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

Percentage Accurate: 84.9% → 89.0%

Time: 24.8s

Alternatives: 25

Speedup: 0.8×

• 50.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.9% 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: 89.0% accurate, 0.5× speedup

Math

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

FPCore

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

Python

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(N[(N[(N[(b * c), $MachinePrecision] - N[(N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(z * N[(x * N[(18.0 * y), $MachinePrecision]), $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[(c * N[(b + N[(N[(j * N[(k / c), $MachinePrecision]), $MachinePrecision] * -27.0), $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 94.6%

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

   3. Simplified 93.7%

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

      1. pow1 93.7%

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

      2. associate-*l* 93.7%

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

      3. associate-*r* 93.3%

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

   6. Applied egg-rr 93.3%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 93.3%

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

      2. associate-*r* 94.6%

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

   8. Simplified 94.6%

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

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #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 21.4%

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

   5. Taylor expanded in b around inf 40.2%

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

   6. Taylor expanded in c around inf 61.3%

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

      1. *-commutative 61.3%

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

      2. associate-/l* 64.8%

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

   8. Simplified 64.8%

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

4. Final simplification 91.4%

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

Alternative 2: 54.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := \left(t \cdot a\right) \cdot -4 + t\_1\\ t_3 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ t_4 := b \cdot \left(c - j \cdot \left(27 \cdot \frac{k}{b}\right)\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+179}:\\ \;\;\;\;b \cdot \left(c + \frac{t\_1}{b}\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{+73}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{+46}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-34}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-107}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 10^{+129}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ (* (* t a) -4.0) t_1))
        (t_3 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
        (t_4 (* b (- c (* j (* 27.0 (/ k b)))))))
   (if (<= (* b c) -2e+179)
     (* b (+ c (/ t_1 b)))
     (if (<= (* b c) -1e+73)
       t_3
       (if (<= (* b c) -4e+46)
         t_4
         (if (<= (* b c) -1e-34)
           t_3
           (if (<= (* b c) -2e-82)
             t_2
             (if (<= (* b c) -1e-107)
               t_3
               (if (<= (* b c) 0.0)
                 t_2
                 (if (<= (* b c) 1e+129) t_3 t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = ((t * a) * -4.0) + t_1;
	double t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_4 = b * (c - (j * (27.0 * (k / b))));
	double tmp;
	if ((b * c) <= -2e+179) {
		tmp = b * (c + (t_1 / b));
	} else if ((b * c) <= -1e+73) {
		tmp = t_3;
	} else if ((b * c) <= -4e+46) {
		tmp = t_4;
	} else if ((b * c) <= -1e-34) {
		tmp = t_3;
	} else if ((b * c) <= -2e-82) {
		tmp = t_2;
	} else if ((b * c) <= -1e-107) {
		tmp = t_3;
	} else if ((b * c) <= 0.0) {
		tmp = t_2;
	} else if ((b * c) <= 1e+129) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = ((t * a) * (-4.0d0)) + t_1
    t_3 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    t_4 = b * (c - (j * (27.0d0 * (k / b))))
    if ((b * c) <= (-2d+179)) then
        tmp = b * (c + (t_1 / b))
    else if ((b * c) <= (-1d+73)) then
        tmp = t_3
    else if ((b * c) <= (-4d+46)) then
        tmp = t_4
    else if ((b * c) <= (-1d-34)) then
        tmp = t_3
    else if ((b * c) <= (-2d-82)) then
        tmp = t_2
    else if ((b * c) <= (-1d-107)) then
        tmp = t_3
    else if ((b * c) <= 0.0d0) then
        tmp = t_2
    else if ((b * c) <= 1d+129) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = ((t * a) * -4.0) + t_1;
	double t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_4 = b * (c - (j * (27.0 * (k / b))));
	double tmp;
	if ((b * c) <= -2e+179) {
		tmp = b * (c + (t_1 / b));
	} else if ((b * c) <= -1e+73) {
		tmp = t_3;
	} else if ((b * c) <= -4e+46) {
		tmp = t_4;
	} else if ((b * c) <= -1e-34) {
		tmp = t_3;
	} else if ((b * c) <= -2e-82) {
		tmp = t_2;
	} else if ((b * c) <= -1e-107) {
		tmp = t_3;
	} else if ((b * c) <= 0.0) {
		tmp = t_2;
	} else if ((b * c) <= 1e+129) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = ((t * a) * -4.0) + t_1
	t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	t_4 = b * (c - (j * (27.0 * (k / b))))
	tmp = 0
	if (b * c) <= -2e+179:
		tmp = b * (c + (t_1 / b))
	elif (b * c) <= -1e+73:
		tmp = t_3
	elif (b * c) <= -4e+46:
		tmp = t_4
	elif (b * c) <= -1e-34:
		tmp = t_3
	elif (b * c) <= -2e-82:
		tmp = t_2
	elif (b * c) <= -1e-107:
		tmp = t_3
	elif (b * c) <= 0.0:
		tmp = t_2
	elif (b * c) <= 1e+129:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(Float64(t * a) * -4.0) + t_1)
	t_3 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	t_4 = Float64(b * Float64(c - Float64(j * Float64(27.0 * Float64(k / b)))))
	tmp = 0.0
	if (Float64(b * c) <= -2e+179)
		tmp = Float64(b * Float64(c + Float64(t_1 / b)));
	elseif (Float64(b * c) <= -1e+73)
		tmp = t_3;
	elseif (Float64(b * c) <= -4e+46)
		tmp = t_4;
	elseif (Float64(b * c) <= -1e-34)
		tmp = t_3;
	elseif (Float64(b * c) <= -2e-82)
		tmp = t_2;
	elseif (Float64(b * c) <= -1e-107)
		tmp = t_3;
	elseif (Float64(b * c) <= 0.0)
		tmp = t_2;
	elseif (Float64(b * c) <= 1e+129)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = ((t * a) * -4.0) + t_1;
	t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	t_4 = b * (c - (j * (27.0 * (k / b))));
	tmp = 0.0;
	if ((b * c) <= -2e+179)
		tmp = b * (c + (t_1 / b));
	elseif ((b * c) <= -1e+73)
		tmp = t_3;
	elseif ((b * c) <= -4e+46)
		tmp = t_4;
	elseif ((b * c) <= -1e-34)
		tmp = t_3;
	elseif ((b * c) <= -2e-82)
		tmp = t_2;
	elseif ((b * c) <= -1e-107)
		tmp = t_3;
	elseif ((b * c) <= 0.0)
		tmp = t_2;
	elseif ((b * c) <= 1e+129)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(c - N[(j * N[(27.0 * N[(k / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+179], N[(b * N[(c + N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1e+73], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], -4e+46], t$95$4, If[LessEqual[N[(b * c), $MachinePrecision], -1e-34], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], -2e-82], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -1e-107], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 0.0], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1e+129], t$95$3, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.99999999999999996e179

   1. Initial program 87.8%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in b around inf 85.7%

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

   6. Taylor expanded in b around inf 88.1%

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

      1. associate-*r/ 88.1%

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

      2. *-commutative 88.1%

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

      3. associate-*l* 88.1%

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

   8. Simplified 88.1%

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

   if -1.99999999999999996e179 < (*.f64 b c) < -9.99999999999999983e72 or -4e46 < (*.f64 b c) < -9.99999999999999928e-35 or -2e-82 < (*.f64 b c) < -1e-107 or 0.0 < (*.f64 b c) < 1e129

   1. Initial program 88.3%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in x around inf 63.0%

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

   if -9.99999999999999983e72 < (*.f64 b c) < -4e46 or 1e129 < (*.f64 b c)

   1. Initial program 72.5%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in b around inf 77.4%

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

   6. Taylor expanded in b around -inf 82.5%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot c + 27 \cdot \frac{j \cdot k}{b}\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 82.5%

         \[\leadsto \color{blue}{-b \cdot \left(-1 \cdot c + 27 \cdot \frac{j \cdot k}{b}\right)} \]

      2. distribute-rgt-neg-in 82.5%

         \[\leadsto \color{blue}{b \cdot \left(-\left(-1 \cdot c + 27 \cdot \frac{j \cdot k}{b}\right)\right)} \]

      3. +-commutative 82.5%

         \[\leadsto b \cdot \left(-\color{blue}{\left(27 \cdot \frac{j \cdot k}{b} + -1 \cdot c\right)}\right) \]

      4. mul-1-neg 82.5%

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

      5. unsub-neg 82.5%

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

      6. *-commutative 82.5%

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

      7. associate-/l* 77.5%

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

      8. associate-*l* 77.6%

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

   8. Simplified 77.6%

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

   if -9.99999999999999928e-35 < (*.f64 b c) < -2e-82 or -1e-107 < (*.f64 b c) < 0.0

   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 88.1%

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

   5. Taylor expanded in a around inf 67.2%

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

      1. *-commutative 67.2%

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

   7. Simplified 67.2%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+179}:\\ \;\;\;\;b \cdot \left(c + \frac{j \cdot \left(k \cdot -27\right)}{b}\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(c - j \cdot \left(27 \cdot \frac{k}{b}\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-82}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4 + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4 + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+129}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c - j \cdot \left(27 \cdot \frac{k}{b}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t\_1 + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ t_3 := b \cdot \left(c - j \cdot \left(27 \cdot \frac{k}{b}\right)\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+179}:\\ \;\;\;\;b \cdot \left(c + \frac{t\_1}{b}\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{+73}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + t\_1\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{+46}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4 + t\_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+148}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ t_1 (* 18.0 (* t (* z (* x y))))))
        (t_3 (* b (- c (* j (* 27.0 (/ k b)))))))
   (if (<= (* b c) -2e+179)
     (* b (+ c (/ t_1 b)))
     (if (<= (* b c) -1e+73)
       (+ (* 18.0 (* t (* x (* y z)))) t_1)
       (if (<= (* b c) -4e+46)
         t_3
         (if (<= (* b c) -1e-34)
           t_2
           (if (<= (* b c) 0.0)
             (+ (* (* t a) -4.0) t_1)
             (if (<= (* b c) 5e-107)
               (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
               (if (<= (* b c) 2e+148) 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 = t_1 + (18.0 * (t * (z * (x * y))));
	double t_3 = b * (c - (j * (27.0 * (k / b))));
	double tmp;
	if ((b * c) <= -2e+179) {
		tmp = b * (c + (t_1 / b));
	} else if ((b * c) <= -1e+73) {
		tmp = (18.0 * (t * (x * (y * z)))) + t_1;
	} else if ((b * c) <= -4e+46) {
		tmp = t_3;
	} else if ((b * c) <= -1e-34) {
		tmp = t_2;
	} else if ((b * c) <= 0.0) {
		tmp = ((t * a) * -4.0) + t_1;
	} else if ((b * c) <= 5e-107) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if ((b * c) <= 2e+148) {
		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 = t_1 + (18.0d0 * (t * (z * (x * y))))
    t_3 = b * (c - (j * (27.0d0 * (k / b))))
    if ((b * c) <= (-2d+179)) then
        tmp = b * (c + (t_1 / b))
    else if ((b * c) <= (-1d+73)) then
        tmp = (18.0d0 * (t * (x * (y * z)))) + t_1
    else if ((b * c) <= (-4d+46)) then
        tmp = t_3
    else if ((b * c) <= (-1d-34)) then
        tmp = t_2
    else if ((b * c) <= 0.0d0) then
        tmp = ((t * a) * (-4.0d0)) + t_1
    else if ((b * c) <= 5d-107) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if ((b * c) <= 2d+148) 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 = t_1 + (18.0 * (t * (z * (x * y))));
	double t_3 = b * (c - (j * (27.0 * (k / b))));
	double tmp;
	if ((b * c) <= -2e+179) {
		tmp = b * (c + (t_1 / b));
	} else if ((b * c) <= -1e+73) {
		tmp = (18.0 * (t * (x * (y * z)))) + t_1;
	} else if ((b * c) <= -4e+46) {
		tmp = t_3;
	} else if ((b * c) <= -1e-34) {
		tmp = t_2;
	} else if ((b * c) <= 0.0) {
		tmp = ((t * a) * -4.0) + t_1;
	} else if ((b * c) <= 5e-107) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if ((b * c) <= 2e+148) {
		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 = t_1 + (18.0 * (t * (z * (x * y))))
	t_3 = b * (c - (j * (27.0 * (k / b))))
	tmp = 0
	if (b * c) <= -2e+179:
		tmp = b * (c + (t_1 / b))
	elif (b * c) <= -1e+73:
		tmp = (18.0 * (t * (x * (y * z)))) + t_1
	elif (b * c) <= -4e+46:
		tmp = t_3
	elif (b * c) <= -1e-34:
		tmp = t_2
	elif (b * c) <= 0.0:
		tmp = ((t * a) * -4.0) + t_1
	elif (b * c) <= 5e-107:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif (b * c) <= 2e+148:
		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(t_1 + Float64(18.0 * Float64(t * Float64(z * Float64(x * y)))))
	t_3 = Float64(b * Float64(c - Float64(j * Float64(27.0 * Float64(k / b)))))
	tmp = 0.0
	if (Float64(b * c) <= -2e+179)
		tmp = Float64(b * Float64(c + Float64(t_1 / b)));
	elseif (Float64(b * c) <= -1e+73)
		tmp = Float64(Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))) + t_1);
	elseif (Float64(b * c) <= -4e+46)
		tmp = t_3;
	elseif (Float64(b * c) <= -1e-34)
		tmp = t_2;
	elseif (Float64(b * c) <= 0.0)
		tmp = Float64(Float64(Float64(t * a) * -4.0) + t_1);
	elseif (Float64(b * c) <= 5e-107)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (Float64(b * c) <= 2e+148)
		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 = t_1 + (18.0 * (t * (z * (x * y))));
	t_3 = b * (c - (j * (27.0 * (k / b))));
	tmp = 0.0;
	if ((b * c) <= -2e+179)
		tmp = b * (c + (t_1 / b));
	elseif ((b * c) <= -1e+73)
		tmp = (18.0 * (t * (x * (y * z)))) + t_1;
	elseif ((b * c) <= -4e+46)
		tmp = t_3;
	elseif ((b * c) <= -1e-34)
		tmp = t_2;
	elseif ((b * c) <= 0.0)
		tmp = ((t * a) * -4.0) + t_1;
	elseif ((b * c) <= 5e-107)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif ((b * c) <= 2e+148)
		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[(t$95$1 + N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(c - N[(j * N[(27.0 * N[(k / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+179], N[(b * N[(c + N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1e+73], N[(N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -4e+46], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], -1e-34], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 0.0], N[(N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e-107], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+148], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 b c) < -1.99999999999999996e179

   1. Initial program 87.8%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in b around inf 85.7%

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

   6. Taylor expanded in b around inf 88.1%

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

      1. associate-*r/ 88.1%

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

      2. *-commutative 88.1%

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

      3. associate-*l* 88.1%

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

   8. Simplified 88.1%

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

   if -1.99999999999999996e179 < (*.f64 b c) < -9.99999999999999983e72

   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 92.7%

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

   5. Taylor expanded in y around inf 79.6%

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

   if -9.99999999999999983e72 < (*.f64 b c) < -4e46 or 2.0000000000000001e148 < (*.f64 b c)

   1. Initial program 75.4%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in b around inf 78.8%

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

   6. Taylor expanded in b around -inf 84.4%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot c + 27 \cdot \frac{j \cdot k}{b}\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 84.4%

         \[\leadsto \color{blue}{-b \cdot \left(-1 \cdot c + 27 \cdot \frac{j \cdot k}{b}\right)} \]

      2. distribute-rgt-neg-in 84.4%

         \[\leadsto \color{blue}{b \cdot \left(-\left(-1 \cdot c + 27 \cdot \frac{j \cdot k}{b}\right)\right)} \]

      3. +-commutative 84.4%

         \[\leadsto b \cdot \left(-\color{blue}{\left(27 \cdot \frac{j \cdot k}{b} + -1 \cdot c\right)}\right) \]

      4. mul-1-neg 84.4%

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

      5. unsub-neg 84.4%

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

      6. *-commutative 84.4%

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

      7. associate-/l* 79.0%

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

      8. associate-*l* 79.0%

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

   8. Simplified 79.0%

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

   if -4e46 < (*.f64 b c) < -9.99999999999999928e-35 or 4.99999999999999971e-107 < (*.f64 b c) < 2.0000000000000001e148

   1. Initial program 90.3%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in y around inf 58.0%

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

      1. associate-*r* 58.0%

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

   7. Simplified 58.0%

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

   8. Taylor expanded in t around 0 58.0%

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

      1. *-commutative 58.0%

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

      2. associate-*r* 65.7%

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

   10. Simplified 65.7%

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

   if -9.99999999999999928e-35 < (*.f64 b c) < 0.0

   1. Initial program 86.2%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in a around inf 61.8%

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

      1. *-commutative 61.8%

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

   7. Simplified 61.8%

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

   if 0.0 < (*.f64 b c) < 4.99999999999999971e-107

   1. Initial program 83.4%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in x around inf 71.7%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+179}:\\ \;\;\;\;b \cdot \left(c + \frac{j \cdot \left(k \cdot -27\right)}{b}\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{+73}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(c - j \cdot \left(27 \cdot \frac{k}{b}\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-34}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4 + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+148}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c - j \cdot \left(27 \cdot \frac{k}{b}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 35.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+179}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+175}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* t (* x (* y z))))))
   (if (<= (* b c) -2e+179)
     (* b c)
     (if (<= (* b c) -1e+73)
       t_1
       (if (<= (* b c) -4e+46)
         (* b c)
         (if (<= (* b c) -1e-34)
           t_1
           (if (<= (* b c) 0.0)
             (* t (* a -4.0))
             (if (<= (* b c) 1e+175) t_1 (* b c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if ((b * c) <= -2e+179) {
		tmp = b * c;
	} else if ((b * c) <= -1e+73) {
		tmp = t_1;
	} else if ((b * c) <= -4e+46) {
		tmp = b * c;
	} else if ((b * c) <= -1e-34) {
		tmp = t_1;
	} else if ((b * c) <= 0.0) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 1e+175) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (t * (x * (y * z)))
    if ((b * c) <= (-2d+179)) then
        tmp = b * c
    else if ((b * c) <= (-1d+73)) then
        tmp = t_1
    else if ((b * c) <= (-4d+46)) then
        tmp = b * c
    else if ((b * c) <= (-1d-34)) then
        tmp = t_1
    else if ((b * c) <= 0.0d0) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= 1d+175) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if ((b * c) <= -2e+179) {
		tmp = b * c;
	} else if ((b * c) <= -1e+73) {
		tmp = t_1;
	} else if ((b * c) <= -4e+46) {
		tmp = b * c;
	} else if ((b * c) <= -1e-34) {
		tmp = t_1;
	} else if ((b * c) <= 0.0) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 1e+175) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (t * (x * (y * z)))
	tmp = 0
	if (b * c) <= -2e+179:
		tmp = b * c
	elif (b * c) <= -1e+73:
		tmp = t_1
	elif (b * c) <= -4e+46:
		tmp = b * c
	elif (b * c) <= -1e-34:
		tmp = t_1
	elif (b * c) <= 0.0:
		tmp = t * (a * -4.0)
	elif (b * c) <= 1e+175:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (Float64(b * c) <= -2e+179)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1e+73)
		tmp = t_1;
	elseif (Float64(b * c) <= -4e+46)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1e-34)
		tmp = t_1;
	elseif (Float64(b * c) <= 0.0)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= 1e+175)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (t * (x * (y * z)));
	tmp = 0.0;
	if ((b * c) <= -2e+179)
		tmp = b * c;
	elseif ((b * c) <= -1e+73)
		tmp = t_1;
	elseif ((b * c) <= -4e+46)
		tmp = b * c;
	elseif ((b * c) <= -1e-34)
		tmp = t_1;
	elseif ((b * c) <= 0.0)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= 1e+175)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+179], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1e+73], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -4e+46], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1e-34], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 0.0], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+175], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.99999999999999996e179 or -9.99999999999999983e72 < (*.f64 b c) < -4e46 or 9.9999999999999994e174 < (*.f64 b c)

   1. Initial program 82.4%

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

   3. Simplified 83.5%

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

      1. pow1 83.5%

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

      2. associate-*l* 83.5%

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

      3. associate-*r* 83.5%

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

   6. Applied egg-rr 83.5%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 83.5%

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

      2. associate-*r* 83.5%

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

   8. Simplified 83.5%

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

   9. Taylor expanded in b around inf 79.0%

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

   if -1.99999999999999996e179 < (*.f64 b c) < -9.99999999999999983e72 or -4e46 < (*.f64 b c) < -9.99999999999999928e-35 or 0.0 < (*.f64 b c) < 9.9999999999999994e174

   1. Initial program 84.7%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in j around 0 71.0%

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

   6. Taylor expanded in x around inf 70.2%

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

   7. Taylor expanded in y around inf 43.2%

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

   if -9.99999999999999928e-35 < (*.f64 b c) < 0.0

   1. Initial program 86.2%

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

   3. Taylor expanded in t around -inf 49.1%

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

      1. associate-*r* 49.1%

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

      2. neg-mul-1 49.1%

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

      3. cancel-sign-sub-inv 49.1%

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

      4. *-commutative 49.1%

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

      5. metadata-eval 49.1%

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

      6. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in x around 0 36.1%

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

      1. *-commutative 36.1%

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

      2. associate-*r* 36.1%

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

      3. *-commutative 36.1%

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

      4. associate-*l* 36.1%

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

   8. Simplified 36.1%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+179}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{+73}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-34}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+175}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 35.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+179}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+175}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* t (* x (* y z))))))
   (if (<= (* b c) -2e+179)
     (* b c)
     (if (<= (* b c) -1e+73)
       t_1
       (if (<= (* b c) -4e+46)
         (* b c)
         (if (<= (* b c) -1e-34)
           t_1
           (if (<= (* b c) 0.0)
             (* t (* a -4.0))
             (if (<= (* b c) 1e+175)
               (* 18.0 (* (* y z) (* x t)))
               (* b c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if ((b * c) <= -2e+179) {
		tmp = b * c;
	} else if ((b * c) <= -1e+73) {
		tmp = t_1;
	} else if ((b * c) <= -4e+46) {
		tmp = b * c;
	} else if ((b * c) <= -1e-34) {
		tmp = t_1;
	} else if ((b * c) <= 0.0) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 1e+175) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (t * (x * (y * z)))
    if ((b * c) <= (-2d+179)) then
        tmp = b * c
    else if ((b * c) <= (-1d+73)) then
        tmp = t_1
    else if ((b * c) <= (-4d+46)) then
        tmp = b * c
    else if ((b * c) <= (-1d-34)) then
        tmp = t_1
    else if ((b * c) <= 0.0d0) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= 1d+175) then
        tmp = 18.0d0 * ((y * z) * (x * t))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if ((b * c) <= -2e+179) {
		tmp = b * c;
	} else if ((b * c) <= -1e+73) {
		tmp = t_1;
	} else if ((b * c) <= -4e+46) {
		tmp = b * c;
	} else if ((b * c) <= -1e-34) {
		tmp = t_1;
	} else if ((b * c) <= 0.0) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 1e+175) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (t * (x * (y * z)))
	tmp = 0
	if (b * c) <= -2e+179:
		tmp = b * c
	elif (b * c) <= -1e+73:
		tmp = t_1
	elif (b * c) <= -4e+46:
		tmp = b * c
	elif (b * c) <= -1e-34:
		tmp = t_1
	elif (b * c) <= 0.0:
		tmp = t * (a * -4.0)
	elif (b * c) <= 1e+175:
		tmp = 18.0 * ((y * z) * (x * t))
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (Float64(b * c) <= -2e+179)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1e+73)
		tmp = t_1;
	elseif (Float64(b * c) <= -4e+46)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1e-34)
		tmp = t_1;
	elseif (Float64(b * c) <= 0.0)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= 1e+175)
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (t * (x * (y * z)));
	tmp = 0.0;
	if ((b * c) <= -2e+179)
		tmp = b * c;
	elseif ((b * c) <= -1e+73)
		tmp = t_1;
	elseif ((b * c) <= -4e+46)
		tmp = b * c;
	elseif ((b * c) <= -1e-34)
		tmp = t_1;
	elseif ((b * c) <= 0.0)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= 1e+175)
		tmp = 18.0 * ((y * z) * (x * t));
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+179], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1e+73], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -4e+46], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1e-34], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 0.0], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+175], N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.99999999999999996e179 or -9.99999999999999983e72 < (*.f64 b c) < -4e46 or 9.9999999999999994e174 < (*.f64 b c)

   1. Initial program 82.4%

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

   3. Simplified 83.5%

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

      1. pow1 83.5%

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

      2. associate-*l* 83.5%

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

      3. associate-*r* 83.5%

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

   6. Applied egg-rr 83.5%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 83.5%

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

      2. associate-*r* 83.5%

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

   8. Simplified 83.5%

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

   9. Taylor expanded in b around inf 79.0%

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

   if -1.99999999999999996e179 < (*.f64 b c) < -9.99999999999999983e72 or -4e46 < (*.f64 b c) < -9.99999999999999928e-35

   1. Initial program 89.2%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in j around 0 78.7%

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

   6. Taylor expanded in x around inf 68.6%

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

   7. Taylor expanded in y around inf 58.1%

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

   if -9.99999999999999928e-35 < (*.f64 b c) < 0.0

   1. Initial program 86.2%

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

   3. Taylor expanded in t around -inf 49.1%

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

      1. associate-*r* 49.1%

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

      2. neg-mul-1 49.1%

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

      3. cancel-sign-sub-inv 49.1%

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

      4. *-commutative 49.1%

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

      5. metadata-eval 49.1%

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

      6. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in x around 0 36.1%

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

      1. *-commutative 36.1%

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

      2. associate-*r* 36.1%

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

      3. *-commutative 36.1%

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

      4. associate-*l* 36.1%

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

   8. Simplified 36.1%

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

   if 0.0 < (*.f64 b c) < 9.9999999999999994e174

   1. Initial program 83.0%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in j around 0 68.2%

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

   6. Taylor expanded in x around inf 70.8%

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

   7. Taylor expanded in y around inf 37.6%

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

      1. associate-*r* 38.7%

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

   9. Simplified 38.7%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+179}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{+73}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-34}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+175}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 35.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot \left(x \cdot y\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+179}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{+73}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+175}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* z (* x y)) (* 18.0 t))))
   (if (<= (* b c) -2e+179)
     (* b c)
     (if (<= (* b c) -1e+73)
       (* 18.0 (* t (* x (* y z))))
       (if (<= (* b c) -4e+46)
         (* b c)
         (if (<= (* b c) -1e-34)
           t_1
           (if (<= (* b c) 0.0)
             (* t (* a -4.0))
             (if (<= (* b c) 1e+175) t_1 (* b c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (z * (x * y)) * (18.0 * t);
	double tmp;
	if ((b * c) <= -2e+179) {
		tmp = b * c;
	} else if ((b * c) <= -1e+73) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= -4e+46) {
		tmp = b * c;
	} else if ((b * c) <= -1e-34) {
		tmp = t_1;
	} else if ((b * c) <= 0.0) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 1e+175) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * (x * y)) * (18.0d0 * t)
    if ((b * c) <= (-2d+179)) then
        tmp = b * c
    else if ((b * c) <= (-1d+73)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if ((b * c) <= (-4d+46)) then
        tmp = b * c
    else if ((b * c) <= (-1d-34)) then
        tmp = t_1
    else if ((b * c) <= 0.0d0) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= 1d+175) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (z * (x * y)) * (18.0 * t);
	double tmp;
	if ((b * c) <= -2e+179) {
		tmp = b * c;
	} else if ((b * c) <= -1e+73) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= -4e+46) {
		tmp = b * c;
	} else if ((b * c) <= -1e-34) {
		tmp = t_1;
	} else if ((b * c) <= 0.0) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 1e+175) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (z * (x * y)) * (18.0 * t)
	tmp = 0
	if (b * c) <= -2e+179:
		tmp = b * c
	elif (b * c) <= -1e+73:
		tmp = 18.0 * (t * (x * (y * z)))
	elif (b * c) <= -4e+46:
		tmp = b * c
	elif (b * c) <= -1e-34:
		tmp = t_1
	elif (b * c) <= 0.0:
		tmp = t * (a * -4.0)
	elif (b * c) <= 1e+175:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(z * Float64(x * y)) * Float64(18.0 * t))
	tmp = 0.0
	if (Float64(b * c) <= -2e+179)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1e+73)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (Float64(b * c) <= -4e+46)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1e-34)
		tmp = t_1;
	elseif (Float64(b * c) <= 0.0)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= 1e+175)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (z * (x * y)) * (18.0 * t);
	tmp = 0.0;
	if ((b * c) <= -2e+179)
		tmp = b * c;
	elseif ((b * c) <= -1e+73)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif ((b * c) <= -4e+46)
		tmp = b * c;
	elseif ((b * c) <= -1e-34)
		tmp = t_1;
	elseif ((b * c) <= 0.0)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= 1e+175)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+179], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1e+73], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -4e+46], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1e-34], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 0.0], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+175], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.99999999999999996e179 or -9.99999999999999983e72 < (*.f64 b c) < -4e46 or 9.9999999999999994e174 < (*.f64 b c)

   1. Initial program 82.4%

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

   3. Simplified 83.5%

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

      1. pow1 83.5%

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

      2. associate-*l* 83.5%

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

      3. associate-*r* 83.5%

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

   6. Applied egg-rr 83.5%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 83.5%

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

      2. associate-*r* 83.5%

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

   8. Simplified 83.5%

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

   9. Taylor expanded in b around inf 79.0%

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

   if -1.99999999999999996e179 < (*.f64 b c) < -9.99999999999999983e72

   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 92.7%

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

   5. Taylor expanded in j around 0 71.5%

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

   6. Taylor expanded in x around inf 71.5%

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

   7. Taylor expanded in y around inf 58.3%

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

   if -4e46 < (*.f64 b c) < -9.99999999999999928e-35 or 0.0 < (*.f64 b c) < 9.9999999999999994e174

   1. Initial program 85.7%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in j around 0 71.0%

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

   6. Taylor expanded in x around inf 70.1%

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

   7. Taylor expanded in y around inf 40.8%

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

      1. *-commutative 40.8%

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

      2. associate-*r* 44.1%

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

      3. *-commutative 44.1%

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

      4. associate-*l* 44.2%

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

      5. *-commutative 44.2%

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

   9. Simplified 44.2%

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

   if -9.99999999999999928e-35 < (*.f64 b c) < 0.0

   1. Initial program 86.2%

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

   3. Taylor expanded in t around -inf 49.1%

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

      1. associate-*r* 49.1%

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

      2. neg-mul-1 49.1%

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

      3. cancel-sign-sub-inv 49.1%

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

      4. *-commutative 49.1%

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

      5. metadata-eval 49.1%

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

      6. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in x around 0 36.1%

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

      1. *-commutative 36.1%

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

      2. associate-*r* 36.1%

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

      3. *-commutative 36.1%

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

      4. associate-*l* 36.1%

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

   8. Simplified 36.1%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+179}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{+73}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-34}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+175}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + \left(t \cdot a\right) \cdot -4\\ t_2 := \left(z \cdot \left(x \cdot y\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+191}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-213}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+134}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* (* t a) -4.0))) (t_2 (* (* z (* x y)) (* 18.0 t))))
   (if (<= t -1.35e+191)
     t_2
     (if (<= t -4.4e+156)
       t_1
       (if (<= t -1.8e+85)
         t_2
         (if (<= t -1.05e+58)
           t_1
           (if (<= t 4.9e-213)
             (- (* b c) (* 4.0 (* x i)))
             (if (<= t 3.3e+134)
               (+ (* b c) (* j (* k -27.0)))
               (* 18.0 (* t (* x (* y z))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + ((t * a) * -4.0);
	double t_2 = (z * (x * y)) * (18.0 * t);
	double tmp;
	if (t <= -1.35e+191) {
		tmp = t_2;
	} else if (t <= -4.4e+156) {
		tmp = t_1;
	} else if (t <= -1.8e+85) {
		tmp = t_2;
	} else if (t <= -1.05e+58) {
		tmp = t_1;
	} else if (t <= 4.9e-213) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 3.3e+134) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = 18.0 * (t * (x * (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + ((t * a) * (-4.0d0))
    t_2 = (z * (x * y)) * (18.0d0 * t)
    if (t <= (-1.35d+191)) then
        tmp = t_2
    else if (t <= (-4.4d+156)) then
        tmp = t_1
    else if (t <= (-1.8d+85)) then
        tmp = t_2
    else if (t <= (-1.05d+58)) then
        tmp = t_1
    else if (t <= 4.9d-213) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t <= 3.3d+134) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = 18.0d0 * (t * (x * (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + ((t * a) * -4.0);
	double t_2 = (z * (x * y)) * (18.0 * t);
	double tmp;
	if (t <= -1.35e+191) {
		tmp = t_2;
	} else if (t <= -4.4e+156) {
		tmp = t_1;
	} else if (t <= -1.8e+85) {
		tmp = t_2;
	} else if (t <= -1.05e+58) {
		tmp = t_1;
	} else if (t <= 4.9e-213) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 3.3e+134) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = 18.0 * (t * (x * (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + ((t * a) * -4.0)
	t_2 = (z * (x * y)) * (18.0 * t)
	tmp = 0
	if t <= -1.35e+191:
		tmp = t_2
	elif t <= -4.4e+156:
		tmp = t_1
	elif t <= -1.8e+85:
		tmp = t_2
	elif t <= -1.05e+58:
		tmp = t_1
	elif t <= 4.9e-213:
		tmp = (b * c) - (4.0 * (x * i))
	elif t <= 3.3e+134:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = 18.0 * (t * (x * (y * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0))
	t_2 = Float64(Float64(z * Float64(x * y)) * Float64(18.0 * t))
	tmp = 0.0
	if (t <= -1.35e+191)
		tmp = t_2;
	elseif (t <= -4.4e+156)
		tmp = t_1;
	elseif (t <= -1.8e+85)
		tmp = t_2;
	elseif (t <= -1.05e+58)
		tmp = t_1;
	elseif (t <= 4.9e-213)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t <= 3.3e+134)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + ((t * a) * -4.0);
	t_2 = (z * (x * y)) * (18.0 * t);
	tmp = 0.0;
	if (t <= -1.35e+191)
		tmp = t_2;
	elseif (t <= -4.4e+156)
		tmp = t_1;
	elseif (t <= -1.8e+85)
		tmp = t_2;
	elseif (t <= -1.05e+58)
		tmp = t_1;
	elseif (t <= 4.9e-213)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t <= 3.3e+134)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = 18.0 * (t * (x * (y * z)));
	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[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+191], t$95$2, If[LessEqual[t, -4.4e+156], t$95$1, If[LessEqual[t, -1.8e+85], t$95$2, If[LessEqual[t, -1.05e+58], t$95$1, If[LessEqual[t, 4.9e-213], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+134], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.34999999999999998e191 or -4.40000000000000008e156 < t < -1.7999999999999999e85

   1. Initial program 90.2%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in j around 0 78.2%

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

   6. Taylor expanded in x around inf 63.1%

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

   7. Taylor expanded in y around inf 51.7%

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

      1. *-commutative 51.7%

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

      2. associate-*r* 54.1%

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

      3. *-commutative 54.1%

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

      4. associate-*l* 54.1%

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

      5. *-commutative 54.1%

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

   9. Simplified 54.1%

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

   if -1.34999999999999998e191 < t < -4.40000000000000008e156 or -1.7999999999999999e85 < t < -1.05000000000000006e58

   1. Initial program 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in j around 0 89.2%

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

   6. Taylor expanded in x around inf 89.1%

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

   7. Taylor expanded in x around 0 76.8%

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

   if -1.05000000000000006e58 < t < 4.8999999999999998e-213

   1. Initial program 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in j around 0 70.9%

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

   6. Taylor expanded in t around 0 67.0%

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

   if 4.8999999999999998e-213 < t < 3.3e134

   1. Initial program 82.8%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in b around inf 61.0%

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

   if 3.3e134 < 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 85.7%

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

   5. Taylor expanded in j around 0 82.9%

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

   6. Taylor expanded in x around inf 66.0%

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

   7. Taylor expanded in y around inf 54.9%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+191}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+156}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+85}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+58}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-213}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+134}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot \left(--18\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-214}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 30000 \lor \neg \left(t \leq 1.55 \cdot 10^{+64}\right) \land t \leq 7.4 \cdot 10^{+115}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (- (* (* x y) (* z (- -18.0))) (* a 4.0)))))
   (if (<= t -7.6e+44)
     t_1
     (if (<= t 5.5e-214)
       (- (* b c) (* 4.0 (* x i)))
       (if (or (<= t 30000.0) (and (not (<= t 1.55e+64)) (<= t 7.4e+115)))
         (+ (* b c) (* j (* k -27.0)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (((x * y) * (z * -(-18.0))) - (a * 4.0));
	double tmp;
	if (t <= -7.6e+44) {
		tmp = t_1;
	} else if (t <= 5.5e-214) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((t <= 30000.0) || (!(t <= 1.55e+64) && (t <= 7.4e+115))) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (((x * y) * (z * -(-18.0d0))) - (a * 4.0d0))
    if (t <= (-7.6d+44)) then
        tmp = t_1
    else if (t <= 5.5d-214) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if ((t <= 30000.0d0) .or. (.not. (t <= 1.55d+64)) .and. (t <= 7.4d+115)) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (((x * y) * (z * -(-18.0))) - (a * 4.0));
	double tmp;
	if (t <= -7.6e+44) {
		tmp = t_1;
	} else if (t <= 5.5e-214) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((t <= 30000.0) || (!(t <= 1.55e+64) && (t <= 7.4e+115))) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (((x * y) * (z * -(-18.0))) - (a * 4.0))
	tmp = 0
	if t <= -7.6e+44:
		tmp = t_1
	elif t <= 5.5e-214:
		tmp = (b * c) - (4.0 * (x * i))
	elif (t <= 30000.0) or (not (t <= 1.55e+64) and (t <= 7.4e+115)):
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(Float64(x * y) * Float64(z * Float64(-(-18.0)))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -7.6e+44)
		tmp = t_1;
	elseif (t <= 5.5e-214)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif ((t <= 30000.0) || (!(t <= 1.55e+64) && (t <= 7.4e+115)))
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (((x * y) * (z * -(-18.0))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -7.6e+44)
		tmp = t_1;
	elseif (t <= 5.5e-214)
		tmp = (b * c) - (4.0 * (x * i));
	elseif ((t <= 30000.0) || (~((t <= 1.55e+64)) && (t <= 7.4e+115)))
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(N[(x * y), $MachinePrecision] * N[(z * (--18.0)), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.6e+44], t$95$1, If[LessEqual[t, 5.5e-214], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 30000.0], And[N[Not[LessEqual[t, 1.55e+64]], $MachinePrecision], LessEqual[t, 7.4e+115]]], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.6000000000000004e44 or 3e4 < t < 1.55e64 or 7.40000000000000012e115 < t

   1. Initial program 85.8%

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

   3. Taylor expanded in t around -inf 75.8%

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

      1. associate-*r* 75.8%

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

      2. neg-mul-1 75.8%

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

      3. cancel-sign-sub-inv 75.8%

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

      4. *-commutative 75.8%

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

      5. metadata-eval 75.8%

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

      6. *-commutative 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in x around 0 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-*r* 76.7%

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

      3. associate-*l* 76.7%

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

   8. Simplified 76.7%

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

   if -7.6000000000000004e44 < t < 5.50000000000000024e-214

   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 83.2%

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

   5. Taylor expanded in j around 0 70.6%

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

   6. Taylor expanded in t around 0 67.7%

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

   if 5.50000000000000024e-214 < t < 3e4 or 1.55e64 < t < 7.40000000000000012e115

   1. Initial program 83.0%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in b around inf 69.4%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot \left(--18\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-214}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 30000 \lor \neg \left(t \leq 1.55 \cdot 10^{+64}\right) \land t \leq 7.4 \cdot 10^{+115}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot \left(--18\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \left(-27 \cdot \frac{j \cdot k}{y} + 18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-22}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+235} \lor \neg \left(z \leq 8.5 \cdot 10^{+256}\right):\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z -3.7e-29)
   (* y (+ (* -27.0 (/ (* j k) y)) (* 18.0 (* t (* x z)))))
   (if (<= z 4.1e-22)
     (- (- (- (* b c) (* 4.0 (* t a))) (* (* x 4.0) i)) (* k (* j 27.0)))
     (if (or (<= z 2.6e+235) (not (<= z 8.5e+256)))
       (- (+ (* b c) (* 18.0 (* t (* x (* y z))))) (* 27.0 (* j k)))
       (- (+ (* b c) (* (* t 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 tmp;
	if (z <= -3.7e-29) {
		tmp = y * ((-27.0 * ((j * k) / y)) + (18.0 * (t * (x * z))));
	} else if (z <= 4.1e-22) {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0));
	} else if ((z <= 2.6e+235) || !(z <= 8.5e+256)) {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (27.0 * (j * k));
	} else {
		tmp = ((b * c) + ((t * 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) :: tmp
    if (z <= (-3.7d-29)) then
        tmp = y * (((-27.0d0) * ((j * k) / y)) + (18.0d0 * (t * (x * z))))
    else if (z <= 4.1d-22) then
        tmp = (((b * c) - (4.0d0 * (t * a))) - ((x * 4.0d0) * i)) - (k * (j * 27.0d0))
    else if ((z <= 2.6d+235) .or. (.not. (z <= 8.5d+256))) then
        tmp = ((b * c) + (18.0d0 * (t * (x * (y * z))))) - (27.0d0 * (j * k))
    else
        tmp = ((b * c) + ((t * 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 tmp;
	if (z <= -3.7e-29) {
		tmp = y * ((-27.0 * ((j * k) / y)) + (18.0 * (t * (x * z))));
	} else if (z <= 4.1e-22) {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0));
	} else if ((z <= 2.6e+235) || !(z <= 8.5e+256)) {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (27.0 * (j * k));
	} else {
		tmp = ((b * c) + ((t * a) * -4.0)) - (4.0 * (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if z <= -3.7e-29:
		tmp = y * ((-27.0 * ((j * k) / y)) + (18.0 * (t * (x * z))))
	elif z <= 4.1e-22:
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0))
	elif (z <= 2.6e+235) or not (z <= 8.5e+256):
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (27.0 * (j * k))
	else:
		tmp = ((b * c) + ((t * a) * -4.0)) - (4.0 * (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= -3.7e-29)
		tmp = Float64(y * Float64(Float64(-27.0 * Float64(Float64(j * k) / y)) + Float64(18.0 * Float64(t * Float64(x * z)))));
	elseif (z <= 4.1e-22)
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(x * 4.0) * i)) - Float64(k * Float64(j * 27.0)));
	elseif ((z <= 2.6e+235) || !(z <= 8.5e+256))
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(t * 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)
	tmp = 0.0;
	if (z <= -3.7e-29)
		tmp = y * ((-27.0 * ((j * k) / y)) + (18.0 * (t * (x * z))));
	elseif (z <= 4.1e-22)
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0));
	elseif ((z <= 2.6e+235) || ~((z <= 8.5e+256)))
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (27.0 * (j * k));
	else
		tmp = ((b * c) + ((t * a) * -4.0)) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, -3.7e-29], 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], If[LessEqual[z, 4.1e-22], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2.6e+235], N[Not[LessEqual[z, 8.5e+256]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.6999999999999997e-29

   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 81.2%

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

   5. Taylor expanded in y around inf 52.3%

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

      1. associate-*r* 50.8%

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

   7. Simplified 50.8%

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

   8. Taylor expanded in y around inf 58.6%

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

   if -3.6999999999999997e-29 < z < 4.0999999999999999e-22

   1. Initial program 89.6%

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

   3. Taylor expanded in x around 0 87.9%

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

   if 4.0999999999999999e-22 < z < 2.5999999999999998e235 or 8.5000000000000006e256 < z

   1. Initial program 82.8%

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

   3. Simplified 76.8%

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

      1. pow1 76.8%

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

      2. associate-*l* 76.7%

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

      3. associate-*r* 76.8%

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

   6. Applied egg-rr 76.8%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 76.8%

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

      2. associate-*r* 84.4%

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

   8. Simplified 84.4%

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

   9. Taylor expanded in x around inf 75.3%

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

       1. associate-*r* 75.1%

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

       2. *-commutative 75.1%

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

       3. associate-*r* 75.2%

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

       4. *-commutative 75.2%

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

       5. associate-*r* 81.4%

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

   11. Simplified 81.4%

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

   12. Taylor expanded in i around 0 73.9%

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

   if 2.5999999999999998e235 < z < 8.5000000000000006e256

   1. Initial program 27.0%

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

   3. Simplified 42.3%

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

   5. Taylor expanded in j around 0 42.3%

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

   6. Taylor expanded in y around 0 51.8%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \left(-27 \cdot \frac{j \cdot k}{y} + 18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-22}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+235} \lor \neg \left(z \leq 8.5 \cdot 10^{+256}\right):\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+194} \lor \neg \left(y \leq 4.1 \cdot 10^{-94}\right):\\ \;\;\;\;\left(b \cdot c + y \cdot \left(z \cdot \left(18 \cdot \left(x \cdot t\right)\right)\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - \left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* x (* 4.0 i)) (* j (* 27.0 k)))))
   (if (or (<= y -7.5e+194) (not (<= y 4.1e-94)))
     (- (+ (* b c) (* y (* z (* 18.0 (* x t))))) t_1)
     (- (- (* b c) (* t (- (* a 4.0) (* (* x 18.0) (* y z))))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * (4.0 * i)) + (j * (27.0 * k));
	double tmp;
	if ((y <= -7.5e+194) || !(y <= 4.1e-94)) {
		tmp = ((b * c) + (y * (z * (18.0 * (x * t))))) - t_1;
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - ((x * 18.0) * (y * z))))) - 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 = (x * (4.0d0 * i)) + (j * (27.0d0 * k))
    if ((y <= (-7.5d+194)) .or. (.not. (y <= 4.1d-94))) then
        tmp = ((b * c) + (y * (z * (18.0d0 * (x * t))))) - t_1
    else
        tmp = ((b * c) - (t * ((a * 4.0d0) - ((x * 18.0d0) * (y * z))))) - 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 = (x * (4.0 * i)) + (j * (27.0 * k));
	double tmp;
	if ((y <= -7.5e+194) || !(y <= 4.1e-94)) {
		tmp = ((b * c) + (y * (z * (18.0 * (x * t))))) - t_1;
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - ((x * 18.0) * (y * z))))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * (4.0 * i)) + (j * (27.0 * k))
	tmp = 0
	if (y <= -7.5e+194) or not (y <= 4.1e-94):
		tmp = ((b * c) + (y * (z * (18.0 * (x * t))))) - t_1
	else:
		tmp = ((b * c) - (t * ((a * 4.0) - ((x * 18.0) * (y * z))))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k)))
	tmp = 0.0
	if ((y <= -7.5e+194) || !(y <= 4.1e-94))
		tmp = Float64(Float64(Float64(b * c) + Float64(y * Float64(z * Float64(18.0 * Float64(x * t))))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(Float64(x * 18.0) * Float64(y * z))))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * (4.0 * i)) + (j * (27.0 * k));
	tmp = 0.0;
	if ((y <= -7.5e+194) || ~((y <= 4.1e-94)))
		tmp = ((b * c) + (y * (z * (18.0 * (x * t))))) - t_1;
	else
		tmp = ((b * c) - (t * ((a * 4.0) - ((x * 18.0) * (y * z))))) - 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[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -7.5e+194], N[Not[LessEqual[y, 4.1e-94]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(y * N[(z * N[(18.0 * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5000000000000002e194 or 4.10000000000000001e-94 < y

   1. Initial program 76.6%

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

   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. Step-by-step derivation

      1. pow1 74.9%

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

      2. associate-*l* 74.8%

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

      3. associate-*r* 73.9%

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

   6. Applied egg-rr 73.9%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 73.9%

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

      2. associate-*r* 77.5%

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

   8. Simplified 77.5%

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

   9. Taylor expanded in x around inf 71.1%

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

       1. associate-*r* 73.6%

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

       2. *-commutative 73.6%

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

       3. associate-*r* 73.6%

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

       4. *-commutative 73.6%

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

       5. associate-*r* 81.5%

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

   11. Simplified 81.5%

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

   if -7.5000000000000002e194 < y < 4.10000000000000001e-94

   1. Initial program 89.9%

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

   3. Simplified 92.5%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+194} \lor \neg \left(y \leq 4.1 \cdot 10^{-94}\right):\\ \;\;\;\;\left(b \cdot c + y \cdot \left(z \cdot \left(18 \cdot \left(x \cdot t\right)\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - \left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 4 \leq -2 \cdot 10^{-38}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;a \cdot 4 \leq 5 \cdot 10^{+114}:\\ \;\;\;\;\left(b \cdot c + y \cdot \left(z \cdot \left(18 \cdot \left(x \cdot t\right)\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* a 4.0) -2e-38)
   (- (- (- (* b c) (* 4.0 (* t a))) (* (* x 4.0) i)) (* k (* j 27.0)))
   (if (<= (* a 4.0) 5e+114)
     (-
      (+ (* b c) (* y (* z (* 18.0 (* x t)))))
      (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
     (-
      (- (* b c) (* t (- (* a 4.0) (* 18.0 (* x (* y z))))))
      (* 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 tmp;
	if ((a * 4.0) <= -2e-38) {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0));
	} else if ((a * 4.0) <= 5e+114) {
		tmp = ((b * c) + (y * (z * (18.0 * (x * t))))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (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) :: tmp
    if ((a * 4.0d0) <= (-2d-38)) then
        tmp = (((b * c) - (4.0d0 * (t * a))) - ((x * 4.0d0) * i)) - (k * (j * 27.0d0))
    else if ((a * 4.0d0) <= 5d+114) then
        tmp = ((b * c) + (y * (z * (18.0d0 * (x * t))))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = ((b * c) - (t * ((a * 4.0d0) - (18.0d0 * (x * (y * z)))))) - (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 tmp;
	if ((a * 4.0) <= -2e-38) {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0));
	} else if ((a * 4.0) <= 5e+114) {
		tmp = ((b * c) + (y * (z * (18.0 * (x * t))))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (a * 4.0) <= -2e-38:
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0))
	elif (a * 4.0) <= 5e+114:
		tmp = ((b * c) + (y * (z * (18.0 * (x * t))))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(a * 4.0) <= -2e-38)
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(x * 4.0) * i)) - Float64(k * Float64(j * 27.0)));
	elseif (Float64(a * 4.0) <= 5e+114)
		tmp = Float64(Float64(Float64(b * c) + Float64(y * Float64(z * Float64(18.0 * Float64(x * t))))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(18.0 * Float64(x * Float64(y * z)))))) - 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)
	tmp = 0.0;
	if ((a * 4.0) <= -2e-38)
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0));
	elseif ((a * 4.0) <= 5e+114)
		tmp = ((b * c) + (y * (z * (18.0 * (x * t))))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(a * 4.0), $MachinePrecision], -2e-38], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 4.0), $MachinePrecision], 5e+114], N[(N[(N[(b * c), $MachinePrecision] + N[(y * N[(z * N[(18.0 * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 4 binary64)) < -1.9999999999999999e-38

   1. Initial program 84.5%

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

   3. Taylor expanded in x around 0 83.3%

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

   if -1.9999999999999999e-38 < (*.f64 a #s(literal 4 binary64)) < 5.0000000000000001e114

   1. Initial program 87.1%

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

   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. Step-by-step derivation

      1. pow1 85.6%

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

      2. associate-*l* 85.6%

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

      3. associate-*r* 85.6%

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

   6. Applied egg-rr 85.6%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 85.6%

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

      2. associate-*r* 87.8%

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

   8. Simplified 87.8%

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

   9. Taylor expanded in x around inf 82.7%

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

       1. associate-*r* 83.4%

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

       2. *-commutative 83.4%

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

       3. associate-*r* 83.4%

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

       4. *-commutative 83.4%

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

       5. associate-*r* 86.9%

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

   11. Simplified 86.9%

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

   if 5.0000000000000001e114 < (*.f64 a #s(literal 4 binary64))

   1. Initial program 73.6%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in j around 0 81.6%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 4 \leq -2 \cdot 10^{-38}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;a \cdot 4 \leq 5 \cdot 10^{+114}:\\ \;\;\;\;\left(b \cdot c + y \cdot \left(z \cdot \left(18 \cdot \left(x \cdot t\right)\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ t_2 := c \cdot \left(b + \left(j \cdot \frac{k}{c}\right) \cdot -27\right)\\ \mathbf{if}\;c \leq -7.2 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;c \leq 2.95 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+72}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* k -27.0)) (* (* x i) -4.0)))
        (t_2 (* c (+ b (* (* j (/ k c)) -27.0)))))
   (if (<= c -7.2e+62)
     t_2
     (if (<= c 6e-171)
       t_1
       (if (<= c 3.3e-113)
         (* t (* a -4.0))
         (if (<= c 2.95e-43)
           t_1
           (if (<= c 1.55e+72) (+ (* b c) (* (* t a) -4.0)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + ((x * i) * -4.0);
	double t_2 = c * (b + ((j * (k / c)) * -27.0));
	double tmp;
	if (c <= -7.2e+62) {
		tmp = t_2;
	} else if (c <= 6e-171) {
		tmp = t_1;
	} else if (c <= 3.3e-113) {
		tmp = t * (a * -4.0);
	} else if (c <= 2.95e-43) {
		tmp = t_1;
	} else if (c <= 1.55e+72) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + ((x * i) * (-4.0d0))
    t_2 = c * (b + ((j * (k / c)) * (-27.0d0)))
    if (c <= (-7.2d+62)) then
        tmp = t_2
    else if (c <= 6d-171) then
        tmp = t_1
    else if (c <= 3.3d-113) then
        tmp = t * (a * (-4.0d0))
    else if (c <= 2.95d-43) then
        tmp = t_1
    else if (c <= 1.55d+72) then
        tmp = (b * c) + ((t * a) * (-4.0d0))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + ((x * i) * -4.0);
	double t_2 = c * (b + ((j * (k / c)) * -27.0));
	double tmp;
	if (c <= -7.2e+62) {
		tmp = t_2;
	} else if (c <= 6e-171) {
		tmp = t_1;
	} else if (c <= 3.3e-113) {
		tmp = t * (a * -4.0);
	} else if (c <= 2.95e-43) {
		tmp = t_1;
	} else if (c <= 1.55e+72) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * -27.0)) + ((x * i) * -4.0)
	t_2 = c * (b + ((j * (k / c)) * -27.0))
	tmp = 0
	if c <= -7.2e+62:
		tmp = t_2
	elif c <= 6e-171:
		tmp = t_1
	elif c <= 3.3e-113:
		tmp = t * (a * -4.0)
	elif c <= 2.95e-43:
		tmp = t_1
	elif c <= 1.55e+72:
		tmp = (b * c) + ((t * a) * -4.0)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * -27.0)) + Float64(Float64(x * i) * -4.0))
	t_2 = Float64(c * Float64(b + Float64(Float64(j * Float64(k / c)) * -27.0)))
	tmp = 0.0
	if (c <= -7.2e+62)
		tmp = t_2;
	elseif (c <= 6e-171)
		tmp = t_1;
	elseif (c <= 3.3e-113)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (c <= 2.95e-43)
		tmp = t_1;
	elseif (c <= 1.55e+72)
		tmp = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + ((x * i) * -4.0);
	t_2 = c * (b + ((j * (k / c)) * -27.0));
	tmp = 0.0;
	if (c <= -7.2e+62)
		tmp = t_2;
	elseif (c <= 6e-171)
		tmp = t_1;
	elseif (c <= 3.3e-113)
		tmp = t * (a * -4.0);
	elseif (c <= 2.95e-43)
		tmp = t_1;
	elseif (c <= 1.55e+72)
		tmp = (b * c) + ((t * a) * -4.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(b + N[(N[(j * N[(k / c), $MachinePrecision]), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.2e+62], t$95$2, If[LessEqual[c, 6e-171], t$95$1, If[LessEqual[c, 3.3e-113], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.95e-43], t$95$1, If[LessEqual[c, 1.55e+72], N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -7.2e62 or 1.54999999999999994e72 < c

   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 83.5%

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

   5. Taylor expanded in b around inf 70.8%

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

   6. Taylor expanded in c around inf 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-/l* 75.4%

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

   8. Simplified 75.4%

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

   if -7.2e62 < c < 5.9999999999999999e-171 or 3.3000000000000002e-113 < c < 2.94999999999999988e-43

   1. Initial program 87.6%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in i around inf 49.0%

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

   if 5.9999999999999999e-171 < c < 3.3000000000000002e-113

   1. Initial program 75.4%

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

   3. Taylor expanded in t around -inf 72.8%

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

      1. associate-*r* 72.8%

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

      2. neg-mul-1 72.8%

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

      3. cancel-sign-sub-inv 72.8%

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

      4. *-commutative 72.8%

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

      5. metadata-eval 72.8%

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

      6. *-commutative 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in x around 0 42.1%

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

      1. *-commutative 42.1%

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

      2. associate-*r* 42.1%

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

      3. *-commutative 42.1%

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

      4. associate-*l* 42.1%

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

   8. Simplified 42.1%

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

   if 2.94999999999999988e-43 < c < 1.54999999999999994e72

   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 72.8%

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

   5. Taylor expanded in j around 0 65.9%

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

   6. Taylor expanded in x around inf 52.4%

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

   7. Taylor expanded in x around 0 57.9%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{+62}:\\ \;\;\;\;c \cdot \left(b + \left(j \cdot \frac{k}{c}\right) \cdot -27\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-171}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;c \leq 2.95 \cdot 10^{-43}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+72}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + \left(j \cdot \frac{k}{c}\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := 27 \cdot \left(j \cdot k\right)\\ t_3 := t \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot \left(--18\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+44}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-63}:\\ \;\;\;\;b \cdot c - \left(t\_1 + t\_2\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+59}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - t\_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+115}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i)))
        (t_2 (* 27.0 (* j k)))
        (t_3 (* t (- (* (* x y) (* z (- -18.0))) (* a 4.0)))))
   (if (<= t -3.6e+44)
     t_3
     (if (<= t 8.4e-63)
       (- (* b c) (+ t_1 t_2))
       (if (<= t 5.2e+59)
         (- (+ (* b c) (* 18.0 (* t (* x (* y z))))) t_1)
         (if (<= t 8e+115) (- (+ (* b c) (* (* t a) -4.0)) 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 = 4.0 * (x * i);
	double t_2 = 27.0 * (j * k);
	double t_3 = t * (((x * y) * (z * -(-18.0))) - (a * 4.0));
	double tmp;
	if (t <= -3.6e+44) {
		tmp = t_3;
	} else if (t <= 8.4e-63) {
		tmp = (b * c) - (t_1 + t_2);
	} else if (t <= 5.2e+59) {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - t_1;
	} else if (t <= 8e+115) {
		tmp = ((b * c) + ((t * a) * -4.0)) - 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 = 4.0d0 * (x * i)
    t_2 = 27.0d0 * (j * k)
    t_3 = t * (((x * y) * (z * -(-18.0d0))) - (a * 4.0d0))
    if (t <= (-3.6d+44)) then
        tmp = t_3
    else if (t <= 8.4d-63) then
        tmp = (b * c) - (t_1 + t_2)
    else if (t <= 5.2d+59) then
        tmp = ((b * c) + (18.0d0 * (t * (x * (y * z))))) - t_1
    else if (t <= 8d+115) then
        tmp = ((b * c) + ((t * a) * (-4.0d0))) - 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 = 4.0 * (x * i);
	double t_2 = 27.0 * (j * k);
	double t_3 = t * (((x * y) * (z * -(-18.0))) - (a * 4.0));
	double tmp;
	if (t <= -3.6e+44) {
		tmp = t_3;
	} else if (t <= 8.4e-63) {
		tmp = (b * c) - (t_1 + t_2);
	} else if (t <= 5.2e+59) {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - t_1;
	} else if (t <= 8e+115) {
		tmp = ((b * c) + ((t * a) * -4.0)) - t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = 27.0 * (j * k)
	t_3 = t * (((x * y) * (z * -(-18.0))) - (a * 4.0))
	tmp = 0
	if t <= -3.6e+44:
		tmp = t_3
	elif t <= 8.4e-63:
		tmp = (b * c) - (t_1 + t_2)
	elif t <= 5.2e+59:
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - t_1
	elif t <= 8e+115:
		tmp = ((b * c) + ((t * a) * -4.0)) - t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(27.0 * Float64(j * k))
	t_3 = Float64(t * Float64(Float64(Float64(x * y) * Float64(z * Float64(-(-18.0)))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -3.6e+44)
		tmp = t_3;
	elseif (t <= 8.4e-63)
		tmp = Float64(Float64(b * c) - Float64(t_1 + t_2));
	elseif (t <= 5.2e+59)
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))) - t_1);
	elseif (t <= 8e+115)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - 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 = 4.0 * (x * i);
	t_2 = 27.0 * (j * k);
	t_3 = t * (((x * y) * (z * -(-18.0))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -3.6e+44)
		tmp = t_3;
	elseif (t <= 8.4e-63)
		tmp = (b * c) - (t_1 + t_2);
	elseif (t <= 5.2e+59)
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - t_1;
	elseif (t <= 8e+115)
		tmp = ((b * c) + ((t * a) * -4.0)) - 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[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(N[(x * y), $MachinePrecision] * N[(z * (--18.0)), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e+44], t$95$3, If[LessEqual[t, 8.4e-63], N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+59], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 8e+115], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.6e44 or 8.0000000000000001e115 < t

   1. Initial program 85.9%

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

   3. Taylor expanded in t around -inf 76.1%

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

      1. associate-*r* 76.1%

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

      2. neg-mul-1 76.1%

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

      3. cancel-sign-sub-inv 76.1%

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

      4. *-commutative 76.1%

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

      5. metadata-eval 76.1%

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

      6. *-commutative 76.1%

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

   5. Simplified 76.1%

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

   6. Taylor expanded in x around 0 76.1%

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

      1. *-commutative 76.1%

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

      2. associate-*r* 77.9%

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

      3. associate-*l* 77.9%

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

   8. Simplified 77.9%

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

   if -3.6e44 < t < 8.4e-63

   1. Initial program 80.9%

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

   3. Simplified 80.1%

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

   5. Taylor expanded in t around 0 80.6%

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

   if 8.4e-63 < t < 5.19999999999999999e59

   1. Initial program 92.7%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in j around 0 87.2%

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

   6. Taylor expanded in a around 0 74.8%

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

   if 5.19999999999999999e59 < t < 8.0000000000000001e115

   1. Initial program 90.0%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in x around 0 90.5%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot \left(--18\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-63}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+59}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+115}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot \left(--18\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 71.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot \left(--18\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+63} \lor \neg \left(t \leq 7.4 \cdot 10^{+115}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (- (* (* x y) (* z (- -18.0))) (* a 4.0)))))
   (if (<= t -2.25e+33)
     t_1
     (if (<= t 1.4e-9)
       (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))
       (if (or (<= t 1.3e+63) (not (<= t 7.4e+115)))
         t_1
         (+ (* b c) (* j (* k -27.0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (((x * y) * (z * -(-18.0))) - (a * 4.0));
	double tmp;
	if (t <= -2.25e+33) {
		tmp = t_1;
	} else if (t <= 1.4e-9) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else if ((t <= 1.3e+63) || !(t <= 7.4e+115)) {
		tmp = t_1;
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (((x * y) * (z * -(-18.0d0))) - (a * 4.0d0))
    if (t <= (-2.25d+33)) then
        tmp = t_1
    else if (t <= 1.4d-9) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    else if ((t <= 1.3d+63) .or. (.not. (t <= 7.4d+115))) then
        tmp = t_1
    else
        tmp = (b * c) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (((x * y) * (z * -(-18.0))) - (a * 4.0));
	double tmp;
	if (t <= -2.25e+33) {
		tmp = t_1;
	} else if (t <= 1.4e-9) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else if ((t <= 1.3e+63) || !(t <= 7.4e+115)) {
		tmp = t_1;
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (((x * y) * (z * -(-18.0))) - (a * 4.0))
	tmp = 0
	if t <= -2.25e+33:
		tmp = t_1
	elif t <= 1.4e-9:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	elif (t <= 1.3e+63) or not (t <= 7.4e+115):
		tmp = t_1
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(Float64(x * y) * Float64(z * Float64(-(-18.0)))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -2.25e+33)
		tmp = t_1;
	elseif (t <= 1.4e-9)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	elseif ((t <= 1.3e+63) || !(t <= 7.4e+115))
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (((x * y) * (z * -(-18.0))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -2.25e+33)
		tmp = t_1;
	elseif (t <= 1.4e-9)
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	elseif ((t <= 1.3e+63) || ~((t <= 7.4e+115)))
		tmp = t_1;
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(N[(x * y), $MachinePrecision] * N[(z * (--18.0)), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.25e+33], t$95$1, If[LessEqual[t, 1.4e-9], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.3e+63], N[Not[LessEqual[t, 7.4e+115]], $MachinePrecision]], t$95$1, N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.25e33 or 1.39999999999999992e-9 < t < 1.3000000000000001e63 or 7.40000000000000012e115 < t

   1. Initial program 86.0%

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

   3. Taylor expanded in t around -inf 75.3%

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

      1. associate-*r* 75.3%

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

      2. neg-mul-1 75.3%

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

      3. cancel-sign-sub-inv 75.3%

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

      4. *-commutative 75.3%

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

      5. metadata-eval 75.3%

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

      6. *-commutative 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in x around 0 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*r* 76.2%

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

      3. associate-*l* 76.2%

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

   8. Simplified 76.2%

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

   if -2.25e33 < t < 1.39999999999999992e-9

   1. Initial program 82.5%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in t around 0 80.0%

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

   if 1.3000000000000001e63 < t < 7.40000000000000012e115

   1. Initial program 88.9%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in b around inf 89.2%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot \left(--18\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+63} \lor \neg \left(t \leq 7.4 \cdot 10^{+115}\right):\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot \left(--18\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 73.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := t \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot \left(--18\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-80}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + t\_1\right)\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+116}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 27.0 (* j k)))
        (t_2 (* t (- (* (* x y) (* z (- -18.0))) (* a 4.0)))))
   (if (<= t -1.7e+49)
     t_2
     (if (<= t 1.55e-80)
       (- (* b c) (+ (* 4.0 (* x i)) t_1))
       (if (<= t 2.55e+116)
         (- (+ (* b c) (* 18.0 (* t (* x (* y z))))) 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 = 27.0 * (j * k);
	double t_2 = t * (((x * y) * (z * -(-18.0))) - (a * 4.0));
	double tmp;
	if (t <= -1.7e+49) {
		tmp = t_2;
	} else if (t <= 1.55e-80) {
		tmp = (b * c) - ((4.0 * (x * i)) + t_1);
	} else if (t <= 2.55e+116) {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - 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 = 27.0d0 * (j * k)
    t_2 = t * (((x * y) * (z * -(-18.0d0))) - (a * 4.0d0))
    if (t <= (-1.7d+49)) then
        tmp = t_2
    else if (t <= 1.55d-80) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + t_1)
    else if (t <= 2.55d+116) then
        tmp = ((b * c) + (18.0d0 * (t * (x * (y * z))))) - 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 = 27.0 * (j * k);
	double t_2 = t * (((x * y) * (z * -(-18.0))) - (a * 4.0));
	double tmp;
	if (t <= -1.7e+49) {
		tmp = t_2;
	} else if (t <= 1.55e-80) {
		tmp = (b * c) - ((4.0 * (x * i)) + t_1);
	} else if (t <= 2.55e+116) {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (j * k)
	t_2 = t * (((x * y) * (z * -(-18.0))) - (a * 4.0))
	tmp = 0
	if t <= -1.7e+49:
		tmp = t_2
	elif t <= 1.55e-80:
		tmp = (b * c) - ((4.0 * (x * i)) + t_1)
	elif t <= 2.55e+116:
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	t_2 = Float64(t * Float64(Float64(Float64(x * y) * Float64(z * Float64(-(-18.0)))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -1.7e+49)
		tmp = t_2;
	elseif (t <= 1.55e-80)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + t_1));
	elseif (t <= 2.55e+116)
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))) - 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 = 27.0 * (j * k);
	t_2 = t * (((x * y) * (z * -(-18.0))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -1.7e+49)
		tmp = t_2;
	elseif (t <= 1.55e-80)
		tmp = (b * c) - ((4.0 * (x * i)) + t_1);
	elseif (t <= 2.55e+116)
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - 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[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(N[(x * y), $MachinePrecision] * N[(z * (--18.0)), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+49], t$95$2, If[LessEqual[t, 1.55e-80], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.55e+116], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7e49 or 2.55e116 < t

   1. Initial program 85.9%

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

   3. Taylor expanded in t around -inf 76.1%

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

      1. associate-*r* 76.1%

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

      2. neg-mul-1 76.1%

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

      3. cancel-sign-sub-inv 76.1%

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

      4. *-commutative 76.1%

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

      5. metadata-eval 76.1%

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

      6. *-commutative 76.1%

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

   5. Simplified 76.1%

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

   6. Taylor expanded in x around 0 76.1%

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

      1. *-commutative 76.1%

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

      2. associate-*r* 77.9%

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

      3. associate-*l* 77.9%

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

   8. Simplified 77.9%

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

   if -1.7e49 < t < 1.55000000000000008e-80

   1. Initial program 82.2%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in t around 0 81.1%

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

   if 1.55000000000000008e-80 < t < 2.55e116

   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 91.5%

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

      1. pow1 91.5%

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

      2. associate-*l* 91.5%

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

      3. associate-*r* 91.5%

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

   6. Applied egg-rr 91.5%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 91.5%

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

      2. associate-*r* 86.8%

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

   8. Simplified 86.8%

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

   9. Taylor expanded in x around inf 80.4%

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

       1. associate-*r* 80.4%

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

       2. *-commutative 80.4%

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

       3. associate-*r* 80.4%

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

       4. *-commutative 80.4%

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

       5. associate-*r* 80.3%

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

   11. Simplified 80.3%

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

   12. Taylor expanded in i around 0 83.4%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot \left(--18\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-80}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+116}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot \left(--18\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 73.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;k \cdot \left(b \cdot \frac{c}{k} - j \cdot 27\right)\\ \mathbf{elif}\;k \leq 3.4 \cdot 10^{+138}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -2.05e+21)
   (* k (- (* b (/ c k)) (* j 27.0)))
   (if (<= k 3.4e+138)
     (- (- (* b c) (* t (- (* a 4.0) (* 18.0 (* x (* y z)))))) (* 4.0 (* x i)))
     (- (- (- (* b c) (* 4.0 (* t a))) (* (* x 4.0) i)) (* 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 <= -2.05e+21) {
		tmp = k * ((b * (c / k)) - (j * 27.0));
	} else if (k <= 3.4e+138) {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	} else {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (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 <= (-2.05d+21)) then
        tmp = k * ((b * (c / k)) - (j * 27.0d0))
    else if (k <= 3.4d+138) then
        tmp = ((b * c) - (t * ((a * 4.0d0) - (18.0d0 * (x * (y * z)))))) - (4.0d0 * (x * i))
    else
        tmp = (((b * c) - (4.0d0 * (t * a))) - ((x * 4.0d0) * i)) - (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 <= -2.05e+21) {
		tmp = k * ((b * (c / k)) - (j * 27.0));
	} else if (k <= 3.4e+138) {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	} else {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -2.05e+21:
		tmp = k * ((b * (c / k)) - (j * 27.0))
	elif k <= 3.4e+138:
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i))
	else:
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -2.05e+21)
		tmp = Float64(k * Float64(Float64(b * Float64(c / k)) - Float64(j * 27.0)));
	elseif (k <= 3.4e+138)
		tmp = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(18.0 * Float64(x * Float64(y * z)))))) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(x * 4.0) * i)) - 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 <= -2.05e+21)
		tmp = k * ((b * (c / k)) - (j * 27.0));
	elseif (k <= 3.4e+138)
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	else
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -2.05e+21], N[(k * N[(N[(b * N[(c / k), $MachinePrecision]), $MachinePrecision] - N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.4e+138], N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -2.05e21

   1. Initial program 77.9%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in b around inf 51.3%

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

   6. Taylor expanded in k around -inf 51.3%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(-1 \cdot \frac{b \cdot c}{k} + 27 \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 51.3%

         \[\leadsto \color{blue}{-k \cdot \left(-1 \cdot \frac{b \cdot c}{k} + 27 \cdot j\right)} \]

      2. *-commutative 51.3%

         \[\leadsto -\color{blue}{\left(-1 \cdot \frac{b \cdot c}{k} + 27 \cdot j\right) \cdot k} \]

      3. distribute-rgt-neg-in 51.3%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{b \cdot c}{k} + 27 \cdot j\right) \cdot \left(-k\right)} \]

      4. +-commutative 51.3%

         \[\leadsto \color{blue}{\left(27 \cdot j + -1 \cdot \frac{b \cdot c}{k}\right)} \cdot \left(-k\right) \]

      5. mul-1-neg 51.3%

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

      6. unsub-neg 51.3%

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

      7. associate-/l* 57.7%

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

   8. Simplified 57.7%

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

   if -2.05e21 < k < 3.40000000000000011e138

   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 87.3%

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

   5. Taylor expanded in j around 0 80.8%

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

   if 3.40000000000000011e138 < k

   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 x around 0 90.5%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;k \cdot \left(b \cdot \frac{c}{k} - j \cdot 27\right)\\ \mathbf{elif}\;k \leq 3.4 \cdot 10^{+138}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 47.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{if}\;k \leq -4.5 \cdot 10^{+98}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 2.6 \cdot 10^{+19}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{elif}\;k \leq 1.45 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* (* t a) -4.0))))
   (if (<= k -4.5e+98)
     (* -27.0 (* j k))
     (if (<= k 2.9e-27)
       t_1
       (if (<= k 2.6e+19)
         (* (* z (* x y)) (* 18.0 t))
         (if (<= k 1.45e+138) t_1 (+ (* b c) (* j (* k -27.0)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + ((t * a) * -4.0);
	double tmp;
	if (k <= -4.5e+98) {
		tmp = -27.0 * (j * k);
	} else if (k <= 2.9e-27) {
		tmp = t_1;
	} else if (k <= 2.6e+19) {
		tmp = (z * (x * y)) * (18.0 * t);
	} else if (k <= 1.45e+138) {
		tmp = t_1;
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + ((t * a) * (-4.0d0))
    if (k <= (-4.5d+98)) then
        tmp = (-27.0d0) * (j * k)
    else if (k <= 2.9d-27) then
        tmp = t_1
    else if (k <= 2.6d+19) then
        tmp = (z * (x * y)) * (18.0d0 * t)
    else if (k <= 1.45d+138) then
        tmp = t_1
    else
        tmp = (b * c) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + ((t * a) * -4.0);
	double tmp;
	if (k <= -4.5e+98) {
		tmp = -27.0 * (j * k);
	} else if (k <= 2.9e-27) {
		tmp = t_1;
	} else if (k <= 2.6e+19) {
		tmp = (z * (x * y)) * (18.0 * t);
	} else if (k <= 1.45e+138) {
		tmp = t_1;
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + ((t * a) * -4.0)
	tmp = 0
	if k <= -4.5e+98:
		tmp = -27.0 * (j * k)
	elif k <= 2.9e-27:
		tmp = t_1
	elif k <= 2.6e+19:
		tmp = (z * (x * y)) * (18.0 * t)
	elif k <= 1.45e+138:
		tmp = t_1
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0))
	tmp = 0.0
	if (k <= -4.5e+98)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (k <= 2.9e-27)
		tmp = t_1;
	elseif (k <= 2.6e+19)
		tmp = Float64(Float64(z * Float64(x * y)) * Float64(18.0 * t));
	elseif (k <= 1.45e+138)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + ((t * a) * -4.0);
	tmp = 0.0;
	if (k <= -4.5e+98)
		tmp = -27.0 * (j * k);
	elseif (k <= 2.9e-27)
		tmp = t_1;
	elseif (k <= 2.6e+19)
		tmp = (z * (x * y)) * (18.0 * t);
	elseif (k <= 1.45e+138)
		tmp = t_1;
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -4.5e+98], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.9e-27], t$95$1, If[LessEqual[k, 2.6e+19], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.45e+138], t$95$1, N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -4.5000000000000002e98

   1. Initial program 71.0%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in j around inf 37.2%

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

   if -4.5000000000000002e98 < k < 2.90000000000000004e-27 or 2.6e19 < k < 1.45000000000000005e138

   1. Initial program 88.3%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in j around 0 83.1%

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

   6. Taylor expanded in x around inf 77.5%

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

   7. Taylor expanded in x around 0 52.1%

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

   if 2.90000000000000004e-27 < k < 2.6e19

   1. Initial program 82.3%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in j around 0 55.1%

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

   6. Taylor expanded in x around inf 64.1%

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

   7. Taylor expanded in y around inf 38.5%

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

      1. *-commutative 38.5%

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

      2. associate-*r* 47.3%

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

      3. *-commutative 47.3%

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

      4. associate-*l* 47.4%

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

      5. *-commutative 47.4%

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

   9. Simplified 47.4%

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

   if 1.45000000000000005e138 < k

   1. Initial program 83.9%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in b around inf 68.5%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -4.5 \cdot 10^{+98}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-27}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;k \leq 2.6 \cdot 10^{+19}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{elif}\;k \leq 1.45 \cdot 10^{+138}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(b + \left(j \cdot \frac{k}{c}\right) \cdot -27\right)\\ \mathbf{if}\;c \leq -7.5 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-171}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;c \leq 3.25 \cdot 10^{+35}:\\ \;\;\;\;k \cdot \left(j \cdot -27 + -4 \cdot \frac{t \cdot a}{k}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* c (+ b (* (* j (/ k c)) -27.0)))))
   (if (<= c -7.5e+62)
     t_1
     (if (<= c 3.5e-171)
       (+ (* j (* k -27.0)) (* (* x i) -4.0))
       (if (<= c 3.25e+35)
         (* k (+ (* j -27.0) (* -4.0 (/ (* t a) k))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = c * (b + ((j * (k / c)) * -27.0));
	double tmp;
	if (c <= -7.5e+62) {
		tmp = t_1;
	} else if (c <= 3.5e-171) {
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0);
	} else if (c <= 3.25e+35) {
		tmp = k * ((j * -27.0) + (-4.0 * ((t * a) / k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (b + ((j * (k / c)) * (-27.0d0)))
    if (c <= (-7.5d+62)) then
        tmp = t_1
    else if (c <= 3.5d-171) then
        tmp = (j * (k * (-27.0d0))) + ((x * i) * (-4.0d0))
    else if (c <= 3.25d+35) then
        tmp = k * ((j * (-27.0d0)) + ((-4.0d0) * ((t * a) / k)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = c * (b + ((j * (k / c)) * -27.0));
	double tmp;
	if (c <= -7.5e+62) {
		tmp = t_1;
	} else if (c <= 3.5e-171) {
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0);
	} else if (c <= 3.25e+35) {
		tmp = k * ((j * -27.0) + (-4.0 * ((t * a) / k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = c * (b + ((j * (k / c)) * -27.0))
	tmp = 0
	if c <= -7.5e+62:
		tmp = t_1
	elif c <= 3.5e-171:
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0)
	elif c <= 3.25e+35:
		tmp = k * ((j * -27.0) + (-4.0 * ((t * a) / k)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(c * Float64(b + Float64(Float64(j * Float64(k / c)) * -27.0)))
	tmp = 0.0
	if (c <= -7.5e+62)
		tmp = t_1;
	elseif (c <= 3.5e-171)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(Float64(x * i) * -4.0));
	elseif (c <= 3.25e+35)
		tmp = Float64(k * Float64(Float64(j * -27.0) + Float64(-4.0 * Float64(Float64(t * a) / k))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = c * (b + ((j * (k / c)) * -27.0));
	tmp = 0.0;
	if (c <= -7.5e+62)
		tmp = t_1;
	elseif (c <= 3.5e-171)
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0);
	elseif (c <= 3.25e+35)
		tmp = k * ((j * -27.0) + (-4.0 * ((t * a) / k)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(c * N[(b + N[(N[(j * N[(k / c), $MachinePrecision]), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.5e+62], t$95$1, If[LessEqual[c, 3.5e-171], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.25e+35], N[(k * N[(N[(j * -27.0), $MachinePrecision] + N[(-4.0 * N[(N[(t * a), $MachinePrecision] / k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -7.49999999999999998e62 or 3.2500000000000002e35 < c

   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 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 b around inf 70.7%

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

   6. Taylor expanded in c around inf 74.2%

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

      1. *-commutative 74.2%

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

      2. associate-/l* 75.1%

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

   8. Simplified 75.1%

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

   if -7.49999999999999998e62 < c < 3.49999999999999994e-171

   1. Initial program 88.8%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in i around inf 50.4%

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

   if 3.49999999999999994e-171 < c < 3.2500000000000002e35

   1. Initial program 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in a around inf 53.5%

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

      1. *-commutative 53.5%

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

   7. Simplified 53.5%

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

   8. Taylor expanded in k around inf 48.8%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.5 \cdot 10^{+62}:\\ \;\;\;\;c \cdot \left(b + \left(j \cdot \frac{k}{c}\right) \cdot -27\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-171}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;c \leq 3.25 \cdot 10^{+35}:\\ \;\;\;\;k \cdot \left(j \cdot -27 + -4 \cdot \frac{t \cdot a}{k}\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + \left(j \cdot \frac{k}{c}\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.9 \cdot 10^{+38}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 7.5 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 6.8 \cdot 10^{+174}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1.9e+38)
   (* b c)
   (if (<= (* b c) 7.5e-42)
     (* t (* a -4.0))
     (if (<= (* b c) 6.8e+174) (* -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 ((b * c) <= -1.9e+38) {
		tmp = b * c;
	} else if ((b * c) <= 7.5e-42) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 6.8e+174) {
		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 ((b * c) <= (-1.9d+38)) then
        tmp = b * c
    else if ((b * c) <= 7.5d-42) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= 6.8d+174) 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 ((b * c) <= -1.9e+38) {
		tmp = b * c;
	} else if ((b * c) <= 7.5e-42) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 6.8e+174) {
		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 (b * c) <= -1.9e+38:
		tmp = b * c
	elif (b * c) <= 7.5e-42:
		tmp = t * (a * -4.0)
	elif (b * c) <= 6.8e+174:
		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 (Float64(b * c) <= -1.9e+38)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 7.5e-42)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= 6.8e+174)
		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 ((b * c) <= -1.9e+38)
		tmp = b * c;
	elseif ((b * c) <= 7.5e-42)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= 6.8e+174)
		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[LessEqual[N[(b * c), $MachinePrecision], -1.9e+38], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 7.5e-42], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 6.8e+174], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.8999999999999999e38 or 6.8000000000000002e174 < (*.f64 b c)

   1. Initial program 82.2%

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

   3. Simplified 85.0%

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

      1. pow1 85.0%

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

      2. associate-*l* 85.0%

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

      3. associate-*r* 85.0%

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

   6. Applied egg-rr 85.0%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 85.0%

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

      2. associate-*r* 84.1%

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

   8. Simplified 84.1%

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

   9. Taylor expanded in b around inf 67.5%

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

   if -1.8999999999999999e38 < (*.f64 b c) < 7.49999999999999972e-42

   1. Initial program 87.9%

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

   3. Taylor expanded in t around -inf 51.9%

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

      1. associate-*r* 51.9%

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

      2. neg-mul-1 51.9%

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

      3. cancel-sign-sub-inv 51.9%

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

      4. *-commutative 51.9%

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

      5. metadata-eval 51.9%

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

      6. *-commutative 51.9%

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

   5. Simplified 51.9%

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

   6. Taylor expanded in x around 0 29.4%

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

      1. *-commutative 29.4%

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

      2. associate-*r* 29.4%

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

      3. *-commutative 29.4%

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

      4. associate-*l* 29.4%

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

   8. Simplified 29.4%

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

   if 7.49999999999999972e-42 < (*.f64 b c) < 6.8000000000000002e174

   1. Initial program 77.0%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in j around inf 34.9%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.9 \cdot 10^{+38}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 7.5 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 6.8 \cdot 10^{+174}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 34.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+38}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+170}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1e+38)
   (* b c)
   (if (<= (* b c) 0.0)
     (* t (* a -4.0))
     (if (<= (* b c) 2e+170) (* i (* x -4.0)) (* b c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1e+38) {
		tmp = b * c;
	} else if ((b * c) <= 0.0) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 2e+170) {
		tmp = i * (x * -4.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-1d+38)) then
        tmp = b * c
    else if ((b * c) <= 0.0d0) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= 2d+170) then
        tmp = i * (x * (-4.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1e+38) {
		tmp = b * c;
	} else if ((b * c) <= 0.0) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 2e+170) {
		tmp = i * (x * -4.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1e+38:
		tmp = b * c
	elif (b * c) <= 0.0:
		tmp = t * (a * -4.0)
	elif (b * c) <= 2e+170:
		tmp = i * (x * -4.0)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1e+38)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 0.0)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= 2e+170)
		tmp = Float64(i * Float64(x * -4.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1e+38)
		tmp = b * c;
	elseif ((b * c) <= 0.0)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= 2e+170)
		tmp = i * (x * -4.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -1e+38], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 0.0], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+170], N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -9.99999999999999977e37 or 2.00000000000000007e170 < (*.f64 b c)

   1. Initial program 81.5%

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

   3. Simplified 84.2%

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

      1. pow1 84.2%

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

      2. associate-*l* 84.2%

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

      3. associate-*r* 84.2%

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

   6. Applied egg-rr 84.2%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 84.2%

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

      2. associate-*r* 83.3%

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

   8. Simplified 83.3%

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

   9. Taylor expanded in b around inf 66.9%

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

   if -9.99999999999999977e37 < (*.f64 b c) < 0.0

   1. Initial program 88.4%

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

   3. Taylor expanded in t around -inf 52.2%

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

      1. associate-*r* 52.2%

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

      2. neg-mul-1 52.2%

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

      3. cancel-sign-sub-inv 52.2%

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

      4. *-commutative 52.2%

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

      5. metadata-eval 52.2%

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

      6. *-commutative 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in x around 0 32.1%

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

      1. *-commutative 32.1%

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

      2. associate-*r* 32.1%

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

      3. *-commutative 32.1%

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

      4. associate-*l* 32.1%

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

   8. Simplified 32.1%

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

   if 0.0 < (*.f64 b c) < 2.00000000000000007e170

   1. Initial program 84.1%

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

   3. Simplified 82.9%

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

      1. pow1 82.9%

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

      2. associate-*l* 82.9%

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

      3. associate-*r* 82.9%

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

   6. Applied egg-rr 82.9%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 82.9%

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

      2. associate-*r* 85.6%

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

   8. Simplified 85.6%

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

   9. Taylor expanded in i around inf 32.2%

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

       1. *-commutative 32.2%

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

       2. associate-*r* 32.2%

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

       3. *-commutative 32.2%

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

   11. Simplified 32.2%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+38}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+170}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 51.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := c \cdot \left(b + \left(j \cdot \frac{k}{c}\right) \cdot -27\right)\\ \mathbf{if}\;c \leq -6.8 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-171}:\\ \;\;\;\;t\_1 + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;c \leq 3.35 \cdot 10^{+34}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4 + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (* c (+ b (* (* j (/ k c)) -27.0)))))
   (if (<= c -6.8e+62)
     t_2
     (if (<= c 4.5e-171)
       (+ t_1 (* (* x i) -4.0))
       (if (<= c 3.35e+34) (+ (* (* t a) -4.0) 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 * (k * -27.0);
	double t_2 = c * (b + ((j * (k / c)) * -27.0));
	double tmp;
	if (c <= -6.8e+62) {
		tmp = t_2;
	} else if (c <= 4.5e-171) {
		tmp = t_1 + ((x * i) * -4.0);
	} else if (c <= 3.35e+34) {
		tmp = ((t * a) * -4.0) + 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 * (k * (-27.0d0))
    t_2 = c * (b + ((j * (k / c)) * (-27.0d0)))
    if (c <= (-6.8d+62)) then
        tmp = t_2
    else if (c <= 4.5d-171) then
        tmp = t_1 + ((x * i) * (-4.0d0))
    else if (c <= 3.35d+34) then
        tmp = ((t * a) * (-4.0d0)) + 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 * (k * -27.0);
	double t_2 = c * (b + ((j * (k / c)) * -27.0));
	double tmp;
	if (c <= -6.8e+62) {
		tmp = t_2;
	} else if (c <= 4.5e-171) {
		tmp = t_1 + ((x * i) * -4.0);
	} else if (c <= 3.35e+34) {
		tmp = ((t * a) * -4.0) + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = c * (b + ((j * (k / c)) * -27.0))
	tmp = 0
	if c <= -6.8e+62:
		tmp = t_2
	elif c <= 4.5e-171:
		tmp = t_1 + ((x * i) * -4.0)
	elif c <= 3.35e+34:
		tmp = ((t * a) * -4.0) + t_1
	else:
		tmp = t_2
	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(c * Float64(b + Float64(Float64(j * Float64(k / c)) * -27.0)))
	tmp = 0.0
	if (c <= -6.8e+62)
		tmp = t_2;
	elseif (c <= 4.5e-171)
		tmp = Float64(t_1 + Float64(Float64(x * i) * -4.0));
	elseif (c <= 3.35e+34)
		tmp = Float64(Float64(Float64(t * a) * -4.0) + 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 * (k * -27.0);
	t_2 = c * (b + ((j * (k / c)) * -27.0));
	tmp = 0.0;
	if (c <= -6.8e+62)
		tmp = t_2;
	elseif (c <= 4.5e-171)
		tmp = t_1 + ((x * i) * -4.0);
	elseif (c <= 3.35e+34)
		tmp = ((t * a) * -4.0) + 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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(b + N[(N[(j * N[(k / c), $MachinePrecision]), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.8e+62], t$95$2, If[LessEqual[c, 4.5e-171], N[(t$95$1 + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.35e+34], N[(N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.80000000000000028e62 or 3.3500000000000001e34 < c

   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 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 b around inf 70.7%

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

   6. Taylor expanded in c around inf 74.2%

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

      1. *-commutative 74.2%

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

      2. associate-/l* 75.1%

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

   8. Simplified 75.1%

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

   if -6.80000000000000028e62 < c < 4.5000000000000004e-171

   1. Initial program 88.8%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in i around inf 50.4%

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

   if 4.5000000000000004e-171 < c < 3.3500000000000001e34

   1. Initial program 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in a around inf 53.5%

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

      1. *-commutative 53.5%

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

   7. Simplified 53.5%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.8 \cdot 10^{+62}:\\ \;\;\;\;c \cdot \left(b + \left(j \cdot \frac{k}{c}\right) \cdot -27\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-171}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;c \leq 3.35 \cdot 10^{+34}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4 + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + \left(j \cdot \frac{k}{c}\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 37.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.3 \cdot 10^{+45} \lor \neg \left(b \cdot c \leq 7.5 \cdot 10^{+174}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -2.3e+45) (not (<= (* b c) 7.5e+174)))
   (* b c)
   (* -27.0 (* j k))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.3e+45) || !((b * c) <= 7.5e+174)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-2.3d+45)) .or. (.not. ((b * c) <= 7.5d+174))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (j * k)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.3e+45) || !((b * c) <= 7.5e+174)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -2.3e+45) or not ((b * c) <= 7.5e+174):
		tmp = b * c
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -2.3e+45) || !(Float64(b * c) <= 7.5e+174))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -2.3e+45) || ~(((b * c) <= 7.5e+174)))
		tmp = b * c;
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -2.3e+45], N[Not[LessEqual[N[(b * c), $MachinePrecision], 7.5e+174]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.30000000000000012e45 or 7.5000000000000004e174 < (*.f64 b c)

   1. Initial program 81.9%

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

   3. Simplified 84.7%

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

      1. pow1 84.7%

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

      2. associate-*l* 84.7%

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

      3. associate-*r* 84.7%

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

   6. Applied egg-rr 84.7%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 84.7%

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

      2. associate-*r* 83.8%

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

   8. Simplified 83.8%

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

   9. Taylor expanded in b around inf 68.8%

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

   if -2.30000000000000012e45 < (*.f64 b c) < 7.5000000000000004e174

   1. Initial program 85.9%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in j around inf 24.3%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.3 \cdot 10^{+45} \lor \neg \left(b \cdot c \leq 7.5 \cdot 10^{+174}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 37.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.65 \cdot 10^{+45} \lor \neg \left(b \cdot c \leq 1.8 \cdot 10^{+175}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -2.65e+45) (not (<= (* b c) 1.8e+175)))
   (* b c)
   (* j (* k -27.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.65e+45) || !((b * c) <= 1.8e+175)) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-2.65d+45)) .or. (.not. ((b * c) <= 1.8d+175))) then
        tmp = b * c
    else
        tmp = j * (k * (-27.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.65e+45) || !((b * c) <= 1.8e+175)) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -2.65e+45) or not ((b * c) <= 1.8e+175):
		tmp = b * c
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -2.65e+45) || !(Float64(b * c) <= 1.8e+175))
		tmp = Float64(b * c);
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -2.65e+45) || ~(((b * c) <= 1.8e+175)))
		tmp = b * c;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -2.65e+45], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.8e+175]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.64999999999999996e45 or 1.80000000000000017e175 < (*.f64 b c)

   1. Initial program 81.9%

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

   3. Simplified 84.7%

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

      1. pow1 84.7%

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

      2. associate-*l* 84.7%

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

      3. associate-*r* 84.7%

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

   6. Applied egg-rr 84.7%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 84.7%

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

      2. associate-*r* 83.8%

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

   8. Simplified 83.8%

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

   9. Taylor expanded in b around inf 68.8%

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

   if -2.64999999999999996e45 < (*.f64 b c) < 1.80000000000000017e175

   1. Initial program 85.9%

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

   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. Step-by-step derivation

      1. pow1 85.2%

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

      2. associate-*l* 85.2%

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

      3. associate-*r* 84.6%

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

   6. Applied egg-rr 84.6%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 84.6%

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

      2. associate-*r* 87.3%

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

   8. Simplified 87.3%

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

   9. Taylor expanded in j around inf 24.3%

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

       1. *-commutative 24.3%

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

       2. associate-*r* 24.4%

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

   11. Simplified 24.4%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.65 \cdot 10^{+45} \lor \neg \left(b \cdot c \leq 1.8 \cdot 10^{+175}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 42.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+203}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-52}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -1e+203)
   (* (* z (* x y)) (* 18.0 t))
   (if (<= y 6e-52)
     (+ (* b c) (* (* t a) -4.0))
     (* 18.0 (* (* y z) (* x t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -1e+203) {
		tmp = (z * (x * y)) * (18.0 * t);
	} else if (y <= 6e-52) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else {
		tmp = 18.0 * ((y * z) * (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (y <= (-1d+203)) then
        tmp = (z * (x * y)) * (18.0d0 * t)
    else if (y <= 6d-52) then
        tmp = (b * c) + ((t * a) * (-4.0d0))
    else
        tmp = 18.0d0 * ((y * z) * (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -1e+203) {
		tmp = (z * (x * y)) * (18.0 * t);
	} else if (y <= 6e-52) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else {
		tmp = 18.0 * ((y * z) * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if y <= -1e+203:
		tmp = (z * (x * y)) * (18.0 * t)
	elif y <= 6e-52:
		tmp = (b * c) + ((t * a) * -4.0)
	else:
		tmp = 18.0 * ((y * z) * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -1e+203)
		tmp = Float64(Float64(z * Float64(x * y)) * Float64(18.0 * t));
	elseif (y <= 6e-52)
		tmp = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0));
	else
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (y <= -1e+203)
		tmp = (z * (x * y)) * (18.0 * t);
	elseif (y <= 6e-52)
		tmp = (b * c) + ((t * a) * -4.0);
	else
		tmp = 18.0 * ((y * z) * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -1e+203], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-52], N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.9999999999999999e202

   1. Initial program 62.1%

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

   3. Simplified 57.9%

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

   5. Taylor expanded in j around 0 53.2%

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

   6. Taylor expanded in x around inf 62.7%

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

   7. Taylor expanded in y around inf 39.4%

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

      1. *-commutative 39.4%

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

      2. associate-*r* 53.0%

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

      3. *-commutative 53.0%

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

      4. associate-*l* 53.1%

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

      5. *-commutative 53.1%

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

   9. Simplified 53.1%

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

   if -9.9999999999999999e202 < y < 6e-52

   1. Initial program 89.9%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in j around 0 78.2%

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

   6. Taylor expanded in x around inf 72.8%

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

   7. Taylor expanded in x around 0 55.2%

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

   if 6e-52 < y

   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 76.5%

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

   5. Taylor expanded in j around 0 70.4%

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

   6. Taylor expanded in x around inf 64.5%

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

   7. Taylor expanded in y around inf 50.9%

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

      1. associate-*r* 47.0%

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

   9. Simplified 47.0%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+203}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-52}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 23.2% accurate, 10.3× speedup

Math

\[\begin{array}{l} \\ b \cdot c \end{array} \]

FPCore

(FPCore (x y z t a b c i j k) :precision binary64 (* b c))

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = b * c
end function

Java

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

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(b * c), $MachinePrecision]

Derivation

1. Initial program 84.3%

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

3. Simplified 85.0%

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

   1. pow1 85.0%

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

   2. associate-*l* 85.0%

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

   3. associate-*r* 84.6%

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

6. Applied egg-rr 84.6%

   \[\leadsto \left(t \cdot \left(\color{blue}{{\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
7. Step-by-step derivation

   1. unpow1 84.6%

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

   2. associate-*r* 85.8%

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

8. Simplified 85.8%

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

9. Taylor expanded in b around inf 31.5%

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

10. Final simplification 31.5%

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

Developer target: 89.1% 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 2024077 
(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)))