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

Percentage Accurate: 85.7% → 91.4%

Time: 20.6s

Alternatives: 20

Speedup: 0.5×

• 50.8% 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: 85.7% 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

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

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<=
      (-
       (-
        (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
        (* (* x 4.0) i))
       (* (* j 27.0) k))
      INFINITY)
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (* 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 tmp;
	if (((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)) <= ((double) INFINITY)) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} 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 tmp;
	if (((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)) <= Double.POSITIVE_INFINITY) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} 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):
	tmp = 0
	if ((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)) <= math.inf:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	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)
	tmp = 0.0
	if (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)) <= Inf)
		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))));
	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)
	tmp = 0.0;
	if (((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)) <= Inf)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	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_] := If[LessEqual[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], Infinity], 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], 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 #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   1. Initial program 95.6%

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

   3. Simplified 96.5%

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

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) 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 19.4%

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

   5. Taylor expanded in y around inf 13.9%

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

   6. Taylor expanded in x around inf 58.6%

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

      1. cancel-sign-sub-inv 58.6%

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

      2. metadata-eval 58.6%

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

      3. associate-*r* 66.8%

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

   8. Simplified 66.8%

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

4. Final simplification 92.3%

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

Alternative 2: 59.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t\_1\\ t_3 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+76}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-17}:\\ \;\;\;\;t\_1 + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-118}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-230}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-145}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) + t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-12}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ (* b c) t_1))
        (t_3 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -1.26e+76)
     t_3
     (if (<= t -2e+19)
       t_2
       (if (<= t -2.7e-17)
         (+ t_1 (* a (* t -4.0)))
         (if (<= t -2.7e-58)
           t_2
           (if (<= t -1.5e-118)
             (* -4.0 (+ (* x i) (* t a)))
             (if (<= t 1.95e-230)
               t_2
               (if (<= t 5.4e-145)
                 (+ (* i (* x -4.0)) t_1)
                 (if (<= t 2.6e-12) 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 * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.26e+76) {
		tmp = t_3;
	} else if (t <= -2e+19) {
		tmp = t_2;
	} else if (t <= -2.7e-17) {
		tmp = t_1 + (a * (t * -4.0));
	} else if (t <= -2.7e-58) {
		tmp = t_2;
	} else if (t <= -1.5e-118) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else if (t <= 1.95e-230) {
		tmp = t_2;
	} else if (t <= 5.4e-145) {
		tmp = (i * (x * -4.0)) + t_1;
	} else if (t <= 2.6e-12) {
		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 * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    t_3 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-1.26d+76)) then
        tmp = t_3
    else if (t <= (-2d+19)) then
        tmp = t_2
    else if (t <= (-2.7d-17)) then
        tmp = t_1 + (a * (t * (-4.0d0)))
    else if (t <= (-2.7d-58)) then
        tmp = t_2
    else if (t <= (-1.5d-118)) then
        tmp = (-4.0d0) * ((x * i) + (t * a))
    else if (t <= 1.95d-230) then
        tmp = t_2
    else if (t <= 5.4d-145) then
        tmp = (i * (x * (-4.0d0))) + t_1
    else if (t <= 2.6d-12) 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 * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.26e+76) {
		tmp = t_3;
	} else if (t <= -2e+19) {
		tmp = t_2;
	} else if (t <= -2.7e-17) {
		tmp = t_1 + (a * (t * -4.0));
	} else if (t <= -2.7e-58) {
		tmp = t_2;
	} else if (t <= -1.5e-118) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else if (t <= 1.95e-230) {
		tmp = t_2;
	} else if (t <= 5.4e-145) {
		tmp = (i * (x * -4.0)) + t_1;
	} else if (t <= 2.6e-12) {
		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 * (k * -27.0)
	t_2 = (b * c) + t_1
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -1.26e+76:
		tmp = t_3
	elif t <= -2e+19:
		tmp = t_2
	elif t <= -2.7e-17:
		tmp = t_1 + (a * (t * -4.0))
	elif t <= -2.7e-58:
		tmp = t_2
	elif t <= -1.5e-118:
		tmp = -4.0 * ((x * i) + (t * a))
	elif t <= 1.95e-230:
		tmp = t_2
	elif t <= 5.4e-145:
		tmp = (i * (x * -4.0)) + t_1
	elif t <= 2.6e-12:
		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(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -1.26e+76)
		tmp = t_3;
	elseif (t <= -2e+19)
		tmp = t_2;
	elseif (t <= -2.7e-17)
		tmp = Float64(t_1 + Float64(a * Float64(t * -4.0)));
	elseif (t <= -2.7e-58)
		tmp = t_2;
	elseif (t <= -1.5e-118)
		tmp = Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a)));
	elseif (t <= 1.95e-230)
		tmp = t_2;
	elseif (t <= 5.4e-145)
		tmp = Float64(Float64(i * Float64(x * -4.0)) + t_1);
	elseif (t <= 2.6e-12)
		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 * (k * -27.0);
	t_2 = (b * c) + t_1;
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -1.26e+76)
		tmp = t_3;
	elseif (t <= -2e+19)
		tmp = t_2;
	elseif (t <= -2.7e-17)
		tmp = t_1 + (a * (t * -4.0));
	elseif (t <= -2.7e-58)
		tmp = t_2;
	elseif (t <= -1.5e-118)
		tmp = -4.0 * ((x * i) + (t * a));
	elseif (t <= 1.95e-230)
		tmp = t_2;
	elseif (t <= 5.4e-145)
		tmp = (i * (x * -4.0)) + t_1;
	elseif (t <= 2.6e-12)
		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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e+76], t$95$3, If[LessEqual[t, -2e+19], t$95$2, If[LessEqual[t, -2.7e-17], N[(t$95$1 + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.7e-58], t$95$2, If[LessEqual[t, -1.5e-118], N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e-230], t$95$2, If[LessEqual[t, 5.4e-145], N[(N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 2.6e-12], t$95$2, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.26000000000000007e76 or 2.59999999999999983e-12 < t

   1. Initial program 77.1%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in t around inf 71.3%

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

   if -1.26000000000000007e76 < t < -2e19 or -2.7000000000000001e-17 < t < -2.6999999999999999e-58 or -1.50000000000000009e-118 < t < 1.9500000000000001e-230 or 5.4000000000000001e-145 < t < 2.59999999999999983e-12

   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 89.8%

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

   5. Taylor expanded in b around inf 71.7%

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

   if -2e19 < t < -2.7000000000000001e-17

   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 100.0%

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

   5. Taylor expanded in a around inf 85.4%

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

      1. metadata-eval 85.4%

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

      2. distribute-lft-neg-in 85.4%

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

      3. *-commutative 85.4%

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

      4. associate-*l* 85.4%

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

      5. distribute-lft-neg-in 85.4%

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

      6. distribute-lft-neg-in 85.4%

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

      7. metadata-eval 85.4%

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

   7. Simplified 85.4%

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

   if -2.6999999999999999e-58 < t < -1.50000000000000009e-118

   1. Initial program 86.7%

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

   3. Taylor expanded in y around 0 79.3%

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

      1. distribute-lft-out 79.3%

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

      2. *-commutative 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in j around 0 71.3%

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

   7. Taylor expanded in b around 0 61.8%

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

   if 1.9500000000000001e-230 < t < 5.4000000000000001e-145

   1. Initial program 79.0%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in i around inf 86.4%

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

      1. metadata-eval 86.4%

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

      2. distribute-lft-neg-in 86.4%

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

      3. *-commutative 86.4%

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

      4. associate-*r* 86.4%

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

      5. distribute-rgt-neg-in 86.4%

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

      6. distribute-rgt-neg-in 86.4%

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

      7. metadata-eval 86.4%

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

      8. *-commutative 86.4%

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

   7. Simplified 86.4%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+76}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+19}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-17}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-58}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-118}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-230}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-145}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-12}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;k \leq -1.56 \cdot 10^{-21}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) + t\_1\\ \mathbf{elif}\;k \leq 1.52 \cdot 10^{-133}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq 6.9 \cdot 10^{-56}:\\ \;\;\;\;t \cdot \left(18 \cdot t\_3 - a \cdot 4\right)\\ \mathbf{elif}\;k \leq 1.3 \cdot 10^{+147} \lor \neg \left(k \leq 1.9 \cdot 10^{+173}\right) \land k \leq 2 \cdot 10^{+189}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + 18 \cdot \left(t \cdot t\_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (- (* b c) (* 4.0 (+ (* x i) (* t a)))))
        (t_3 (* x (* y z))))
   (if (<= k -1.56e-21)
     (+ (* i (* x -4.0)) t_1)
     (if (<= k 1.52e-133)
       t_2
       (if (<= k 6.9e-56)
         (* t (- (* 18.0 t_3) (* a 4.0)))
         (if (or (<= k 1.3e+147) (and (not (<= k 1.9e+173)) (<= k 2e+189)))
           t_2
           (+ t_1 (* 18.0 (* t 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 * (k * -27.0);
	double t_2 = (b * c) - (4.0 * ((x * i) + (t * a)));
	double t_3 = x * (y * z);
	double tmp;
	if (k <= -1.56e-21) {
		tmp = (i * (x * -4.0)) + t_1;
	} else if (k <= 1.52e-133) {
		tmp = t_2;
	} else if (k <= 6.9e-56) {
		tmp = t * ((18.0 * t_3) - (a * 4.0));
	} else if ((k <= 1.3e+147) || (!(k <= 1.9e+173) && (k <= 2e+189))) {
		tmp = t_2;
	} else {
		tmp = t_1 + (18.0 * (t * 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 * (k * (-27.0d0))
    t_2 = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    t_3 = x * (y * z)
    if (k <= (-1.56d-21)) then
        tmp = (i * (x * (-4.0d0))) + t_1
    else if (k <= 1.52d-133) then
        tmp = t_2
    else if (k <= 6.9d-56) then
        tmp = t * ((18.0d0 * t_3) - (a * 4.0d0))
    else if ((k <= 1.3d+147) .or. (.not. (k <= 1.9d+173)) .and. (k <= 2d+189)) then
        tmp = t_2
    else
        tmp = t_1 + (18.0d0 * (t * 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 * (k * -27.0);
	double t_2 = (b * c) - (4.0 * ((x * i) + (t * a)));
	double t_3 = x * (y * z);
	double tmp;
	if (k <= -1.56e-21) {
		tmp = (i * (x * -4.0)) + t_1;
	} else if (k <= 1.52e-133) {
		tmp = t_2;
	} else if (k <= 6.9e-56) {
		tmp = t * ((18.0 * t_3) - (a * 4.0));
	} else if ((k <= 1.3e+147) || (!(k <= 1.9e+173) && (k <= 2e+189))) {
		tmp = t_2;
	} else {
		tmp = t_1 + (18.0 * (t * t_3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) - (4.0 * ((x * i) + (t * a)))
	t_3 = x * (y * z)
	tmp = 0
	if k <= -1.56e-21:
		tmp = (i * (x * -4.0)) + t_1
	elif k <= 1.52e-133:
		tmp = t_2
	elif k <= 6.9e-56:
		tmp = t * ((18.0 * t_3) - (a * 4.0))
	elif (k <= 1.3e+147) or (not (k <= 1.9e+173) and (k <= 2e+189)):
		tmp = t_2
	else:
		tmp = t_1 + (18.0 * (t * t_3))
	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(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))))
	t_3 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (k <= -1.56e-21)
		tmp = Float64(Float64(i * Float64(x * -4.0)) + t_1);
	elseif (k <= 1.52e-133)
		tmp = t_2;
	elseif (k <= 6.9e-56)
		tmp = Float64(t * Float64(Float64(18.0 * t_3) - Float64(a * 4.0)));
	elseif ((k <= 1.3e+147) || (!(k <= 1.9e+173) && (k <= 2e+189)))
		tmp = t_2;
	else
		tmp = Float64(t_1 + Float64(18.0 * Float64(t * t_3)));
	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 = (b * c) - (4.0 * ((x * i) + (t * a)));
	t_3 = x * (y * z);
	tmp = 0.0;
	if (k <= -1.56e-21)
		tmp = (i * (x * -4.0)) + t_1;
	elseif (k <= 1.52e-133)
		tmp = t_2;
	elseif (k <= 6.9e-56)
		tmp = t * ((18.0 * t_3) - (a * 4.0));
	elseif ((k <= 1.3e+147) || (~((k <= 1.9e+173)) && (k <= 2e+189)))
		tmp = t_2;
	else
		tmp = t_1 + (18.0 * (t * t_3));
	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[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.56e-21], N[(N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[k, 1.52e-133], t$95$2, If[LessEqual[k, 6.9e-56], N[(t * N[(N[(18.0 * t$95$3), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[k, 1.3e+147], And[N[Not[LessEqual[k, 1.9e+173]], $MachinePrecision], LessEqual[k, 2e+189]]], t$95$2, N[(t$95$1 + N[(18.0 * N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -1.55999999999999999e-21

   1. Initial program 80.4%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in i around inf 55.0%

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

      1. metadata-eval 55.0%

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

      2. distribute-lft-neg-in 55.0%

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

      3. *-commutative 55.0%

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

      4. associate-*r* 55.0%

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

      5. distribute-rgt-neg-in 55.0%

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

      6. distribute-rgt-neg-in 55.0%

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

      7. metadata-eval 55.0%

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

      8. *-commutative 55.0%

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

   7. Simplified 55.0%

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

   if -1.55999999999999999e-21 < k < 1.52000000000000001e-133 or 6.8999999999999996e-56 < k < 1.2999999999999999e147 or 1.90000000000000005e173 < k < 2e189

   1. Initial program 83.9%

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

   3. Taylor expanded in y around 0 82.4%

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

      1. distribute-lft-out 82.4%

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

      2. *-commutative 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in j around 0 77.5%

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

   if 1.52000000000000001e-133 < k < 6.8999999999999996e-56

   1. Initial program 99.3%

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

   3. Simplified 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. Add Preprocessing

   5. Taylor expanded in t around inf 72.3%

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

   if 1.2999999999999999e147 < k < 1.90000000000000005e173 or 2e189 < k

   1. Initial program 74.6%

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

   3. Simplified 76.8%

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

   5. Taylor expanded in y around inf 77.3%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.56 \cdot 10^{-21}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.52 \cdot 10^{-133}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;k \leq 6.9 \cdot 10^{-56}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;k \leq 1.3 \cdot 10^{+147} \lor \neg \left(k \leq 1.9 \cdot 10^{+173}\right) \land k \leq 2 \cdot 10^{+189}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ t_2 := x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+170}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+106}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+184}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k)))
        (t_2 (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))))
   (if (<= x -4.5e+170)
     t_2
     (if (<= x 8.8e+45)
       t_1
       (if (<= x 1.8e+65)
         t_2
         (if (<= x 3.3e+106)
           (- (* b c) (* 4.0 (+ (* x i) (* t a))))
           (if (<= x 2.35e+184)
             (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
             (if (<= x 1.12e+204) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	double t_2 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -4.5e+170) {
		tmp = t_2;
	} else if (x <= 8.8e+45) {
		tmp = t_1;
	} else if (x <= 1.8e+65) {
		tmp = t_2;
	} else if (x <= 3.3e+106) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else if (x <= 2.35e+184) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (x <= 1.12e+204) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    t_2 = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    if (x <= (-4.5d+170)) then
        tmp = t_2
    else if (x <= 8.8d+45) then
        tmp = t_1
    else if (x <= 1.8d+65) then
        tmp = t_2
    else if (x <= 3.3d+106) then
        tmp = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    else if (x <= 2.35d+184) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (x <= 1.12d+204) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	double t_2 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -4.5e+170) {
		tmp = t_2;
	} else if (x <= 8.8e+45) {
		tmp = t_1;
	} else if (x <= 1.8e+65) {
		tmp = t_2;
	} else if (x <= 3.3e+106) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else if (x <= 2.35e+184) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (x <= 1.12e+204) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	t_2 = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	tmp = 0
	if x <= -4.5e+170:
		tmp = t_2
	elif x <= 8.8e+45:
		tmp = t_1
	elif x <= 1.8e+65:
		tmp = t_2
	elif x <= 3.3e+106:
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)))
	elif x <= 2.35e+184:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif x <= 1.12e+204:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k))
	t_2 = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)))
	tmp = 0.0
	if (x <= -4.5e+170)
		tmp = t_2;
	elseif (x <= 8.8e+45)
		tmp = t_1;
	elseif (x <= 1.8e+65)
		tmp = t_2;
	elseif (x <= 3.3e+106)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))));
	elseif (x <= 2.35e+184)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (x <= 1.12e+204)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	t_2 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	tmp = 0.0;
	if (x <= -4.5e+170)
		tmp = t_2;
	elseif (x <= 8.8e+45)
		tmp = t_1;
	elseif (x <= 1.8e+65)
		tmp = t_2;
	elseif (x <= 3.3e+106)
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	elseif (x <= 2.35e+184)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (x <= 1.12e+204)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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+170], t$95$2, If[LessEqual[x, 8.8e+45], t$95$1, If[LessEqual[x, 1.8e+65], t$95$2, If[LessEqual[x, 3.3e+106], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.35e+184], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.12e+204], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.50000000000000022e170 or 8.8000000000000001e45 < x < 1.79999999999999989e65 or 1.11999999999999996e204 < x

   1. Initial program 63.2%

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

   3. Simplified 74.9%

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

   5. Taylor expanded in y around inf 63.5%

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

   6. Taylor expanded in x around inf 75.6%

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

      1. cancel-sign-sub-inv 75.6%

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

      2. metadata-eval 75.6%

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

      3. associate-*r* 78.9%

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

   8. Simplified 78.9%

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

   if -4.50000000000000022e170 < x < 8.8000000000000001e45 or 2.3500000000000002e184 < x < 1.11999999999999996e204

   1. Initial program 90.2%

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

   3. Taylor expanded in x around 0 79.2%

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

   if 1.79999999999999989e65 < x < 3.30000000000000008e106

   1. Initial program 90.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. distribute-lft-out 100.0%

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

      2. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in j around 0 100.0%

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

   if 3.30000000000000008e106 < x < 2.3500000000000002e184

   1. Initial program 69.7%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in t around inf 66.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+45}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+106}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+184}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+204}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+125} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+136}\right):\\ \;\;\;\;y \cdot \left(-27 \cdot \frac{j \cdot k}{y} + 18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= t_1 -5e+125) (not (<= t_1 5e+136)))
     (* y (+ (* -27.0 (/ (* j k) y)) (* 18.0 (* t (* x z)))))
     (-
      (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
      (* 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 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -5e+125) || !(t_1 <= 5e+136)) {
		tmp = y * ((-27.0 * ((j * k) / y)) + (18.0 * (t * (x * z))));
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (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 = (j * 27.0d0) * k
    if ((t_1 <= (-5d+125)) .or. (.not. (t_1 <= 5d+136))) then
        tmp = y * (((-27.0d0) * ((j * k) / y)) + (18.0d0 * (t * (x * z))))
    else
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (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 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -5e+125) || !(t_1 <= 5e+136)) {
		tmp = y * ((-27.0 * ((j * k) / y)) + (18.0 * (t * (x * z))));
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (t_1 <= -5e+125) or not (t_1 <= 5e+136):
		tmp = y * ((-27.0 * ((j * k) / y)) + (18.0 * (t * (x * z))))
	else:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_1 <= -5e+125) || !(t_1 <= 5e+136))
		tmp = Float64(y * Float64(Float64(-27.0 * Float64(Float64(j * k) / y)) + Float64(18.0 * Float64(t * Float64(x * z)))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - 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 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_1 <= -5e+125) || ~((t_1 <= 5e+136)))
		tmp = y * ((-27.0 * ((j * k) / y)) + (18.0 * (t * (x * z))));
	else
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (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[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+125], N[Not[LessEqual[t$95$1, 5e+136]], $MachinePrecision]], N[(y * N[(N[(-27.0 * N[(N[(j * k), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999962e125 or 5.0000000000000002e136 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 74.5%

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

   3. Simplified 73.5%

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

   5. Taylor expanded in y around inf 74.9%

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

   6. Taylor expanded in y around inf 74.9%

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

   if -4.99999999999999962e125 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.0000000000000002e136

   1. Initial program 85.5%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in j around 0 84.2%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+125} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+136}\right):\\ \;\;\;\;y \cdot \left(-27 \cdot \frac{j \cdot k}{y} + 18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ t_2 := \left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;z \leq -480000000:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+77}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+205}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
        (t_2 (- (- (* b c) (* 4.0 (+ (* x i) (* t a)))) (* (* j 27.0) k))))
   (if (<= z -480000000.0)
     (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))
     (if (<= z 5.6e+32)
       t_2
       (if (<= z 4.8e+77) (+ (* b c) t_1) (if (<= z 2.6e+205) t_2 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 * (x * (y * z))) - (a * 4.0));
	double t_2 = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	double tmp;
	if (z <= -480000000.0) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (z <= 5.6e+32) {
		tmp = t_2;
	} else if (z <= 4.8e+77) {
		tmp = (b * c) + t_1;
	} else if (z <= 2.6e+205) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    t_2 = ((b * c) - (4.0d0 * ((x * i) + (t * a)))) - ((j * 27.0d0) * k)
    if (z <= (-480000000.0d0)) then
        tmp = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    else if (z <= 5.6d+32) then
        tmp = t_2
    else if (z <= 4.8d+77) then
        tmp = (b * c) + t_1
    else if (z <= 2.6d+205) then
        tmp = t_2
    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 * (x * (y * z))) - (a * 4.0));
	double t_2 = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	double tmp;
	if (z <= -480000000.0) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (z <= 5.6e+32) {
		tmp = t_2;
	} else if (z <= 4.8e+77) {
		tmp = (b * c) + t_1;
	} else if (z <= 2.6e+205) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	t_2 = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k)
	tmp = 0
	if z <= -480000000.0:
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	elif z <= 5.6e+32:
		tmp = t_2
	elif z <= 4.8e+77:
		tmp = (b * c) + t_1
	elif z <= 2.6e+205:
		tmp = t_2
	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(x * Float64(y * z))) - Float64(a * 4.0)))
	t_2 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (z <= -480000000.0)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)));
	elseif (z <= 5.6e+32)
		tmp = t_2;
	elseif (z <= 4.8e+77)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (z <= 2.6e+205)
		tmp = t_2;
	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 * (x * (y * z))) - (a * 4.0));
	t_2 = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	tmp = 0.0;
	if (z <= -480000000.0)
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	elseif (z <= 5.6e+32)
		tmp = t_2;
	elseif (z <= 4.8e+77)
		tmp = (b * c) + t_1;
	elseif (z <= 2.6e+205)
		tmp = t_2;
	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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -480000000.0], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+32], t$95$2, If[LessEqual[z, 4.8e+77], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 2.6e+205], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.8e8

   1. Initial program 81.8%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in y around inf 60.3%

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

   6. Taylor expanded in x around inf 54.0%

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

      1. cancel-sign-sub-inv 54.0%

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

      2. metadata-eval 54.0%

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

      3. associate-*r* 56.8%

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

   8. Simplified 56.8%

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

   if -4.8e8 < z < 5.6e32 or 4.7999999999999997e77 < z < 2.5999999999999999e205

   1. Initial program 83.3%

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

   3. Taylor expanded in y around 0 86.5%

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

      1. distribute-lft-out 86.5%

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

      2. *-commutative 86.5%

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

   5. Simplified 86.5%

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

   if 5.6e32 < z < 4.7999999999999997e77

   1. Initial program 66.4%

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

   3. Simplified 66.4%

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

   5. Taylor expanded in j around 0 66.4%

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

   6. Taylor expanded in i around 0 83.1%

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

   if 2.5999999999999999e205 < z

   1. Initial program 78.7%

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

   3. Simplified 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. Add Preprocessing

   5. Taylor expanded in t around inf 79.2%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -480000000:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+32}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+77}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+205}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{if}\;k \leq -6.6 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) + t\_1\\ \mathbf{elif}\;k \leq 1.15 \cdot 10^{-133}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq 2.6 \cdot 10^{-56}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+177}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + a \cdot \left(t \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (- (* b c) (* 4.0 (+ (* x i) (* t a))))))
   (if (<= k -6.6e-22)
     (+ (* i (* x -4.0)) t_1)
     (if (<= k 1.15e-133)
       t_2
       (if (<= k 2.6e-56)
         (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
         (if (<= k 7.5e+177) t_2 (+ t_1 (* a (* t -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 * (k * -27.0);
	double t_2 = (b * c) - (4.0 * ((x * i) + (t * a)));
	double tmp;
	if (k <= -6.6e-22) {
		tmp = (i * (x * -4.0)) + t_1;
	} else if (k <= 1.15e-133) {
		tmp = t_2;
	} else if (k <= 2.6e-56) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (k <= 7.5e+177) {
		tmp = t_2;
	} else {
		tmp = t_1 + (a * (t * -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 * (k * (-27.0d0))
    t_2 = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    if (k <= (-6.6d-22)) then
        tmp = (i * (x * (-4.0d0))) + t_1
    else if (k <= 1.15d-133) then
        tmp = t_2
    else if (k <= 2.6d-56) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (k <= 7.5d+177) then
        tmp = t_2
    else
        tmp = t_1 + (a * (t * (-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 * (k * -27.0);
	double t_2 = (b * c) - (4.0 * ((x * i) + (t * a)));
	double tmp;
	if (k <= -6.6e-22) {
		tmp = (i * (x * -4.0)) + t_1;
	} else if (k <= 1.15e-133) {
		tmp = t_2;
	} else if (k <= 2.6e-56) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (k <= 7.5e+177) {
		tmp = t_2;
	} else {
		tmp = t_1 + (a * (t * -4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) - (4.0 * ((x * i) + (t * a)))
	tmp = 0
	if k <= -6.6e-22:
		tmp = (i * (x * -4.0)) + t_1
	elif k <= 1.15e-133:
		tmp = t_2
	elif k <= 2.6e-56:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif k <= 7.5e+177:
		tmp = t_2
	else:
		tmp = t_1 + (a * (t * -4.0))
	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(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))))
	tmp = 0.0
	if (k <= -6.6e-22)
		tmp = Float64(Float64(i * Float64(x * -4.0)) + t_1);
	elseif (k <= 1.15e-133)
		tmp = t_2;
	elseif (k <= 2.6e-56)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (k <= 7.5e+177)
		tmp = t_2;
	else
		tmp = Float64(t_1 + Float64(a * Float64(t * -4.0)));
	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 = (b * c) - (4.0 * ((x * i) + (t * a)));
	tmp = 0.0;
	if (k <= -6.6e-22)
		tmp = (i * (x * -4.0)) + t_1;
	elseif (k <= 1.15e-133)
		tmp = t_2;
	elseif (k <= 2.6e-56)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (k <= 7.5e+177)
		tmp = t_2;
	else
		tmp = t_1 + (a * (t * -4.0));
	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[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -6.6e-22], N[(N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[k, 1.15e-133], t$95$2, If[LessEqual[k, 2.6e-56], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7.5e+177], t$95$2, N[(t$95$1 + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -6.6000000000000002e-22

   1. Initial program 80.4%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in i around inf 55.0%

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

      1. metadata-eval 55.0%

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

      2. distribute-lft-neg-in 55.0%

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

      3. *-commutative 55.0%

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

      4. associate-*r* 55.0%

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

      5. distribute-rgt-neg-in 55.0%

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

      6. distribute-rgt-neg-in 55.0%

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

      7. metadata-eval 55.0%

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

      8. *-commutative 55.0%

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

   7. Simplified 55.0%

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

   if -6.6000000000000002e-22 < k < 1.15e-133 or 2.59999999999999997e-56 < k < 7.50000000000000039e177

   1. Initial program 83.5%

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

   3. Taylor expanded in y around 0 81.4%

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

      1. distribute-lft-out 81.4%

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

      2. *-commutative 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in j around 0 74.7%

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

   if 1.15e-133 < k < 2.59999999999999997e-56

   1. Initial program 99.3%

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

   3. Simplified 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. Add Preprocessing

   5. Taylor expanded in t around inf 72.3%

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

   if 7.50000000000000039e177 < k

   1. Initial program 73.8%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in a around inf 59.0%

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

      1. metadata-eval 59.0%

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

      2. distribute-lft-neg-in 59.0%

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

      3. *-commutative 59.0%

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

      4. associate-*l* 59.0%

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

      5. distribute-lft-neg-in 59.0%

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

      6. distribute-lft-neg-in 59.0%

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

      7. metadata-eval 59.0%

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

   7. Simplified 59.0%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -6.6 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.15 \cdot 10^{-133}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;k \leq 2.6 \cdot 10^{-56}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+177}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-111}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-52}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))))
   (if (<= t -1.6e+77)
     t_2
     (if (<= t -8.5e-111)
       (- (- (* b c) (* 4.0 (* t a))) t_1)
       (if (<= t 2.9e-52) (- (- (* b c) (* 4.0 (* x i))) t_1) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -1.6e+77) {
		tmp = t_2;
	} else if (t <= -8.5e-111) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (t <= 2.9e-52) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    if (t <= (-1.6d+77)) then
        tmp = t_2
    else if (t <= (-8.5d-111)) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if (t <= 2.9d-52) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -1.6e+77) {
		tmp = t_2;
	} else if (t <= -8.5e-111) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (t <= 2.9e-52) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = t_2;
	}
	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) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	tmp = 0
	if t <= -1.6e+77:
		tmp = t_2
	elif t <= -8.5e-111:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif t <= 2.9e-52:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	else:
		tmp = t_2
	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(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))))
	tmp = 0.0
	if (t <= -1.6e+77)
		tmp = t_2;
	elseif (t <= -8.5e-111)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (t <= 2.9e-52)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	tmp = 0.0;
	if (t <= -1.6e+77)
		tmp = t_2;
	elseif (t <= -8.5e-111)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif (t <= 2.9e-52)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+77], t$95$2, If[LessEqual[t, -8.5e-111], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 2.9e-52], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6000000000000001e77 or 2.9000000000000002e-52 < t

   1. Initial program 77.4%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in j around 0 73.9%

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

   6. Taylor expanded in i around 0 72.6%

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

   if -1.6000000000000001e77 < t < -8.5000000000000003e-111

   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. Add Preprocessing

   3. Taylor expanded in x around 0 71.1%

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

   if -8.5000000000000003e-111 < t < 2.9000000000000002e-52

   1. Initial program 88.2%

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

   3. Taylor expanded in t around 0 93.6%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+77}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-111}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-52}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-113}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-20}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -5.4e+76)
     t_2
     (if (<= t -3.6e-113)
       (- (- (* b c) (* 4.0 (* t a))) t_1)
       (if (<= t 2.6e-20) (- (- (* b c) (* 4.0 (* x i))) t_1) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -5.4e+76) {
		tmp = t_2;
	} else if (t <= -3.6e-113) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (t <= 2.6e-20) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-5.4d+76)) then
        tmp = t_2
    else if (t <= (-3.6d-113)) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if (t <= 2.6d-20) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -5.4e+76) {
		tmp = t_2;
	} else if (t <= -3.6e-113) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (t <= 2.6e-20) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -5.4e+76:
		tmp = t_2
	elif t <= -3.6e-113:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif t <= 2.6e-20:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	else:
		tmp = t_2
	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(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -5.4e+76)
		tmp = t_2;
	elseif (t <= -3.6e-113)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (t <= 2.6e-20)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -5.4e+76)
		tmp = t_2;
	elseif (t <= -3.6e-113)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif (t <= 2.6e-20)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.4e+76], t$95$2, If[LessEqual[t, -3.6e-113], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 2.6e-20], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.3999999999999998e76 or 2.59999999999999995e-20 < t

   1. Initial program 77.1%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in t around inf 71.3%

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

   if -5.3999999999999998e76 < t < -3.59999999999999975e-113

   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. Add Preprocessing

   3. Taylor expanded in x around 0 71.1%

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

   if -3.59999999999999975e-113 < t < 2.59999999999999995e-20

   1. Initial program 87.3%

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

   3. Taylor expanded in t around 0 89.7%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+76}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-113}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-20}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -1.56 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq 1020000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 10^{+176}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a)))) (t_2 (* -27.0 (* j k))))
   (if (<= k -1.56e-21)
     t_2
     (if (<= k 1020000000.0)
       t_1
       (if (<= k 1e+176)
         (* -4.0 (+ (* x i) (* t a)))
         (if (<= k 6.2e+188) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = -27.0 * (j * k);
	double tmp;
	if (k <= -1.56e-21) {
		tmp = t_2;
	} else if (k <= 1020000000.0) {
		tmp = t_1;
	} else if (k <= 1e+176) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else if (k <= 6.2e+188) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    t_2 = (-27.0d0) * (j * k)
    if (k <= (-1.56d-21)) then
        tmp = t_2
    else if (k <= 1020000000.0d0) then
        tmp = t_1
    else if (k <= 1d+176) then
        tmp = (-4.0d0) * ((x * i) + (t * a))
    else if (k <= 6.2d+188) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = -27.0 * (j * k);
	double tmp;
	if (k <= -1.56e-21) {
		tmp = t_2;
	} else if (k <= 1020000000.0) {
		tmp = t_1;
	} else if (k <= 1e+176) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else if (k <= 6.2e+188) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	t_2 = -27.0 * (j * k)
	tmp = 0
	if k <= -1.56e-21:
		tmp = t_2
	elif k <= 1020000000.0:
		tmp = t_1
	elif k <= 1e+176:
		tmp = -4.0 * ((x * i) + (t * a))
	elif k <= 6.2e+188:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_2 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (k <= -1.56e-21)
		tmp = t_2;
	elseif (k <= 1020000000.0)
		tmp = t_1;
	elseif (k <= 1e+176)
		tmp = Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a)));
	elseif (k <= 6.2e+188)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	t_2 = -27.0 * (j * k);
	tmp = 0.0;
	if (k <= -1.56e-21)
		tmp = t_2;
	elseif (k <= 1020000000.0)
		tmp = t_1;
	elseif (k <= 1e+176)
		tmp = -4.0 * ((x * i) + (t * a));
	elseif (k <= 6.2e+188)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.56e-21], t$95$2, If[LessEqual[k, 1020000000.0], t$95$1, If[LessEqual[k, 1e+176], N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6.2e+188], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if k < -1.55999999999999999e-21 or 6.2000000000000004e188 < k

   1. Initial program 78.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in j around inf 47.9%

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

   if -1.55999999999999999e-21 < k < 1.02e9 or 1e176 < k < 6.2000000000000004e188

   1. Initial program 84.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in j around 0 85.5%

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

   6. Taylor expanded in x around 0 58.6%

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

   if 1.02e9 < k < 1e176

   1. Initial program 87.1%

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

   3. Taylor expanded in y around 0 82.3%

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

      1. distribute-lft-out 82.3%

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

      2. *-commutative 82.3%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in j around 0 65.9%

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

   7. Taylor expanded in b around 0 53.6%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.56 \cdot 10^{-21}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 1020000000:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 10^{+176}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{+188}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-17}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) + t\_2\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-253}:\\ \;\;\;\;b \cdot c + t\_2\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a)))) (t_2 (* j (* k -27.0))))
   (if (<= a -1.4e+87)
     t_1
     (if (<= a -6.5e-17)
       (+ (* i (* x -4.0)) t_2)
       (if (<= a 7.5e-253)
         (+ (* b c) t_2)
         (if (<= a 1.25e+73) (- (* b c) (* 4.0 (* x i))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (a <= -1.4e+87) {
		tmp = t_1;
	} else if (a <= -6.5e-17) {
		tmp = (i * (x * -4.0)) + t_2;
	} else if (a <= 7.5e-253) {
		tmp = (b * c) + t_2;
	} else if (a <= 1.25e+73) {
		tmp = (b * c) - (4.0 * (x * i));
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    t_2 = j * (k * (-27.0d0))
    if (a <= (-1.4d+87)) then
        tmp = t_1
    else if (a <= (-6.5d-17)) then
        tmp = (i * (x * (-4.0d0))) + t_2
    else if (a <= 7.5d-253) then
        tmp = (b * c) + t_2
    else if (a <= 1.25d+73) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (a <= -1.4e+87) {
		tmp = t_1;
	} else if (a <= -6.5e-17) {
		tmp = (i * (x * -4.0)) + t_2;
	} else if (a <= 7.5e-253) {
		tmp = (b * c) + t_2;
	} else if (a <= 1.25e+73) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	t_2 = j * (k * -27.0)
	tmp = 0
	if a <= -1.4e+87:
		tmp = t_1
	elif a <= -6.5e-17:
		tmp = (i * (x * -4.0)) + t_2
	elif a <= 7.5e-253:
		tmp = (b * c) + t_2
	elif a <= 1.25e+73:
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_2 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (a <= -1.4e+87)
		tmp = t_1;
	elseif (a <= -6.5e-17)
		tmp = Float64(Float64(i * Float64(x * -4.0)) + t_2);
	elseif (a <= 7.5e-253)
		tmp = Float64(Float64(b * c) + t_2);
	elseif (a <= 1.25e+73)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	t_2 = j * (k * -27.0);
	tmp = 0.0;
	if (a <= -1.4e+87)
		tmp = t_1;
	elseif (a <= -6.5e-17)
		tmp = (i * (x * -4.0)) + t_2;
	elseif (a <= 7.5e-253)
		tmp = (b * c) + t_2;
	elseif (a <= 1.25e+73)
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+87], t$95$1, If[LessEqual[a, -6.5e-17], N[(N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[a, 7.5e-253], N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[a, 1.25e+73], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.40000000000000008e87 or 1.24999999999999994e73 < a

   1. Initial program 81.8%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in j around 0 76.1%

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

   6. Taylor expanded in x around 0 65.2%

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

   if -1.40000000000000008e87 < a < -6.4999999999999996e-17

   1. Initial program 81.7%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in i around inf 63.0%

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

      1. metadata-eval 63.0%

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

      2. distribute-lft-neg-in 63.0%

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

      3. *-commutative 63.0%

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

      4. associate-*r* 63.0%

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

      5. distribute-rgt-neg-in 63.0%

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

      6. distribute-rgt-neg-in 63.0%

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

      7. metadata-eval 63.0%

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

      8. *-commutative 63.0%

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

   7. Simplified 63.0%

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

   if -6.4999999999999996e-17 < a < 7.49999999999999987e-253

   1. Initial program 82.9%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in b around inf 60.3%

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

   if 7.49999999999999987e-253 < a < 1.24999999999999994e73

   1. Initial program 81.8%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in j around 0 76.9%

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

   6. Taylor expanded in t around 0 55.1%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-17}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-253}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{if}\;a \leq -8.1 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-79}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (+ (* x i) (* t a)))))
   (if (<= a -8.1e-16)
     t_1
     (if (<= a 4.6e-79)
       (+ (* b c) (* j (* k -27.0)))
       (if (<= a 2.5e+36) t_1 (+ (* b c) (* -4.0 (* t a))))))))

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) + (t * a));
	double tmp;
	if (a <= -8.1e-16) {
		tmp = t_1;
	} else if (a <= 4.6e-79) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (a <= 2.5e+36) {
		tmp = t_1;
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	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) + (t * a))
    if (a <= (-8.1d-16)) then
        tmp = t_1
    else if (a <= 4.6d-79) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (a <= 2.5d+36) then
        tmp = t_1
    else
        tmp = (b * c) + ((-4.0d0) * (t * a))
    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) + (t * a));
	double tmp;
	if (a <= -8.1e-16) {
		tmp = t_1;
	} else if (a <= 4.6e-79) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (a <= 2.5e+36) {
		tmp = t_1;
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * ((x * i) + (t * a))
	tmp = 0
	if a <= -8.1e-16:
		tmp = t_1
	elif a <= 4.6e-79:
		tmp = (b * c) + (j * (k * -27.0))
	elif a <= 2.5e+36:
		tmp = t_1
	else:
		tmp = (b * c) + (-4.0 * (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a)))
	tmp = 0.0
	if (a <= -8.1e-16)
		tmp = t_1;
	elseif (a <= 4.6e-79)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (a <= 2.5e+36)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * ((x * i) + (t * a));
	tmp = 0.0;
	if (a <= -8.1e-16)
		tmp = t_1;
	elseif (a <= 4.6e-79)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (a <= 2.5e+36)
		tmp = t_1;
	else
		tmp = (b * c) + (-4.0 * (t * a));
	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[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.1e-16], t$95$1, If[LessEqual[a, 4.6e-79], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+36], t$95$1, N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.10000000000000047e-16 or 4.60000000000000023e-79 < a < 2.49999999999999988e36

   1. Initial program 77.3%

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

   3. Taylor expanded in y around 0 76.1%

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

      1. distribute-lft-out 76.1%

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

      2. *-commutative 76.1%

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

   5. Simplified 76.1%

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

   6. Taylor expanded in j around 0 64.7%

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

   7. Taylor expanded in b around 0 54.5%

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

   if -8.10000000000000047e-16 < a < 4.60000000000000023e-79

   1. Initial program 86.3%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in b around inf 55.8%

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

   if 2.49999999999999988e36 < a

   1. Initial program 81.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in j around 0 77.4%

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

   6. Taylor expanded in x around 0 67.0%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.1 \cdot 10^{-16}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-79}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+36}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-16}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-253}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= a -2e-16)
   (* -4.0 (+ (* x i) (* t a)))
   (if (<= a 8.2e-253)
     (+ (* b c) (* j (* k -27.0)))
     (if (<= a 1.55e+73)
       (- (* b c) (* 4.0 (* x i)))
       (+ (* b c) (* -4.0 (* t a)))))))

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 (a <= -2e-16) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else if (a <= 8.2e-253) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (a <= 1.55e+73) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	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 (a <= (-2d-16)) then
        tmp = (-4.0d0) * ((x * i) + (t * a))
    else if (a <= 8.2d-253) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (a <= 1.55d+73) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = (b * c) + ((-4.0d0) * (t * a))
    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 (a <= -2e-16) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else if (a <= 8.2e-253) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (a <= 1.55e+73) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if a <= -2e-16:
		tmp = -4.0 * ((x * i) + (t * a))
	elif a <= 8.2e-253:
		tmp = (b * c) + (j * (k * -27.0))
	elif a <= 1.55e+73:
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = (b * c) + (-4.0 * (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (a <= -2e-16)
		tmp = Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a)));
	elseif (a <= 8.2e-253)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (a <= 1.55e+73)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (a <= -2e-16)
		tmp = -4.0 * ((x * i) + (t * a));
	elseif (a <= 8.2e-253)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (a <= 1.55e+73)
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = (b * c) + (-4.0 * (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[a, -2e-16], N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e-253], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e+73], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2e-16

   1. Initial program 80.6%

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

   3. Taylor expanded in y around 0 80.3%

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

      1. distribute-lft-out 80.3%

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

      2. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in j around 0 62.7%

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

   7. Taylor expanded in b around 0 53.6%

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

   if -2e-16 < a < 8.20000000000000004e-253

   1. Initial program 82.9%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in b around inf 60.3%

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

   if 8.20000000000000004e-253 < a < 1.55e73

   1. Initial program 81.8%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in j around 0 76.9%

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

   6. Taylor expanded in t around 0 55.1%

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

   if 1.55e73 < a

   1. Initial program 83.2%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in j around 0 78.5%

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

   6. Taylor expanded in x around 0 68.8%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-16}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-253}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{-39}:\\ \;\;\;\;t\_1 + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-261}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= a -1.45e-39)
     (+ t_1 (* a (* t -4.0)))
     (if (<= a 2.45e-261)
       (+ (* b c) t_1)
       (if (<= a 1.55e+73)
         (- (* b c) (* 4.0 (* x i)))
         (+ (* b c) (* -4.0 (* t a))))))))

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 tmp;
	if (a <= -1.45e-39) {
		tmp = t_1 + (a * (t * -4.0));
	} else if (a <= 2.45e-261) {
		tmp = (b * c) + t_1;
	} else if (a <= 1.55e+73) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	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 = j * (k * (-27.0d0))
    if (a <= (-1.45d-39)) then
        tmp = t_1 + (a * (t * (-4.0d0)))
    else if (a <= 2.45d-261) then
        tmp = (b * c) + t_1
    else if (a <= 1.55d+73) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = (b * c) + ((-4.0d0) * (t * a))
    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 tmp;
	if (a <= -1.45e-39) {
		tmp = t_1 + (a * (t * -4.0));
	} else if (a <= 2.45e-261) {
		tmp = (b * c) + t_1;
	} else if (a <= 1.55e+73) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if a <= -1.45e-39:
		tmp = t_1 + (a * (t * -4.0))
	elif a <= 2.45e-261:
		tmp = (b * c) + t_1
	elif a <= 1.55e+73:
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = (b * c) + (-4.0 * (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (a <= -1.45e-39)
		tmp = Float64(t_1 + Float64(a * Float64(t * -4.0)));
	elseif (a <= 2.45e-261)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (a <= 1.55e+73)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	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);
	tmp = 0.0;
	if (a <= -1.45e-39)
		tmp = t_1 + (a * (t * -4.0));
	elseif (a <= 2.45e-261)
		tmp = (b * c) + t_1;
	elseif (a <= 1.55e+73)
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = (b * c) + (-4.0 * (t * a));
	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]}, If[LessEqual[a, -1.45e-39], N[(t$95$1 + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.45e-261], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[a, 1.55e+73], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.44999999999999994e-39

   1. Initial program 76.9%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in a around inf 62.5%

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

      1. metadata-eval 62.5%

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

      2. distribute-lft-neg-in 62.5%

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

      3. *-commutative 62.5%

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

      4. associate-*l* 62.5%

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

      5. distribute-lft-neg-in 62.5%

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

      6. distribute-lft-neg-in 62.5%

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

      7. metadata-eval 62.5%

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

   7. Simplified 62.5%

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

   if -1.44999999999999994e-39 < a < 2.45000000000000002e-261

   1. Initial program 86.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in b around inf 63.4%

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

   if 2.45000000000000002e-261 < a < 1.55e73

   1. Initial program 81.8%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in j around 0 76.9%

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

   6. Taylor expanded in t around 0 55.1%

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

   if 1.55e73 < a

   1. Initial program 83.2%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in j around 0 78.5%

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

   6. Taylor expanded in x around 0 68.8%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-39}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-261}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;a \leq -6.8 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-199}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= a -6.8e+71)
     t_1
     (if (<= a 4.5e-199) (* -27.0 (* j k)) (if (<= a 5.4e+73) (* b c) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (a <= -6.8e+71) {
		tmp = t_1;
	} else if (a <= 4.5e-199) {
		tmp = -27.0 * (j * k);
	} else if (a <= 5.4e+73) {
		tmp = b * c;
	} 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 <= (-6.8d+71)) then
        tmp = t_1
    else if (a <= 4.5d-199) then
        tmp = (-27.0d0) * (j * k)
    else if (a <= 5.4d+73) then
        tmp = b * c
    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 <= -6.8e+71) {
		tmp = t_1;
	} else if (a <= 4.5e-199) {
		tmp = -27.0 * (j * k);
	} else if (a <= 5.4e+73) {
		tmp = b * c;
	} 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 <= -6.8e+71:
		tmp = t_1
	elif a <= 4.5e-199:
		tmp = -27.0 * (j * k)
	elif a <= 5.4e+73:
		tmp = b * c
	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 <= -6.8e+71)
		tmp = t_1;
	elseif (a <= 4.5e-199)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (a <= 5.4e+73)
		tmp = Float64(b * c);
	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 <= -6.8e+71)
		tmp = t_1;
	elseif (a <= 4.5e-199)
		tmp = -27.0 * (j * k);
	elseif (a <= 5.4e+73)
		tmp = b * c;
	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, -6.8e+71], t$95$1, If[LessEqual[a, 4.5e-199], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.4e+73], N[(b * c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.7999999999999997e71 or 5.3999999999999998e73 < a

   1. Initial program 81.0%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in j around 0 76.3%

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

   6. Taylor expanded in a around inf 53.9%

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

      1. *-commutative 53.9%

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

      2. *-commutative 53.9%

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

      3. associate-*l* 53.9%

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

   8. Simplified 53.9%

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

   if -6.7999999999999997e71 < a < 4.49999999999999998e-199

   1. Initial program 85.4%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in j around inf 38.0%

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

   if 4.49999999999999998e-199 < a < 5.3999999999999998e73

   1. Initial program 78.2%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in y around inf 73.5%

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

   6. Taylor expanded in b around inf 30.9%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-199}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 31.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-256}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= a -9.5e+69)
     t_1
     (if (<= a 9.6e-256)
       (* -27.0 (* j k))
       (if (<= a 1.12e+73) (* x (* i -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 = t * (a * -4.0);
	double tmp;
	if (a <= -9.5e+69) {
		tmp = t_1;
	} else if (a <= 9.6e-256) {
		tmp = -27.0 * (j * k);
	} else if (a <= 1.12e+73) {
		tmp = x * (i * -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 = t * (a * (-4.0d0))
    if (a <= (-9.5d+69)) then
        tmp = t_1
    else if (a <= 9.6d-256) then
        tmp = (-27.0d0) * (j * k)
    else if (a <= 1.12d+73) then
        tmp = x * (i * (-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 = t * (a * -4.0);
	double tmp;
	if (a <= -9.5e+69) {
		tmp = t_1;
	} else if (a <= 9.6e-256) {
		tmp = -27.0 * (j * k);
	} else if (a <= 1.12e+73) {
		tmp = x * (i * -4.0);
	} 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 <= -9.5e+69:
		tmp = t_1
	elif a <= 9.6e-256:
		tmp = -27.0 * (j * k)
	elif a <= 1.12e+73:
		tmp = x * (i * -4.0)
	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 <= -9.5e+69)
		tmp = t_1;
	elseif (a <= 9.6e-256)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (a <= 1.12e+73)
		tmp = Float64(x * Float64(i * -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 = t * (a * -4.0);
	tmp = 0.0;
	if (a <= -9.5e+69)
		tmp = t_1;
	elseif (a <= 9.6e-256)
		tmp = -27.0 * (j * k);
	elseif (a <= 1.12e+73)
		tmp = x * (i * -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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.5e+69], t$95$1, If[LessEqual[a, 9.6e-256], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.12e+73], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.4999999999999995e69 or 1.12e73 < a

   1. Initial program 81.0%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in j around 0 76.3%

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

   6. Taylor expanded in a around inf 53.9%

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

      1. *-commutative 53.9%

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

      2. *-commutative 53.9%

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

      3. associate-*l* 53.9%

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

   8. Simplified 53.9%

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

   if -9.4999999999999995e69 < a < 9.5999999999999998e-256

   1. Initial program 83.5%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in j around inf 41.0%

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

   if 9.5999999999999998e-256 < a < 1.12e73

   1. Initial program 81.8%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in y around inf 76.7%

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

   6. Taylor expanded in i around inf 30.5%

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

      1. *-commutative 30.5%

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

      2. *-commutative 30.5%

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

      3. associate-*l* 30.5%

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

      4. *-commutative 30.5%

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

   8. Simplified 30.5%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-256}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 42.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -2.55 \cdot 10^{-14} \lor \neg \left(k \leq 1.2 \cdot 10^{+189}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= k -2.55e-14) (not (<= k 1.2e+189)))
   (* -27.0 (* j k))
   (* -4.0 (+ (* x i) (* t a)))))

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 <= -2.55e-14) || !(k <= 1.2e+189)) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = -4.0 * ((x * i) + (t * a));
	}
	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 <= (-2.55d-14)) .or. (.not. (k <= 1.2d+189))) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = (-4.0d0) * ((x * i) + (t * a))
    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 <= -2.55e-14) || !(k <= 1.2e+189)) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = -4.0 * ((x * i) + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (k <= -2.55e-14) or not (k <= 1.2e+189):
		tmp = -27.0 * (j * k)
	else:
		tmp = -4.0 * ((x * i) + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((k <= -2.55e-14) || !(k <= 1.2e+189))
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((k <= -2.55e-14) || ~((k <= 1.2e+189)))
		tmp = -27.0 * (j * k);
	else
		tmp = -4.0 * ((x * i) + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[k, -2.55e-14], N[Not[LessEqual[k, 1.2e+189]], $MachinePrecision]], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -2.5499999999999999e-14 or 1.2e189 < k

   1. Initial program 79.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in j around inf 49.2%

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

   if -2.5499999999999999e-14 < k < 1.2e189

   1. Initial program 84.0%

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

   3. Taylor expanded in y around 0 79.6%

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

      1. distribute-lft-out 79.6%

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

      2. *-commutative 79.6%

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

   5. Simplified 79.6%

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

   6. Taylor expanded in j around 0 71.4%

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

   7. Taylor expanded in b around 0 48.9%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.55 \cdot 10^{-14} \lor \neg \left(k \leq 1.2 \cdot 10^{+189}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 32.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -2.1 \cdot 10^{-25} \lor \neg \left(k \leq 5.7 \cdot 10^{+104}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= k -2.1e-25) (not (<= k 5.7e+104))) (* -27.0 (* j k)) (* b c)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((k <= -2.1e-25) || !(k <= 5.7e+104)) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((k <= (-2.1d-25)) .or. (.not. (k <= 5.7d+104))) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((k <= -2.1e-25) || !(k <= 5.7e+104)) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (k <= -2.1e-25) or not (k <= 5.7e+104):
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((k <= -2.1e-25) || !(k <= 5.7e+104))
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((k <= -2.1e-25) || ~((k <= 5.7e+104)))
		tmp = -27.0 * (j * k);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[k, -2.1e-25], N[Not[LessEqual[k, 5.7e+104]], $MachinePrecision]], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -2.10000000000000002e-25 or 5.69999999999999985e104 < k

   1. Initial program 79.6%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in j around inf 44.4%

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

   if -2.10000000000000002e-25 < k < 5.69999999999999985e104

   1. Initial program 84.4%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in y around inf 74.5%

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

   6. Taylor expanded in b around inf 29.6%

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

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.1 \cdot 10^{-25} \lor \neg \left(k \leq 5.7 \cdot 10^{+104}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 32.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -1.2 \cdot 10^{-21}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 1.32 \cdot 10^{+104}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -1.2e-21)
   (* -27.0 (* j k))
   (if (<= k 1.32e+104) (* 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 <= -1.2e-21) {
		tmp = -27.0 * (j * k);
	} else if (k <= 1.32e+104) {
		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 <= (-1.2d-21)) then
        tmp = (-27.0d0) * (j * k)
    else if (k <= 1.32d+104) 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 <= -1.2e-21) {
		tmp = -27.0 * (j * k);
	} else if (k <= 1.32e+104) {
		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 <= -1.2e-21:
		tmp = -27.0 * (j * k)
	elif k <= 1.32e+104:
		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 <= -1.2e-21)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (k <= 1.32e+104)
		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 <= -1.2e-21)
		tmp = -27.0 * (j * k);
	elseif (k <= 1.32e+104)
		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, -1.2e-21], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.32e+104], N[(b * c), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -1.2e-21

   1. Initial program 80.4%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in j around inf 44.5%

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

   if -1.2e-21 < k < 1.32000000000000003e104

   1. Initial program 84.4%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in y around inf 74.5%

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

   6. Taylor expanded in b around inf 29.6%

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

   if 1.32000000000000003e104 < k

   1. Initial program 78.6%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in y around inf 73.8%

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

   6. Taylor expanded in j around inf 44.4%

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

      1. associate-*r* 44.4%

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

      2. *-commutative 44.4%

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

      3. *-commutative 44.4%

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

   8. Simplified 44.4%

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

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.2 \cdot 10^{-21}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 1.32 \cdot 10^{+104}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 23.3% 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 82.1%

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

3. Simplified 85.6%

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

5. Taylor expanded in y around inf 74.7%

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

6. Taylor expanded in b around inf 21.1%

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

7. Final simplification 21.1%

   \[\leadsto b \cdot c \]
8. Add Preprocessing

Developer target: 89.5% accurate, 0.8× 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 2024095 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (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)))