 1.7e-76:
		tmp = (b * c) - (27.0 * (j * k))
	elif i <= 1.7e-42:
		tmp = t * (a * -4.0)
	elif i <= 540000000000.0:
		tmp = (18.0 * y) * (x * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(k * Float64(j * -27.0)) + Float64(-4.0 * Float64(x * i)))
	tmp = 0.0
	if (i <= -4.8e+69)
		tmp = t_1;
	elseif (i <= 1.7e-76)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (i <= 1.7e-42)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (i <= 540000000000.0)
		tmp = Float64(Float64(18.0 * y) * Float64(x * Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (k * (j * -27.0)) + (-4.0 * (x * i));
	tmp = 0.0;
	if (i <= -4.8e+69)
		tmp = t_1;
	elseif (i <= 1.7e-76)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (i <= 1.7e-42)
		tmp = t * (a * -4.0);
	elseif (i <= 540000000000.0)
		tmp = (18.0 * y) * (x * (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.8e+69], t$95$1, If[LessEqual[i, 1.7e-76], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.7e-42], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 540000000000.0], N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -4.8000000000000003e69 or 5.4e11 < i

   1. Initial program 87.7%

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

   2. Taylor expanded in t around 0 66.3%

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

   3. Taylor expanded in c around 0 58.3%

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

      1. distribute-lft-in 58.3%

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

      2. *-commutative 58.3%

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

      3. neg-mul-1 58.3%

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

      4. neg-mul-1 58.3%

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

      5. distribute-lft-neg-in 58.3%

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

      6. metadata-eval 58.3%

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

      7. distribute-lft-neg-in 58.3%

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

      8. metadata-eval 58.3%

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

      9. *-commutative 58.3%

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

      10. associate-*r* 58.3%

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

   5. Simplified 58.3%

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

   if -4.8000000000000003e69 < i < 1.7e-76

   1. Initial program 91.8%

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

      1. associate--l- 91.8%

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

      2. associate-+l- 91.8%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in i around 0 90.1%

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

   5. Taylor expanded in t around 0 63.9%

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

   if 1.7e-76 < i < 1.70000000000000011e-42

   1. Initial program 100.0%

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

   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 a around inf 75.4%

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

      1. *-commutative 75.4%

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

      2. *-commutative 75.4%

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

      3. associate-*r* 75.4%

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

   6. Simplified 75.4%

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

   if 1.70000000000000011e-42 < i < 5.4e11

   1. Initial program 81.9%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in a around 0 69.5%

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

   5. Taylor expanded in y around inf 39.7%

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

      1. associate-*r* 39.7%

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

      2. associate-*r* 39.7%

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

   7. Simplified 39.7%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.8 \cdot 10^{+69}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-76}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;i \leq 540000000000:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 13: 58.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-133}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+105}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (+ (* 18.0 (* y (* x z))) (* a -4.0)))))
   (if (<= t -1.4e-7)
     t_1
     (if (<= t 4.8e-133)
       (+ (* k (* j -27.0)) (* -4.0 (* x i)))
       (if (<= t 2.7e+105) (- (* b c) (* 27.0 (* j k))) 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 = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	double tmp;
	if (t <= -1.4e-7) {
		tmp = t_1;
	} else if (t <= 4.8e-133) {
		tmp = (k * (j * -27.0)) + (-4.0 * (x * i));
	} else if (t <= 2.7e+105) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((18.0d0 * (y * (x * z))) + (a * (-4.0d0)))
    if (t <= (-1.4d-7)) then
        tmp = t_1
    else if (t <= 4.8d-133) then
        tmp = (k * (j * (-27.0d0))) + ((-4.0d0) * (x * i))
    else if (t <= 2.7d+105) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	double tmp;
	if (t <= -1.4e-7) {
		tmp = t_1;
	} else if (t <= 4.8e-133) {
		tmp = (k * (j * -27.0)) + (-4.0 * (x * i));
	} else if (t <= 2.7e+105) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((18.0 * (y * (x * z))) + (a * -4.0))
	tmp = 0
	if t <= -1.4e-7:
		tmp = t_1
	elif t <= 4.8e-133:
		tmp = (k * (j * -27.0)) + (-4.0 * (x * i))
	elif t <= 2.7e+105:
		tmp = (b * c) - (27.0 * (j * k))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) + Float64(a * -4.0)))
	tmp = 0.0
	if (t <= -1.4e-7)
		tmp = t_1;
	elseif (t <= 4.8e-133)
		tmp = Float64(Float64(k * Float64(j * -27.0)) + Float64(-4.0 * Float64(x * i)));
	elseif (t <= 2.7e+105)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	tmp = 0.0;
	if (t <= -1.4e-7)
		tmp = t_1;
	elseif (t <= 4.8e-133)
		tmp = (k * (j * -27.0)) + (-4.0 * (x * i));
	elseif (t <= 2.7e+105)
		tmp = (b * c) - (27.0 * (j * k));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e-7], t$95$1, If[LessEqual[t, 4.8e-133], N[(N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+105], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4000000000000001e-7 or 2.70000000000000016e105 < t

   1. Initial program 90.9%

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

      1. associate--l- 90.9%

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

      2. associate-+l- 90.9%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in t around inf 71.6%

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

   if -1.4000000000000001e-7 < t < 4.8e-133

   1. Initial program 85.0%

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

   2. Taylor expanded in t around 0 81.4%

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

   3. Taylor expanded in c around 0 62.7%

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

      1. distribute-lft-in 62.7%

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

      2. *-commutative 62.7%

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

      3. neg-mul-1 62.7%

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

      4. neg-mul-1 62.7%

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

      5. distribute-lft-neg-in 62.7%

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

      6. metadata-eval 62.7%

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

      7. distribute-lft-neg-in 62.7%

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

      8. metadata-eval 62.7%

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

      9. *-commutative 62.7%

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

      10. associate-*r* 62.7%

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

   5. Simplified 62.7%

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

   if 4.8e-133 < t < 2.70000000000000016e105

   1. Initial program 98.0%

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

      1. associate--l- 98.0%

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

      2. associate-+l- 98.0%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in i around 0 83.0%

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

   5. Taylor expanded in t around 0 59.0%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-133}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+105}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 14: 44.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;i \leq -3.2 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-76}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;i \leq 2.05 \cdot 10^{+14}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= i -3.2e+192)
     t_1
     (if (<= i 1.7e-76)
       (- (* b c) (* 27.0 (* j k)))
       (if (<= i 2.5e-43)
         (* t (* a -4.0))
         (if (<= i 2.05e+14) (* (* 18.0 y) (* x (* z t))) 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 = -4.0 * (x * i);
	double tmp;
	if (i <= -3.2e+192) {
		tmp = t_1;
	} else if (i <= 1.7e-76) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (i <= 2.5e-43) {
		tmp = t * (a * -4.0);
	} else if (i <= 2.05e+14) {
		tmp = (18.0 * y) * (x * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (x * i)
    if (i <= (-3.2d+192)) then
        tmp = t_1
    else if (i <= 1.7d-76) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (i <= 2.5d-43) then
        tmp = t * (a * (-4.0d0))
    else if (i <= 2.05d+14) then
        tmp = (18.0d0 * y) * (x * (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (i <= -3.2e+192) {
		tmp = t_1;
	} else if (i <= 1.7e-76) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (i <= 2.5e-43) {
		tmp = t * (a * -4.0);
	} else if (i <= 2.05e+14) {
		tmp = (18.0 * y) * (x * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	tmp = 0
	if i <= -3.2e+192:
		tmp = t_1
	elif i <= 1.7e-76:
		tmp = (b * c) - (27.0 * (j * k))
	elif i <= 2.5e-43:
		tmp = t * (a * -4.0)
	elif i <= 2.05e+14:
		tmp = (18.0 * y) * (x * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (i <= -3.2e+192)
		tmp = t_1;
	elseif (i <= 1.7e-76)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (i <= 2.5e-43)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (i <= 2.05e+14)
		tmp = Float64(Float64(18.0 * y) * Float64(x * Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	tmp = 0.0;
	if (i <= -3.2e+192)
		tmp = t_1;
	elseif (i <= 1.7e-76)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (i <= 2.5e-43)
		tmp = t * (a * -4.0);
	elseif (i <= 2.05e+14)
		tmp = (18.0 * y) * (x * (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.2e+192], t$95$1, If[LessEqual[i, 1.7e-76], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.5e-43], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.05e+14], N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -3.20000000000000023e192 or 2.05e14 < i

   1. Initial program 86.8%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in i around inf 51.3%

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

      1. *-commutative 51.3%

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

      2. *-commutative 51.3%

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

   6. Simplified 51.3%

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

   if -3.20000000000000023e192 < i < 1.7e-76

   1. Initial program 91.7%

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

      1. associate--l- 91.7%

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

      2. associate-+l- 91.7%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in i around 0 89.0%

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

   5. Taylor expanded in t around 0 60.2%

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

   if 1.7e-76 < i < 2.50000000000000009e-43

   1. Initial program 100.0%

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

   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 a around inf 75.4%

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

      1. *-commutative 75.4%

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

      2. *-commutative 75.4%

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

      3. associate-*r* 75.4%

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

   6. Simplified 75.4%

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

   if 2.50000000000000009e-43 < i < 2.05e14

   1. Initial program 81.9%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in a around 0 69.5%

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

   5. Taylor expanded in y around inf 39.7%

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

      1. associate-*r* 39.7%

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

      2. associate-*r* 39.7%

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

   7. Simplified 39.7%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.2 \cdot 10^{+192}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-76}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;i \leq 2.05 \cdot 10^{+14}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 15: 59.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-28} \lor \neg \left(x \leq 6.8 \cdot 10^{+55}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -1.25e-28) (not (<= x 6.8e+55)))
   (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))
   (- (* b c) (* 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 tmp;
	if ((x <= -1.25e-28) || !(x <= 6.8e+55)) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else {
		tmp = (b * c) - (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) :: tmp
    if ((x <= (-1.25d-28)) .or. (.not. (x <= 6.8d+55))) then
        tmp = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    else
        tmp = (b * c) - (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 tmp;
	if ((x <= -1.25e-28) || !(x <= 6.8e+55)) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -1.25e-28) or not (x <= 6.8e+55):
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	else:
		tmp = (b * c) - (27.0 * (j * k))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -1.25e-28) || !(x <= 6.8e+55))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)));
	else
		tmp = Float64(Float64(b * c) - 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)
	tmp = 0.0;
	if ((x <= -1.25e-28) || ~((x <= 6.8e+55)))
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	else
		tmp = (b * c) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -1.25e-28], N[Not[LessEqual[x, 6.8e+55]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25e-28 or 6.7999999999999996e55 < x

   1. Initial program 83.7%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in x around inf 63.3%

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

      1. *-commutative 63.3%

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

      2. cancel-sign-sub-inv 63.3%

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

      3. metadata-eval 63.3%

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

      4. associate-*r* 62.6%

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

      5. *-commutative 62.6%

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

   6. Simplified 62.6%

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

   if -1.25e-28 < x < 6.7999999999999996e55

   1. Initial program 96.1%

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

      1. associate--l- 96.1%

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

      2. associate-+l- 96.1%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in i around 0 92.5%

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

   5. Taylor expanded in t around 0 56.3%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-28} \lor \neg \left(x \leq 6.8 \cdot 10^{+55}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 16: 31.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;i \leq -8.8 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-115}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;i \leq -3 \cdot 10^{-235}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;i \leq 1.08 \cdot 10^{-83}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= i -8.8e+53)
     t_1
     (if (<= i -5.2e-115)
       (* k (* j -27.0))
       (if (<= i -3e-235)
         (* b c)
         (if (<= i 1.08e-83)
           (* (* j k) -27.0)
           (if (<= i 2.5e+106) (* t (* a -4.0)) 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 = -4.0 * (x * i);
	double tmp;
	if (i <= -8.8e+53) {
		tmp = t_1;
	} else if (i <= -5.2e-115) {
		tmp = k * (j * -27.0);
	} else if (i <= -3e-235) {
		tmp = b * c;
	} else if (i <= 1.08e-83) {
		tmp = (j * k) * -27.0;
	} else if (i <= 2.5e+106) {
		tmp = t * (a * -4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (x * i)
    if (i <= (-8.8d+53)) then
        tmp = t_1
    else if (i <= (-5.2d-115)) then
        tmp = k * (j * (-27.0d0))
    else if (i <= (-3d-235)) then
        tmp = b * c
    else if (i <= 1.08d-83) then
        tmp = (j * k) * (-27.0d0)
    else if (i <= 2.5d+106) then
        tmp = t * (a * (-4.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (i <= -8.8e+53) {
		tmp = t_1;
	} else if (i <= -5.2e-115) {
		tmp = k * (j * -27.0);
	} else if (i <= -3e-235) {
		tmp = b * c;
	} else if (i <= 1.08e-83) {
		tmp = (j * k) * -27.0;
	} else if (i <= 2.5e+106) {
		tmp = t * (a * -4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	tmp = 0
	if i <= -8.8e+53:
		tmp = t_1
	elif i <= -5.2e-115:
		tmp = k * (j * -27.0)
	elif i <= -3e-235:
		tmp = b * c
	elif i <= 1.08e-83:
		tmp = (j * k) * -27.0
	elif i <= 2.5e+106:
		tmp = t * (a * -4.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (i <= -8.8e+53)
		tmp = t_1;
	elseif (i <= -5.2e-115)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (i <= -3e-235)
		tmp = Float64(b * c);
	elseif (i <= 1.08e-83)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (i <= 2.5e+106)
		tmp = Float64(t * Float64(a * -4.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	tmp = 0.0;
	if (i <= -8.8e+53)
		tmp = t_1;
	elseif (i <= -5.2e-115)
		tmp = k * (j * -27.0);
	elseif (i <= -3e-235)
		tmp = b * c;
	elseif (i <= 1.08e-83)
		tmp = (j * k) * -27.0;
	elseif (i <= 2.5e+106)
		tmp = t * (a * -4.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8.8e+53], t$95$1, If[LessEqual[i, -5.2e-115], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3e-235], N[(b * c), $MachinePrecision], If[LessEqual[i, 1.08e-83], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[i, 2.5e+106], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -8.79999999999999994e53 or 2.4999999999999999e106 < i

   1. Initial program 89.3%

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

   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 i around inf 48.9%

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

      1. *-commutative 48.9%

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

      2. *-commutative 48.9%

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

   6. Simplified 48.9%

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

   if -8.79999999999999994e53 < i < -5.20000000000000008e-115

   1. Initial program 90.8%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in j around inf 36.7%

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

      1. *-commutative 36.7%

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

      2. associate-*l* 36.7%

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

   6. Simplified 36.7%

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

   if -5.20000000000000008e-115 < i < -2.9999999999999999e-235

   1. Initial program 91.1%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in b around inf 51.5%

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

   if -2.9999999999999999e-235 < i < 1.08e-83

   1. Initial program 92.5%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in j around inf 38.6%

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

      1. *-commutative 38.6%

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

   6. Simplified 38.6%

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

   if 1.08e-83 < i < 2.4999999999999999e106

   1. Initial program 86.0%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in a around inf 39.4%

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

      1. *-commutative 39.4%

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

      2. *-commutative 39.4%

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

      3. associate-*r* 39.4%

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

   6. Simplified 39.4%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.8 \cdot 10^{+53}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-115}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;i \leq -3 \cdot 10^{-235}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;i \leq 1.08 \cdot 10^{-83}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 17: 31.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.6 \cdot 10^{+15}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-182}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{+197}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= c -6.6e+15)
   (* b c)
   (if (<= c 3.4e-182)
     (* k (* j -27.0))
     (if (<= c 4.3e+197) (* 18.0 (* y (* t (* x z)))) (* 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 (c <= -6.6e+15) {
		tmp = b * c;
	} else if (c <= 3.4e-182) {
		tmp = k * (j * -27.0);
	} else if (c <= 4.3e+197) {
		tmp = 18.0 * (y * (t * (x * z)));
	} 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 (c <= (-6.6d+15)) then
        tmp = b * c
    else if (c <= 3.4d-182) then
        tmp = k * (j * (-27.0d0))
    else if (c <= 4.3d+197) then
        tmp = 18.0d0 * (y * (t * (x * z)))
    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 (c <= -6.6e+15) {
		tmp = b * c;
	} else if (c <= 3.4e-182) {
		tmp = k * (j * -27.0);
	} else if (c <= 4.3e+197) {
		tmp = 18.0 * (y * (t * (x * z)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if c <= -6.6e+15:
		tmp = b * c
	elif c <= 3.4e-182:
		tmp = k * (j * -27.0)
	elif c <= 4.3e+197:
		tmp = 18.0 * (y * (t * (x * z)))
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (c <= -6.6e+15)
		tmp = Float64(b * c);
	elseif (c <= 3.4e-182)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (c <= 4.3e+197)
		tmp = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))));
	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 (c <= -6.6e+15)
		tmp = b * c;
	elseif (c <= 3.4e-182)
		tmp = k * (j * -27.0);
	elseif (c <= 4.3e+197)
		tmp = 18.0 * (y * (t * (x * z)));
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[c, -6.6e+15], N[(b * c), $MachinePrecision], If[LessEqual[c, 3.4e-182], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.3e+197], N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.6e15 or 4.29999999999999996e197 < c

   1. Initial program 91.0%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in b around inf 42.0%

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

   if -6.6e15 < c < 3.39999999999999989e-182

   1. Initial program 88.0%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in j around inf 33.8%

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

      1. *-commutative 33.8%

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

      2. associate-*l* 33.8%

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

   6. Simplified 33.8%

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

   if 3.39999999999999989e-182 < c < 4.29999999999999996e197

   1. Initial program 91.3%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in y around inf 27.8%

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

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.6 \cdot 10^{+15}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-182}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{+197}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 18: 31.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-178}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+61}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= a -1.35e+150)
     t_1
     (if (<= a -1.42e-178)
       (* b c)
       (if (<= a 1.7e+61) (* k (* j -27.0)) 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 = t * (a * -4.0);
	double tmp;
	if (a <= -1.35e+150) {
		tmp = t_1;
	} else if (a <= -1.42e-178) {
		tmp = b * c;
	} else if (a <= 1.7e+61) {
		tmp = k * (j * -27.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (a <= (-1.35d+150)) then
        tmp = t_1
    else if (a <= (-1.42d-178)) then
        tmp = b * c
    else if (a <= 1.7d+61) then
        tmp = k * (j * (-27.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (a <= -1.35e+150) {
		tmp = t_1;
	} else if (a <= -1.42e-178) {
		tmp = b * c;
	} else if (a <= 1.7e+61) {
		tmp = k * (j * -27.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	tmp = 0
	if a <= -1.35e+150:
		tmp = t_1
	elif a <= -1.42e-178:
		tmp = b * c
	elif a <= 1.7e+61:
		tmp = k * (j * -27.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (a <= -1.35e+150)
		tmp = t_1;
	elseif (a <= -1.42e-178)
		tmp = Float64(b * c);
	elseif (a <= 1.7e+61)
		tmp = Float64(k * Float64(j * -27.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (a <= -1.35e+150)
		tmp = t_1;
	elseif (a <= -1.42e-178)
		tmp = b * c;
	elseif (a <= 1.7e+61)
		tmp = k * (j * -27.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.35e+150], t$95$1, If[LessEqual[a, -1.42e-178], N[(b * c), $MachinePrecision], If[LessEqual[a, 1.7e+61], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.35000000000000004e150 or 1.70000000000000013e61 < a

   1. Initial program 82.8%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in a around inf 53.7%

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

      1. *-commutative 53.7%

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

      2. *-commutative 53.7%

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

      3. associate-*r* 53.7%

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

   6. Simplified 53.7%

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

   if -1.35000000000000004e150 < a < -1.4200000000000001e-178

   1. Initial program 94.4%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in b around inf 36.4%

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

   if -1.4200000000000001e-178 < a < 1.70000000000000013e61

   1. Initial program 92.3%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in j around inf 32.7%

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

      1. *-commutative 32.7%

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

      2. associate-*l* 32.7%

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

   6. Simplified 32.7%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-178}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+61}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \]

Alternative 19: 32.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -1.65 \cdot 10^{-74} \lor \neg \left(k \leq 2 \cdot 10^{-36}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= k -1.65e-74) (not (<= k 2e-36))) (* j (* k -27.0)) (* 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 <= -1.65e-74) || !(k <= 2e-36)) {
		tmp = j * (k * -27.0);
	} 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 <= (-1.65d-74)) .or. (.not. (k <= 2d-36))) then
        tmp = j * (k * (-27.0d0))
    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 <= -1.65e-74) || !(k <= 2e-36)) {
		tmp = j * (k * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (k <= -1.65e-74) or not (k <= 2e-36):
		tmp = j * (k * -27.0)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((k <= -1.65e-74) || !(k <= 2e-36))
		tmp = Float64(j * Float64(k * -27.0));
	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 <= -1.65e-74) || ~((k <= 2e-36)))
		tmp = j * (k * -27.0);
	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, -1.65e-74], N[Not[LessEqual[k, 2e-36]], $MachinePrecision]], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -1.64999999999999998e-74 or 1.9999999999999999e-36 < k

   1. Initial program 89.8%

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

   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 j around inf 34.6%

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

      1. *-commutative 34.6%

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

      2. *-commutative 34.6%

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

      3. associate-*l* 34.6%

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

   6. Simplified 34.6%

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

   if -1.64999999999999998e-74 < k < 1.9999999999999999e-36

   1. Initial program 90.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in b around inf 27.6%

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

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.65 \cdot 10^{-74} \lor \neg \left(k \leq 2 \cdot 10^{-36}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 20: 32.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -8 \cdot 10^{-73}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.45 \cdot 10^{-37}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -8e-73)
   (* j (* k -27.0))
   (if (<= k 1.45e-37) (* b c) (* 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 (k <= -8e-73) {
		tmp = j * (k * -27.0);
	} else if (k <= 1.45e-37) {
		tmp = b * c;
	} else {
		tmp = 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 (k <= (-8d-73)) then
        tmp = j * (k * (-27.0d0))
    else if (k <= 1.45d-37) then
        tmp = b * c
    else
        tmp = 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 (k <= -8e-73) {
		tmp = j * (k * -27.0);
	} else if (k <= 1.45e-37) {
		tmp = b * c;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -8e-73:
		tmp = j * (k * -27.0)
	elif k <= 1.45e-37:
		tmp = b * c
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -8e-73)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (k <= 1.45e-37)
		tmp = Float64(b * c);
	else
		tmp = 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 (k <= -8e-73)
		tmp = j * (k * -27.0);
	elseif (k <= 1.45e-37)
		tmp = b * c;
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -8e-73], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.45e-37], N[(b * c), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -7.99999999999999998e-73

   1. Initial program 88.6%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in j around inf 39.1%

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

      1. *-commutative 39.1%

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

      2. *-commutative 39.1%

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

      3. associate-*l* 39.0%

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

   6. Simplified 39.0%

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

   if -7.99999999999999998e-73 < k < 1.45000000000000002e-37

   1. Initial program 90.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in b around inf 27.6%

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

   if 1.45000000000000002e-37 < k

   1. Initial program 91.6%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in j around inf 27.4%

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

      1. *-commutative 27.4%

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

      2. associate-*l* 27.4%

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

   6. Simplified 27.4%

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

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -8 \cdot 10^{-73}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.45 \cdot 10^{-37}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 21: 23.8% 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 89.9%

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

3. Simplified 91.1%

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

4. Taylor expanded in b around inf 23.6%

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

5. Final simplification 23.6%

   \[\leadsto b \cdot c \]

Developer target: 89.6% 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 2023274 
(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)))