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

Percentage Accurate: 85.1% → 92.4%

Time: 33.4s

Alternatives: 19

Speedup: 1.0×

• 50.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (-
           (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
           (* (* x 4.0) i))
          (* (* j 27.0) k))))
   (if (<= t_1 2e+306)
     t_1
     (if (<= t_1 INFINITY)
       (-
        (+ (* b c) (* t (- (* x (* 18.0 (* y z))) (* a 4.0))))
        (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
       (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= 2e+306) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((b * c) + (t * ((x * (18.0 * (y * z))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= 2e+306) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = ((b * c) + (t * ((x * (18.0 * (y * z))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	tmp = 0
	if t_1 <= 2e+306:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = ((b * c) + (t * ((x * (18.0 * (y * z))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (t_1 <= 2e+306)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(x * Float64(18.0 * Float64(y * z))) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	tmp = 0.0;
	if (t_1 <= 2e+306)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = ((b * c) + (t * ((x * (18.0 * (y * z))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+306], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(x * N[(18.0 * N[(y * z), $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[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k)) < 2.00000000000000003e306

   1. Initial program 99.4%

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

   if 2.00000000000000003e306 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k)) < +inf.0

   1. Initial program 91.3%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in x around 0 96.6%

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

      1. associate-*r* 96.6%

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

      2. *-commutative 96.6%

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

      3. associate-*l* 96.6%

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

   6. Simplified 96.6%

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

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

   1. Initial program 0.0%

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

   3. Simplified 20.8%

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

   4. Taylor expanded in x around inf 54.9%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 2: 36.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -6.1 \cdot 10^{+172}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -14600000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -5.6 \cdot 10^{-108}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -7.3 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -2.6 \cdot 10^{-228}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 1.75 \cdot 10^{-82}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 7.5 \cdot 10^{+161}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))) (t_2 (* x (* i -4.0))))
   (if (<= (* b c) -6.1e+172)
     (* b c)
     (if (<= (* b c) -14600000.0)
       t_1
       (if (<= (* b c) -5.6e-108)
         (* j (* k -27.0))
         (if (<= (* b c) -7.3e-140)
           t_1
           (if (<= (* b c) -2.6e-228)
             t_2
             (if (<= (* b c) 1.75e-82)
               (* k (* j -27.0))
               (if (<= (* b c) 7.5e+161) t_2 (* 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 = t * (a * -4.0);
	double t_2 = x * (i * -4.0);
	double tmp;
	if ((b * c) <= -6.1e+172) {
		tmp = b * c;
	} else if ((b * c) <= -14600000.0) {
		tmp = t_1;
	} else if ((b * c) <= -5.6e-108) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= -7.3e-140) {
		tmp = t_1;
	} else if ((b * c) <= -2.6e-228) {
		tmp = t_2;
	} else if ((b * c) <= 1.75e-82) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 7.5e+161) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    t_2 = x * (i * (-4.0d0))
    if ((b * c) <= (-6.1d+172)) then
        tmp = b * c
    else if ((b * c) <= (-14600000.0d0)) then
        tmp = t_1
    else if ((b * c) <= (-5.6d-108)) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= (-7.3d-140)) then
        tmp = t_1
    else if ((b * c) <= (-2.6d-228)) then
        tmp = t_2
    else if ((b * c) <= 1.75d-82) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 7.5d+161) then
        tmp = t_2
    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 = t * (a * -4.0);
	double t_2 = x * (i * -4.0);
	double tmp;
	if ((b * c) <= -6.1e+172) {
		tmp = b * c;
	} else if ((b * c) <= -14600000.0) {
		tmp = t_1;
	} else if ((b * c) <= -5.6e-108) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= -7.3e-140) {
		tmp = t_1;
	} else if ((b * c) <= -2.6e-228) {
		tmp = t_2;
	} else if ((b * c) <= 1.75e-82) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 7.5e+161) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	t_2 = x * (i * -4.0)
	tmp = 0
	if (b * c) <= -6.1e+172:
		tmp = b * c
	elif (b * c) <= -14600000.0:
		tmp = t_1
	elif (b * c) <= -5.6e-108:
		tmp = j * (k * -27.0)
	elif (b * c) <= -7.3e-140:
		tmp = t_1
	elif (b * c) <= -2.6e-228:
		tmp = t_2
	elif (b * c) <= 1.75e-82:
		tmp = k * (j * -27.0)
	elif (b * c) <= 7.5e+161:
		tmp = t_2
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	t_2 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -6.1e+172)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -14600000.0)
		tmp = t_1;
	elseif (Float64(b * c) <= -5.6e-108)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= -7.3e-140)
		tmp = t_1;
	elseif (Float64(b * c) <= -2.6e-228)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.75e-82)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 7.5e+161)
		tmp = t_2;
	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 = t * (a * -4.0);
	t_2 = x * (i * -4.0);
	tmp = 0.0;
	if ((b * c) <= -6.1e+172)
		tmp = b * c;
	elseif ((b * c) <= -14600000.0)
		tmp = t_1;
	elseif ((b * c) <= -5.6e-108)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= -7.3e-140)
		tmp = t_1;
	elseif ((b * c) <= -2.6e-228)
		tmp = t_2;
	elseif ((b * c) <= 1.75e-82)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 7.5e+161)
		tmp = t_2;
	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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -6.1e+172], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -14600000.0], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -5.6e-108], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -7.3e-140], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -2.6e-228], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.75e-82], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 7.5e+161], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -6.0999999999999998e172 or 7.4999999999999995e161 < (*.f64 b c)

   1. Initial program 87.3%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in b around inf 64.8%

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

   if -6.0999999999999998e172 < (*.f64 b c) < -1.46e7 or -5.6e-108 < (*.f64 b c) < -7.30000000000000027e-140

   1. Initial program 84.0%

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

   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. Taylor expanded in a around inf 48.9%

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

      1. *-commutative 48.9%

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

      2. *-commutative 48.9%

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

      3. associate-*r* 48.9%

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

   6. Simplified 48.9%

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

   if -1.46e7 < (*.f64 b c) < -5.6e-108

   1. Initial program 91.8%

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

   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. Taylor expanded in j around inf 42.1%

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

      1. *-commutative 42.1%

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

      2. associate-*l* 42.2%

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

   6. Simplified 42.2%

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

   if -7.30000000000000027e-140 < (*.f64 b c) < -2.6e-228 or 1.7499999999999999e-82 < (*.f64 b c) < 7.4999999999999995e161

   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 85.8%

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

   4. Taylor expanded in i around inf 42.8%

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

      1. associate-*r* 42.8%

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

      2. *-commutative 42.8%

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

   6. Simplified 42.8%

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

   if -2.6e-228 < (*.f64 b c) < 1.7499999999999999e-82

   1. Initial program 94.2%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in j around inf 41.0%

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

      1. associate-*r* 41.0%

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

   6. Simplified 41.0%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.1 \cdot 10^{+172}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -14600000:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -5.6 \cdot 10^{-108}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -7.3 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -2.6 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.75 \cdot 10^{-82}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 7.5 \cdot 10^{+161}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 3: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.4 \cdot 10^{+249}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z 2.4e+249)
   (-
    (+ (* b c) (* t (- (* x (* 18.0 (* y z))) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (* 18.0 (* x (* z (* y 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 (z <= 2.4e+249) {
		tmp = ((b * c) + (t * ((x * (18.0 * (y * z))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = 18.0 * (x * (z * (y * 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 (z <= 2.4d+249) then
        tmp = ((b * c) + (t * ((x * (18.0d0 * (y * z))) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = 18.0d0 * (x * (z * (y * 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 (z <= 2.4e+249) {
		tmp = ((b * c) + (t * ((x * (18.0 * (y * z))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = 18.0 * (x * (z * (y * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if z <= 2.4e+249:
		tmp = ((b * c) + (t * ((x * (18.0 * (y * z))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = 18.0 * (x * (z * (y * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= 2.4e+249)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(x * Float64(18.0 * Float64(y * z))) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(18.0 * Float64(x * Float64(z * Float64(y * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (z <= 2.4e+249)
		tmp = ((b * c) + (t * ((x * (18.0 * (y * z))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = 18.0 * (x * (z * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, 2.4e+249], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(x * N[(18.0 * N[(y * z), $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[(18.0 * N[(x * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.4e249

   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 89.7%

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

   4. Taylor expanded in x around 0 89.7%

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

      1. associate-*r* 89.7%

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

      2. *-commutative 89.7%

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

      3. associate-*l* 89.7%

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

   6. Simplified 89.7%

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

   if 2.4e249 < z

   1. Initial program 57.5%

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

   3. Simplified 57.5%

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

   4. Taylor expanded in y around inf 58.6%

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

      1. *-commutative 58.6%

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

      2. associate-*l* 58.6%

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

      3. *-commutative 58.6%

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

      4. associate-*l* 71.9%

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

   6. Simplified 71.9%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.4 \cdot 10^{+249}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 4: 78.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ t_2 := b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+56}:\\ \;\;\;\;t_2 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+61}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+136}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
        (t_2 (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))))
   (if (<= x -1.75e+248)
     t_1
     (if (<= x -1.9e+56)
       (- t_2 (* 27.0 (* j k)))
       (if (<= x 3e+61)
         (- (+ (* b c) (* -4.0 (* t a))) (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
         (if (<= x 3.8e+136) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (x <= -1.75e+248) {
		tmp = t_1;
	} else if (x <= -1.9e+56) {
		tmp = t_2 - (27.0 * (j * k));
	} else if (x <= 3e+61) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else if (x <= 3.8e+136) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    t_2 = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    if (x <= (-1.75d+248)) then
        tmp = t_1
    else if (x <= (-1.9d+56)) then
        tmp = t_2 - (27.0d0 * (j * k))
    else if (x <= 3d+61) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else if (x <= 3.8d+136) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (x <= -1.75e+248) {
		tmp = t_1;
	} else if (x <= -1.9e+56) {
		tmp = t_2 - (27.0 * (j * k));
	} else if (x <= 3e+61) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else if (x <= 3.8e+136) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	tmp = 0
	if x <= -1.75e+248:
		tmp = t_1
	elif x <= -1.9e+56:
		tmp = t_2 - (27.0 * (j * k))
	elif x <= 3e+61:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	elif x <= 3.8e+136:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	t_2 = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))))
	tmp = 0.0
	if (x <= -1.75e+248)
		tmp = t_1;
	elseif (x <= -1.9e+56)
		tmp = Float64(t_2 - Float64(27.0 * Float64(j * k)));
	elseif (x <= 3e+61)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	elseif (x <= 3.8e+136)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	tmp = 0.0;
	if (x <= -1.75e+248)
		tmp = t_1;
	elseif (x <= -1.9e+56)
		tmp = t_2 - (27.0 * (j * k));
	elseif (x <= 3e+61)
		tmp = ((b * c) + (-4.0 * (t * a))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	elseif (x <= 3.8e+136)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.75e+248], t$95$1, If[LessEqual[x, -1.9e+56], N[(t$95$2 - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+61], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e+136], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.75000000000000011e248 or 3.80000000000000015e136 < x

   1. Initial program 78.2%

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

   3. Simplified 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. Taylor expanded in x around inf 86.4%

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

   if -1.75000000000000011e248 < x < -1.89999999999999998e56

   1. Initial program 76.8%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in i around 0 80.0%

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

   if -1.89999999999999998e56 < x < 3e61

   1. Initial program 93.1%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around 0 87.6%

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

   if 3e61 < x < 3.80000000000000015e136

   1. Initial program 99.9%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in i around 0 100.0%

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

   5. Taylor expanded in j around 0 100.0%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+248}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+56}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+61}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+136}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 5: 82.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+81} \lor \neg \left(a \leq 3.4 \cdot 10^{+44}\right):\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + \left(b \cdot c - x \cdot \left(4 \cdot i + \left(t \cdot \left(y \cdot z\right)\right) \cdot -18\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= a -9.6e+81) (not (<= a 3.4e+44)))
   (- (+ (* b c) (* -4.0 (* t a))) (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (+
    (* -27.0 (* j k))
    (- (* b c) (* x (+ (* 4.0 i) (* (* t (* y z)) -18.0)))))))

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 ((a <= -9.6e+81) || !(a <= 3.4e+44)) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (-27.0 * (j * k)) + ((b * c) - (x * ((4.0 * i) + ((t * (y * z)) * -18.0))));
	}
	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 ((a <= (-9.6d+81)) .or. (.not. (a <= 3.4d+44))) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = ((-27.0d0) * (j * k)) + ((b * c) - (x * ((4.0d0 * i) + ((t * (y * z)) * (-18.0d0)))))
    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 ((a <= -9.6e+81) || !(a <= 3.4e+44)) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (-27.0 * (j * k)) + ((b * c) - (x * ((4.0 * i) + ((t * (y * z)) * -18.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (a <= -9.6e+81) or not (a <= 3.4e+44):
		tmp = ((b * c) + (-4.0 * (t * a))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = (-27.0 * (j * k)) + ((b * c) - (x * ((4.0 * i) + ((t * (y * z)) * -18.0))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((a <= -9.6e+81) || !(a <= 3.4e+44))
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(-27.0 * Float64(j * k)) + Float64(Float64(b * c) - Float64(x * Float64(Float64(4.0 * i) + Float64(Float64(t * Float64(y * z)) * -18.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((a <= -9.6e+81) || ~((a <= 3.4e+44)))
		tmp = ((b * c) + (-4.0 * (t * a))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = (-27.0 * (j * k)) + ((b * c) - (x * ((4.0 * i) + ((t * (y * z)) * -18.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[a, -9.6e+81], N[Not[LessEqual[a, 3.4e+44]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] - N[(x * N[(N[(4.0 * i), $MachinePrecision] + N[(N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.59999999999999958e81 or 3.4e44 < a

   1. Initial program 88.4%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in x around 0 89.1%

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

   if -9.59999999999999958e81 < a < 3.4e44

   1. Initial program 88.4%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in x around -inf 89.6%

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

   6. Simplified 91.6%

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

   7. Taylor expanded in a around 0 88.4%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + 4 \cdot i\right)\right) + b \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+81} \lor \neg \left(a \leq 3.4 \cdot 10^{+44}\right):\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + \left(b \cdot c - x \cdot \left(4 \cdot i + \left(t \cdot \left(y \cdot z\right)\right) \cdot -18\right)\right)\\ \end{array} \]

Alternative 6: 37.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+171}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -6100000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 24500000000:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 3.65 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 3.5 \cdot 10^{+100}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= (* b c) -4e+171)
     (* b c)
     (if (<= (* b c) -6100000.0)
       t_1
       (if (<= (* b c) 24500000000.0)
         (* j (* k -27.0))
         (if (<= (* b c) 3.65e+98)
           t_1
           (if (<= (* b c) 3.5e+100) (* -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 t_1 = t * (a * -4.0);
	double tmp;
	if ((b * c) <= -4e+171) {
		tmp = b * c;
	} else if ((b * c) <= -6100000.0) {
		tmp = t_1;
	} else if ((b * c) <= 24500000000.0) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 3.65e+98) {
		tmp = t_1;
	} else if ((b * c) <= 3.5e+100) {
		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) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if ((b * c) <= (-4d+171)) then
        tmp = b * c
    else if ((b * c) <= (-6100000.0d0)) then
        tmp = t_1
    else if ((b * c) <= 24500000000.0d0) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 3.65d+98) then
        tmp = t_1
    else if ((b * c) <= 3.5d+100) 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 t_1 = t * (a * -4.0);
	double tmp;
	if ((b * c) <= -4e+171) {
		tmp = b * c;
	} else if ((b * c) <= -6100000.0) {
		tmp = t_1;
	} else if ((b * c) <= 24500000000.0) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 3.65e+98) {
		tmp = t_1;
	} else if ((b * c) <= 3.5e+100) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	tmp = 0
	if (b * c) <= -4e+171:
		tmp = b * c
	elif (b * c) <= -6100000.0:
		tmp = t_1
	elif (b * c) <= 24500000000.0:
		tmp = j * (k * -27.0)
	elif (b * c) <= 3.65e+98:
		tmp = t_1
	elif (b * c) <= 3.5e+100:
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -4e+171)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -6100000.0)
		tmp = t_1;
	elseif (Float64(b * c) <= 24500000000.0)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 3.65e+98)
		tmp = t_1;
	elseif (Float64(b * c) <= 3.5e+100)
		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)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if ((b * c) <= -4e+171)
		tmp = b * c;
	elseif ((b * c) <= -6100000.0)
		tmp = t_1;
	elseif ((b * c) <= 24500000000.0)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 3.65e+98)
		tmp = t_1;
	elseif ((b * c) <= 3.5e+100)
		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_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -4e+171], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -6100000.0], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 24500000000.0], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.65e+98], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 3.5e+100], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -3.99999999999999982e171 or 3.49999999999999976e100 < (*.f64 b c)

   1. Initial program 88.1%

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

   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. Taylor expanded in b around inf 62.0%

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

   if -3.99999999999999982e171 < (*.f64 b c) < -6.1e6 or 2.45e10 < (*.f64 b c) < 3.6500000000000001e98

   1. Initial program 79.7%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in a around inf 39.5%

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

      1. *-commutative 39.5%

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

      2. *-commutative 39.5%

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

      3. associate-*r* 39.5%

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

   6. Simplified 39.5%

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

   if -6.1e6 < (*.f64 b c) < 2.45e10

   1. Initial program 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in j around inf 35.3%

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

      1. *-commutative 35.3%

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

      2. associate-*l* 35.3%

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

   6. Simplified 35.3%

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

   if 3.6500000000000001e98 < (*.f64 b c) < 3.49999999999999976e100

   1. Initial program 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in j around inf 98.4%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+171}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -6100000:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 24500000000:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 3.65 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 3.5 \cdot 10^{+100}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 7: 49.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -4.1 \cdot 10^{+228}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.5 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-314}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.3 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (+ (* t a) (* x i)))))
   (if (<= (* b c) -4.1e+228)
     (* b c)
     (if (<= (* b c) -1.5e-228)
       t_1
       (if (<= (* b c) -1e-314)
         (* k (* j -27.0))
         (if (<= (* b c) 1.3e+177) t_1 (* b c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if ((b * c) <= -4.1e+228) {
		tmp = b * c;
	} else if ((b * c) <= -1.5e-228) {
		tmp = t_1;
	} else if ((b * c) <= -1e-314) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 1.3e+177) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * ((t * a) + (x * i))
    if ((b * c) <= (-4.1d+228)) then
        tmp = b * c
    else if ((b * c) <= (-1.5d-228)) then
        tmp = t_1
    else if ((b * c) <= (-1d-314)) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 1.3d+177) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if ((b * c) <= -4.1e+228) {
		tmp = b * c;
	} else if ((b * c) <= -1.5e-228) {
		tmp = t_1;
	} else if ((b * c) <= -1e-314) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 1.3e+177) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * ((t * a) + (x * i))
	tmp = 0
	if (b * c) <= -4.1e+228:
		tmp = b * c
	elif (b * c) <= -1.5e-228:
		tmp = t_1
	elif (b * c) <= -1e-314:
		tmp = k * (j * -27.0)
	elif (b * c) <= 1.3e+177:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)))
	tmp = 0.0
	if (Float64(b * c) <= -4.1e+228)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.5e-228)
		tmp = t_1;
	elseif (Float64(b * c) <= -1e-314)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 1.3e+177)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * ((t * a) + (x * i));
	tmp = 0.0;
	if ((b * c) <= -4.1e+228)
		tmp = b * c;
	elseif ((b * c) <= -1.5e-228)
		tmp = t_1;
	elseif ((b * c) <= -1e-314)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 1.3e+177)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -4.1e+228], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.5e-228], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1e-314], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.3e+177], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -4.1e228 or 1.2999999999999999e177 < (*.f64 b c)

   1. Initial program 83.3%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in b around inf 76.4%

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

   if -4.1e228 < (*.f64 b c) < -1.5e-228 or -9.9999999996e-315 < (*.f64 b c) < 1.2999999999999999e177

   1. Initial program 89.8%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in x around 0 80.0%

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

   5. Taylor expanded in j around 0 59.5%

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

   6. Taylor expanded in b around 0 52.1%

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

      1. cancel-sign-sub-inv 52.1%

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

      2. *-commutative 52.1%

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

      3. metadata-eval 52.1%

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

      4. *-commutative 52.1%

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

      5. distribute-lft-out 52.1%

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

      6. *-commutative 52.1%

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

   8. Simplified 52.1%

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

   if -1.5e-228 < (*.f64 b c) < -9.9999999996e-315

   1. Initial program 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in j around inf 77.5%

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

      1. associate-*r* 78.0%

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

   6. Simplified 78.0%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.1 \cdot 10^{+228}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.5 \cdot 10^{-228}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-314}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.3 \cdot 10^{+177}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 8: 51.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -8.5 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -3.2 \cdot 10^{-228}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-314}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{+170}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a)))) (t_2 (* -4.0 (+ (* t a) (* x i)))))
   (if (<= (* b c) -8.5e+132)
     t_1
     (if (<= (* b c) -3.2e-228)
       t_2
       (if (<= (* b c) -1e-314)
         (* k (* j -27.0))
         (if (<= (* b c) 9.5e+170) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if ((b * c) <= -8.5e+132) {
		tmp = t_1;
	} else if ((b * c) <= -3.2e-228) {
		tmp = t_2;
	} else if ((b * c) <= -1e-314) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 9.5e+170) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    t_2 = (-4.0d0) * ((t * a) + (x * i))
    if ((b * c) <= (-8.5d+132)) then
        tmp = t_1
    else if ((b * c) <= (-3.2d-228)) then
        tmp = t_2
    else if ((b * c) <= (-1d-314)) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 9.5d+170) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if ((b * c) <= -8.5e+132) {
		tmp = t_1;
	} else if ((b * c) <= -3.2e-228) {
		tmp = t_2;
	} else if ((b * c) <= -1e-314) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 9.5e+170) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	t_2 = -4.0 * ((t * a) + (x * i))
	tmp = 0
	if (b * c) <= -8.5e+132:
		tmp = t_1
	elif (b * c) <= -3.2e-228:
		tmp = t_2
	elif (b * c) <= -1e-314:
		tmp = k * (j * -27.0)
	elif (b * c) <= 9.5e+170:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_2 = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)))
	tmp = 0.0
	if (Float64(b * c) <= -8.5e+132)
		tmp = t_1;
	elseif (Float64(b * c) <= -3.2e-228)
		tmp = t_2;
	elseif (Float64(b * c) <= -1e-314)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 9.5e+170)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	t_2 = -4.0 * ((t * a) + (x * i));
	tmp = 0.0;
	if ((b * c) <= -8.5e+132)
		tmp = t_1;
	elseif ((b * c) <= -3.2e-228)
		tmp = t_2;
	elseif ((b * c) <= -1e-314)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 9.5e+170)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -8.5e+132], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -3.2e-228], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -1e-314], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 9.5e+170], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -8.49999999999999969e132 or 9.5000000000000005e170 < (*.f64 b c)

   1. Initial program 87.9%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in x around -inf 85.3%

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

   6. Simplified 88.0%

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

   7. Taylor expanded in j around 0 83.4%

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

   8. Taylor expanded in x around 0 69.6%

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

   if -8.49999999999999969e132 < (*.f64 b c) < -3.20000000000000022e-228 or -9.9999999996e-315 < (*.f64 b c) < 9.5000000000000005e170

   1. Initial program 88.5%

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

   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. Taylor expanded in x around 0 79.5%

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

   5. Taylor expanded in j around 0 58.8%

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

   6. Taylor expanded in b around 0 54.0%

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

      1. cancel-sign-sub-inv 54.0%

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

      2. *-commutative 54.0%

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

      3. metadata-eval 54.0%

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

      4. *-commutative 54.0%

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

      5. distribute-lft-out 54.0%

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

      6. *-commutative 54.0%

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

   8. Simplified 54.0%

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

   if -3.20000000000000022e-228 < (*.f64 b c) < -9.9999999996e-315

   1. Initial program 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in j around inf 77.5%

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

      1. associate-*r* 78.0%

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

   6. Simplified 78.0%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -8.5 \cdot 10^{+132}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -3.2 \cdot 10^{-228}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-314}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{+170}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 9: 51.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -8.2 \cdot 10^{+132}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -1.5 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-314}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.16 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (+ (* t a) (* x i)))))
   (if (<= (* b c) -8.2e+132)
     (+ (* b c) (* -4.0 (* t a)))
     (if (<= (* b c) -1.5e-228)
       t_1
       (if (<= (* b c) -1e-314)
         (* k (* j -27.0))
         (if (<= (* b c) 1.16e+85) t_1 (- (* b c) (* 4.0 (* x i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if ((b * c) <= -8.2e+132) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if ((b * c) <= -1.5e-228) {
		tmp = t_1;
	} else if ((b * c) <= -1e-314) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 1.16e+85) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * ((t * a) + (x * i))
    if ((b * c) <= (-8.2d+132)) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if ((b * c) <= (-1.5d-228)) then
        tmp = t_1
    else if ((b * c) <= (-1d-314)) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 1.16d+85) then
        tmp = t_1
    else
        tmp = (b * c) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if ((b * c) <= -8.2e+132) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if ((b * c) <= -1.5e-228) {
		tmp = t_1;
	} else if ((b * c) <= -1e-314) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 1.16e+85) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * ((t * a) + (x * i))
	tmp = 0
	if (b * c) <= -8.2e+132:
		tmp = (b * c) + (-4.0 * (t * a))
	elif (b * c) <= -1.5e-228:
		tmp = t_1
	elif (b * c) <= -1e-314:
		tmp = k * (j * -27.0)
	elif (b * c) <= 1.16e+85:
		tmp = t_1
	else:
		tmp = (b * c) - (4.0 * (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)))
	tmp = 0.0
	if (Float64(b * c) <= -8.2e+132)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (Float64(b * c) <= -1.5e-228)
		tmp = t_1;
	elseif (Float64(b * c) <= -1e-314)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 1.16e+85)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * ((t * a) + (x * i));
	tmp = 0.0;
	if ((b * c) <= -8.2e+132)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif ((b * c) <= -1.5e-228)
		tmp = t_1;
	elseif ((b * c) <= -1e-314)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 1.16e+85)
		tmp = t_1;
	else
		tmp = (b * c) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -8.2e+132], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.5e-228], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1e-314], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.16e+85], t$95$1, N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -8.19999999999999983e132

   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 87.7%

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

   4. Taylor expanded in x around -inf 85.3%

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

   6. Simplified 90.2%

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

   7. Taylor expanded in j around 0 82.0%

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

   8. Taylor expanded in x around 0 62.9%

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

   if -8.19999999999999983e132 < (*.f64 b c) < -1.5e-228 or -9.9999999996e-315 < (*.f64 b c) < 1.15999999999999995e85

   1. Initial program 88.5%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in x around 0 78.8%

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

   5. Taylor expanded in j around 0 58.1%

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

   6. Taylor expanded in b around 0 54.2%

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

      1. cancel-sign-sub-inv 54.2%

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

      2. *-commutative 54.2%

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

      3. metadata-eval 54.2%

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

      4. *-commutative 54.2%

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

      5. distribute-lft-out 54.2%

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

      6. *-commutative 54.2%

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

   8. Simplified 54.2%

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

   if -1.5e-228 < (*.f64 b c) < -9.9999999996e-315

   1. Initial program 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in j around inf 77.5%

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

      1. associate-*r* 78.0%

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

   6. Simplified 78.0%

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

   if 1.15999999999999995e85 < (*.f64 b c)

   1. Initial program 86.3%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in x around 0 84.2%

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

   5. Taylor expanded in j around 0 80.7%

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

   6. Taylor expanded in a around 0 74.0%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -8.2 \cdot 10^{+132}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -1.5 \cdot 10^{-228}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-314}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.16 \cdot 10^{+85}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 10: 48.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ t_2 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_3 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+81}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-257}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+211}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
        (t_2 (- (* b c) (* 27.0 (* j k))))
        (t_3 (* -4.0 (+ (* t a) (* x i)))))
   (if (<= a -3.3e+81)
     t_3
     (if (<= a -9e-156)
       t_2
       (if (<= a -3e-238)
         t_1
         (if (<= a -5e-257)
           t_2
           (if (<= a 2.2e+50) t_1 (if (<= a 2.55e+211) 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 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_2 = (b * c) - (27.0 * (j * k));
	double t_3 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if (a <= -3.3e+81) {
		tmp = t_3;
	} else if (a <= -9e-156) {
		tmp = t_2;
	} else if (a <= -3e-238) {
		tmp = t_1;
	} else if (a <= -5e-257) {
		tmp = t_2;
	} else if (a <= 2.2e+50) {
		tmp = t_1;
	} else if (a <= 2.55e+211) {
		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 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    t_2 = (b * c) - (27.0d0 * (j * k))
    t_3 = (-4.0d0) * ((t * a) + (x * i))
    if (a <= (-3.3d+81)) then
        tmp = t_3
    else if (a <= (-9d-156)) then
        tmp = t_2
    else if (a <= (-3d-238)) then
        tmp = t_1
    else if (a <= (-5d-257)) then
        tmp = t_2
    else if (a <= 2.2d+50) then
        tmp = t_1
    else if (a <= 2.55d+211) 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 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_2 = (b * c) - (27.0 * (j * k));
	double t_3 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if (a <= -3.3e+81) {
		tmp = t_3;
	} else if (a <= -9e-156) {
		tmp = t_2;
	} else if (a <= -3e-238) {
		tmp = t_1;
	} else if (a <= -5e-257) {
		tmp = t_2;
	} else if (a <= 2.2e+50) {
		tmp = t_1;
	} else if (a <= 2.55e+211) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	t_2 = (b * c) - (27.0 * (j * k))
	t_3 = -4.0 * ((t * a) + (x * i))
	tmp = 0
	if a <= -3.3e+81:
		tmp = t_3
	elif a <= -9e-156:
		tmp = t_2
	elif a <= -3e-238:
		tmp = t_1
	elif a <= -5e-257:
		tmp = t_2
	elif a <= 2.2e+50:
		tmp = t_1
	elif a <= 2.55e+211:
		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(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	t_2 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_3 = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)))
	tmp = 0.0
	if (a <= -3.3e+81)
		tmp = t_3;
	elseif (a <= -9e-156)
		tmp = t_2;
	elseif (a <= -3e-238)
		tmp = t_1;
	elseif (a <= -5e-257)
		tmp = t_2;
	elseif (a <= 2.2e+50)
		tmp = t_1;
	elseif (a <= 2.55e+211)
		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 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	t_2 = (b * c) - (27.0 * (j * k));
	t_3 = -4.0 * ((t * a) + (x * i));
	tmp = 0.0;
	if (a <= -3.3e+81)
		tmp = t_3;
	elseif (a <= -9e-156)
		tmp = t_2;
	elseif (a <= -3e-238)
		tmp = t_1;
	elseif (a <= -5e-257)
		tmp = t_2;
	elseif (a <= 2.2e+50)
		tmp = t_1;
	elseif (a <= 2.55e+211)
		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[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.3e+81], t$95$3, If[LessEqual[a, -9e-156], t$95$2, If[LessEqual[a, -3e-238], t$95$1, If[LessEqual[a, -5e-257], t$95$2, If[LessEqual[a, 2.2e+50], t$95$1, If[LessEqual[a, 2.55e+211], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.3e81 or 2.54999999999999981e211 < a

   1. Initial program 89.1%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in x around 0 89.0%

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

   5. Taylor expanded in j around 0 81.2%

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

   6. Taylor expanded in b around 0 77.6%

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

      1. cancel-sign-sub-inv 77.6%

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

      2. *-commutative 77.6%

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

      3. metadata-eval 77.6%

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

      4. *-commutative 77.6%

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

      5. distribute-lft-out 77.6%

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

      6. *-commutative 77.6%

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

   8. Simplified 77.6%

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

   if -3.3e81 < a < -8.99999999999999971e-156 or -3e-238 < a < -4.99999999999999989e-257 or 2.20000000000000017e50 < a < 2.54999999999999981e211

   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 88.2%

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

   4. Taylor expanded in i around 0 80.4%

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

   5. Taylor expanded in t around 0 65.4%

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

   if -8.99999999999999971e-156 < a < -3e-238 or -4.99999999999999989e-257 < a < 2.20000000000000017e50

   1. Initial program 89.0%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in x around inf 64.9%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+81}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-156}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-257}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+211}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \]

Alternative 11: 48.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_2 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(z \cdot \left(t \cdot \left(18 \cdot y\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+212}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 27.0 (* j k)))) (t_2 (* -4.0 (+ (* t a) (* x i)))))
   (if (<= a -3.2e+81)
     t_2
     (if (<= a -1.05e-155)
       t_1
       (if (<= a -4e-238)
         (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
         (if (<= a -2.8e-258)
           t_1
           (if (<= a 2.3e+50)
             (* x (- (* z (* t (* 18.0 y))) (* 4.0 i)))
             (if (<= a 1.45e+212) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (j * k));
	double t_2 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if (a <= -3.2e+81) {
		tmp = t_2;
	} else if (a <= -1.05e-155) {
		tmp = t_1;
	} else if (a <= -4e-238) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (a <= -2.8e-258) {
		tmp = t_1;
	} else if (a <= 2.3e+50) {
		tmp = x * ((z * (t * (18.0 * y))) - (4.0 * i));
	} else if (a <= 1.45e+212) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - (27.0d0 * (j * k))
    t_2 = (-4.0d0) * ((t * a) + (x * i))
    if (a <= (-3.2d+81)) then
        tmp = t_2
    else if (a <= (-1.05d-155)) then
        tmp = t_1
    else if (a <= (-4d-238)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (a <= (-2.8d-258)) then
        tmp = t_1
    else if (a <= 2.3d+50) then
        tmp = x * ((z * (t * (18.0d0 * y))) - (4.0d0 * i))
    else if (a <= 1.45d+212) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (j * k));
	double t_2 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if (a <= -3.2e+81) {
		tmp = t_2;
	} else if (a <= -1.05e-155) {
		tmp = t_1;
	} else if (a <= -4e-238) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (a <= -2.8e-258) {
		tmp = t_1;
	} else if (a <= 2.3e+50) {
		tmp = x * ((z * (t * (18.0 * y))) - (4.0 * i));
	} else if (a <= 1.45e+212) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (27.0 * (j * k))
	t_2 = -4.0 * ((t * a) + (x * i))
	tmp = 0
	if a <= -3.2e+81:
		tmp = t_2
	elif a <= -1.05e-155:
		tmp = t_1
	elif a <= -4e-238:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif a <= -2.8e-258:
		tmp = t_1
	elif a <= 2.3e+50:
		tmp = x * ((z * (t * (18.0 * y))) - (4.0 * i))
	elif a <= 1.45e+212:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_2 = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)))
	tmp = 0.0
	if (a <= -3.2e+81)
		tmp = t_2;
	elseif (a <= -1.05e-155)
		tmp = t_1;
	elseif (a <= -4e-238)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (a <= -2.8e-258)
		tmp = t_1;
	elseif (a <= 2.3e+50)
		tmp = Float64(x * Float64(Float64(z * Float64(t * Float64(18.0 * y))) - Float64(4.0 * i)));
	elseif (a <= 1.45e+212)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (27.0 * (j * k));
	t_2 = -4.0 * ((t * a) + (x * i));
	tmp = 0.0;
	if (a <= -3.2e+81)
		tmp = t_2;
	elseif (a <= -1.05e-155)
		tmp = t_1;
	elseif (a <= -4e-238)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (a <= -2.8e-258)
		tmp = t_1;
	elseif (a <= 2.3e+50)
		tmp = x * ((z * (t * (18.0 * y))) - (4.0 * i));
	elseif (a <= 1.45e+212)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e+81], t$95$2, If[LessEqual[a, -1.05e-155], t$95$1, If[LessEqual[a, -4e-238], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.8e-258], t$95$1, If[LessEqual[a, 2.3e+50], N[(x * N[(N[(z * N[(t * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e+212], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.2e81 or 1.4499999999999999e212 < a

   1. Initial program 89.1%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in x around 0 89.0%

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

   5. Taylor expanded in j around 0 81.2%

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

   6. Taylor expanded in b around 0 77.6%

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

      1. cancel-sign-sub-inv 77.6%

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

      2. *-commutative 77.6%

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

      3. metadata-eval 77.6%

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

      4. *-commutative 77.6%

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

      5. distribute-lft-out 77.6%

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

      6. *-commutative 77.6%

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

   8. Simplified 77.6%

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

   if -3.2e81 < a < -1.0500000000000001e-155 or -4e-238 < a < -2.8000000000000002e-258 or 2.29999999999999997e50 < a < 1.4499999999999999e212

   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 88.2%

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

   4. Taylor expanded in i around 0 80.4%

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

   5. Taylor expanded in t around 0 65.4%

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

   if -1.0500000000000001e-155 < a < -4e-238

   1. Initial program 95.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 75.2%

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

   if -2.8000000000000002e-258 < a < 2.29999999999999997e50

   1. Initial program 86.7%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in x around inf 61.5%

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

      1. pow1 61.5%

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

      2. *-commutative 61.5%

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

      3. associate-*r* 62.8%

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

      4. *-commutative 62.8%

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

      5. *-commutative 62.8%

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

   6. Applied egg-rr 62.8%

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

      1. unpow1 62.8%

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

      2. associate-*l* 62.8%

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

      3. *-commutative 62.8%

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

      4. associate-*l* 62.8%

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

   8. Simplified 62.8%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+81}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-155}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-258}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(z \cdot \left(t \cdot \left(18 \cdot y\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+212}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \]

Alternative 12: 70.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.8 \cdot 10^{+28} \lor \neg \left(b \cdot c \leq 5.5 \cdot 10^{+15}\right):\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -2.8e+28) (not (<= (* b c) 5.5e+15)))
   (- (+ (* b c) (* -4.0 (* t a))) (* 4.0 (* x i)))
   (+ (* j (* k -27.0)) (* -4.0 (+ (* t a) (* 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 (((b * c) <= -2.8e+28) || !((b * c) <= 5.5e+15)) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i));
	} else {
		tmp = (j * (k * -27.0)) + (-4.0 * ((t * a) + (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 (((b * c) <= (-2.8d+28)) .or. (.not. ((b * c) <= 5.5d+15))) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (4.0d0 * (x * i))
    else
        tmp = (j * (k * (-27.0d0))) + ((-4.0d0) * ((t * a) + (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 (((b * c) <= -2.8e+28) || !((b * c) <= 5.5e+15)) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i));
	} else {
		tmp = (j * (k * -27.0)) + (-4.0 * ((t * a) + (x * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -2.8e+28) or not ((b * c) <= 5.5e+15):
		tmp = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i))
	else:
		tmp = (j * (k * -27.0)) + (-4.0 * ((t * a) + (x * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -2.8e+28) || !(Float64(b * c) <= 5.5e+15))
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(Float64(t * a) + 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 (((b * c) <= -2.8e+28) || ~(((b * c) <= 5.5e+15)))
		tmp = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i));
	else
		tmp = (j * (k * -27.0)) + (-4.0 * ((t * a) + (x * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -2.8e+28], N[Not[LessEqual[N[(b * c), $MachinePrecision], 5.5e+15]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.8000000000000001e28 or 5.5e15 < (*.f64 b c)

   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 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. Taylor expanded in x around 0 79.7%

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

   5. Taylor expanded in j around 0 76.4%

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

   if -2.8000000000000001e28 < (*.f64 b c) < 5.5e15

   1. Initial program 90.7%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in x around 0 79.2%

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

   5. Taylor expanded in b around 0 77.7%

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

      1. associate--r+ 77.7%

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

      2. cancel-sign-sub-inv 77.7%

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

      3. cancel-sign-sub-inv 77.7%

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

      4. metadata-eval 77.7%

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

      5. distribute-lft-out 77.7%

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

      6. metadata-eval 77.7%

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

      7. *-commutative 77.7%

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

      8. associate-*l* 77.7%

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

   7. Simplified 77.7%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.8 \cdot 10^{+28} \lor \neg \left(b \cdot c \leq 5.5 \cdot 10^{+15}\right):\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \]

Alternative 13: 68.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.6 \cdot 10^{+178}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.1 \cdot 10^{+176}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -2.6e+178)
   (+ (* b c) (* 18.0 (* t (* x (* y z)))))
   (if (<= (* b c) 3.1e+176)
     (+ (* j (* k -27.0)) (* -4.0 (+ (* t a) (* x i))))
     (- (* b c) (* 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 ((b * c) <= -2.6e+178) {
		tmp = (b * c) + (18.0 * (t * (x * (y * z))));
	} else if ((b * c) <= 3.1e+176) {
		tmp = (j * (k * -27.0)) + (-4.0 * ((t * a) + (x * i)));
	} else {
		tmp = (b * c) - (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 ((b * c) <= (-2.6d+178)) then
        tmp = (b * c) + (18.0d0 * (t * (x * (y * z))))
    else if ((b * c) <= 3.1d+176) then
        tmp = (j * (k * (-27.0d0))) + ((-4.0d0) * ((t * a) + (x * i)))
    else
        tmp = (b * c) - (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 ((b * c) <= -2.6e+178) {
		tmp = (b * c) + (18.0 * (t * (x * (y * z))));
	} else if ((b * c) <= 3.1e+176) {
		tmp = (j * (k * -27.0)) + (-4.0 * ((t * a) + (x * i)));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -2.6e+178:
		tmp = (b * c) + (18.0 * (t * (x * (y * z))))
	elif (b * c) <= 3.1e+176:
		tmp = (j * (k * -27.0)) + (-4.0 * ((t * a) + (x * i)))
	else:
		tmp = (b * c) - (4.0 * (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -2.6e+178)
		tmp = Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))));
	elseif (Float64(b * c) <= 3.1e+176)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))));
	else
		tmp = Float64(Float64(b * c) - 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 ((b * c) <= -2.6e+178)
		tmp = (b * c) + (18.0 * (t * (x * (y * z))));
	elseif ((b * c) <= 3.1e+176)
		tmp = (j * (k * -27.0)) + (-4.0 * ((t * a) + (x * i)));
	else
		tmp = (b * c) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -2.6e+178], N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.1e+176], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.6000000000000001e178

   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 84.8%

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

   4. Taylor expanded in i around 0 81.8%

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

   5. Taylor expanded in a around 0 76.0%

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

   6. Taylor expanded in j around 0 75.4%

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

   if -2.6000000000000001e178 < (*.f64 b c) < 3.0999999999999999e176

   1. Initial program 89.1%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around 0 79.8%

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

   5. Taylor expanded in b around 0 74.0%

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

      1. associate--r+ 74.0%

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

      2. cancel-sign-sub-inv 74.0%

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

      3. cancel-sign-sub-inv 74.0%

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

      4. metadata-eval 74.0%

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

      5. distribute-lft-out 74.0%

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

      6. metadata-eval 74.0%

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

      7. *-commutative 74.0%

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

      8. associate-*l* 74.0%

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

   7. Simplified 74.0%

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

   if 3.0999999999999999e176 < (*.f64 b c)

   1. Initial program 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around 0 82.0%

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

   5. Taylor expanded in j around 0 85.0%

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

   6. Taylor expanded in a around 0 79.5%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.6 \cdot 10^{+178}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.1 \cdot 10^{+176}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 14: 70.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.8 \cdot 10^{+134}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq 7.5 \cdot 10^{+15}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -3.8e+134)
   (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
   (if (<= (* b c) 7.5e+15)
     (+ (* j (* k -27.0)) (* -4.0 (+ (* t a) (* x i))))
     (- (+ (* b c) (* -4.0 (* t a))) (* 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 ((b * c) <= -3.8e+134) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else if ((b * c) <= 7.5e+15) {
		tmp = (j * (k * -27.0)) + (-4.0 * ((t * a) + (x * i)));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - (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 ((b * c) <= (-3.8d+134)) then
        tmp = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    else if ((b * c) <= 7.5d+15) then
        tmp = (j * (k * (-27.0d0))) + ((-4.0d0) * ((t * a) + (x * i)))
    else
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (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 ((b * c) <= -3.8e+134) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else if ((b * c) <= 7.5e+15) {
		tmp = (j * (k * -27.0)) + (-4.0 * ((t * a) + (x * i)));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -3.8e+134:
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	elif (b * c) <= 7.5e+15:
		tmp = (j * (k * -27.0)) + (-4.0 * ((t * a) + (x * i)))
	else:
		tmp = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -3.8e+134)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))));
	elseif (Float64(b * c) <= 7.5e+15)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - 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 ((b * c) <= -3.8e+134)
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	elseif ((b * c) <= 7.5e+15)
		tmp = (j * (k * -27.0)) + (-4.0 * ((t * a) + (x * i)));
	else
		tmp = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -3.8e+134], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 7.5e+15], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -3.79999999999999998e134

   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 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. Taylor expanded in i around 0 84.0%

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

   5. Taylor expanded in j around 0 77.6%

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

   if -3.79999999999999998e134 < (*.f64 b c) < 7.5e15

   1. Initial program 89.8%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in x around 0 80.3%

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

   5. Taylor expanded in b around 0 77.8%

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

      1. associate--r+ 77.8%

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

      2. cancel-sign-sub-inv 77.8%

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

      3. cancel-sign-sub-inv 77.8%

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

      4. metadata-eval 77.8%

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

      5. distribute-lft-out 77.8%

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

      6. metadata-eval 77.8%

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

      7. *-commutative 77.8%

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

      8. associate-*l* 77.8%

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

   7. Simplified 77.8%

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

   if 7.5e15 < (*.f64 b c)

   1. Initial program 83.6%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in x around 0 79.2%

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

   5. Taylor expanded in j around 0 78.2%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.8 \cdot 10^{+134}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq 7.5 \cdot 10^{+15}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 15: 76.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.9 \cdot 10^{+192}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(t \cdot \left(18 \cdot y\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z 2.9e+192)
   (- (+ (* b c) (* -4.0 (* t a))) (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (* x (- (* z (* t (* 18.0 y))) (* 4.0 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 <= 2.9e+192) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = x * ((z * (t * (18.0 * y))) - (4.0 * 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 <= 2.9d+192) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = x * ((z * (t * (18.0d0 * y))) - (4.0d0 * 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 <= 2.9e+192) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = x * ((z * (t * (18.0 * y))) - (4.0 * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if z <= 2.9e+192:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = x * ((z * (t * (18.0 * y))) - (4.0 * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= 2.9e+192)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(x * Float64(Float64(z * Float64(t * Float64(18.0 * y))) - Float64(4.0 * 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 <= 2.9e+192)
		tmp = ((b * c) + (-4.0 * (t * a))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = x * ((z * (t * (18.0 * y))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, 2.9e+192], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z * N[(t * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.9000000000000001e192

   1. Initial program 89.1%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in x around 0 81.9%

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

   if 2.9000000000000001e192 < z

   1. Initial program 79.1%

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

   3. Simplified 79.1%

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

   4. Taylor expanded in x around inf 79.3%

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

      1. pow1 79.3%

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

      2. *-commutative 79.3%

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

      3. associate-*r* 84.2%

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

      4. *-commutative 84.2%

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

      5. *-commutative 84.2%

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

   6. Applied egg-rr 84.2%

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

      1. unpow1 84.2%

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

      2. associate-*l* 84.3%

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

      3. *-commutative 84.3%

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

      4. associate-*l* 84.3%

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

   8. Simplified 84.3%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.9 \cdot 10^{+192}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(t \cdot \left(18 \cdot y\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 16: 49.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_3 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;a \leq -5.1 \cdot 10^{+81}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-259}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-281}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (* x i))))
        (t_2 (- (* b c) (* 27.0 (* j k))))
        (t_3 (* -4.0 (+ (* t a) (* x i)))))
   (if (<= a -5.1e+81)
     t_3
     (if (<= a -2e-155)
       t_2
       (if (<= a -1.35e-236)
         t_1
         (if (<= a -1.1e-259)
           t_2
           (if (<= a -1.15e-281)
             (* 18.0 (* x (* z (* y t))))
             (if (<= a 1.7e+164) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double t_2 = (b * c) - (27.0 * (j * k));
	double t_3 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if (a <= -5.1e+81) {
		tmp = t_3;
	} else if (a <= -2e-155) {
		tmp = t_2;
	} else if (a <= -1.35e-236) {
		tmp = t_1;
	} else if (a <= -1.1e-259) {
		tmp = t_2;
	} else if (a <= -1.15e-281) {
		tmp = 18.0 * (x * (z * (y * t)));
	} else if (a <= 1.7e+164) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * (x * i))
    t_2 = (b * c) - (27.0d0 * (j * k))
    t_3 = (-4.0d0) * ((t * a) + (x * i))
    if (a <= (-5.1d+81)) then
        tmp = t_3
    else if (a <= (-2d-155)) then
        tmp = t_2
    else if (a <= (-1.35d-236)) then
        tmp = t_1
    else if (a <= (-1.1d-259)) then
        tmp = t_2
    else if (a <= (-1.15d-281)) then
        tmp = 18.0d0 * (x * (z * (y * t)))
    else if (a <= 1.7d+164) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double t_2 = (b * c) - (27.0 * (j * k));
	double t_3 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if (a <= -5.1e+81) {
		tmp = t_3;
	} else if (a <= -2e-155) {
		tmp = t_2;
	} else if (a <= -1.35e-236) {
		tmp = t_1;
	} else if (a <= -1.1e-259) {
		tmp = t_2;
	} else if (a <= -1.15e-281) {
		tmp = 18.0 * (x * (z * (y * t)));
	} else if (a <= 1.7e+164) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (x * i))
	t_2 = (b * c) - (27.0 * (j * k))
	t_3 = -4.0 * ((t * a) + (x * i))
	tmp = 0
	if a <= -5.1e+81:
		tmp = t_3
	elif a <= -2e-155:
		tmp = t_2
	elif a <= -1.35e-236:
		tmp = t_1
	elif a <= -1.1e-259:
		tmp = t_2
	elif a <= -1.15e-281:
		tmp = 18.0 * (x * (z * (y * t)))
	elif a <= 1.7e+164:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	t_2 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_3 = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)))
	tmp = 0.0
	if (a <= -5.1e+81)
		tmp = t_3;
	elseif (a <= -2e-155)
		tmp = t_2;
	elseif (a <= -1.35e-236)
		tmp = t_1;
	elseif (a <= -1.1e-259)
		tmp = t_2;
	elseif (a <= -1.15e-281)
		tmp = Float64(18.0 * Float64(x * Float64(z * Float64(y * t))));
	elseif (a <= 1.7e+164)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (x * i));
	t_2 = (b * c) - (27.0 * (j * k));
	t_3 = -4.0 * ((t * a) + (x * i));
	tmp = 0.0;
	if (a <= -5.1e+81)
		tmp = t_3;
	elseif (a <= -2e-155)
		tmp = t_2;
	elseif (a <= -1.35e-236)
		tmp = t_1;
	elseif (a <= -1.1e-259)
		tmp = t_2;
	elseif (a <= -1.15e-281)
		tmp = 18.0 * (x * (z * (y * t)));
	elseif (a <= 1.7e+164)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.1e+81], t$95$3, If[LessEqual[a, -2e-155], t$95$2, If[LessEqual[a, -1.35e-236], t$95$1, If[LessEqual[a, -1.1e-259], t$95$2, If[LessEqual[a, -1.15e-281], N[(18.0 * N[(x * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e+164], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.1000000000000003e81 or 1.7000000000000001e164 < a

   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 85.5%

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

   4. Taylor expanded in x around 0 89.1%

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

   5. Taylor expanded in j around 0 78.6%

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

   6. Taylor expanded in b around 0 73.3%

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

      1. cancel-sign-sub-inv 73.3%

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

      2. *-commutative 73.3%

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

      3. metadata-eval 73.3%

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

      4. *-commutative 73.3%

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

      5. distribute-lft-out 73.3%

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

      6. *-commutative 73.3%

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

   8. Simplified 73.3%

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

   if -5.1000000000000003e81 < a < -2.00000000000000003e-155 or -1.35e-236 < a < -1.10000000000000005e-259

   1. Initial program 86.5%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in i around 0 79.9%

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

   5. Taylor expanded in t around 0 66.5%

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

   if -2.00000000000000003e-155 < a < -1.35e-236 or -1.14999999999999994e-281 < a < 1.7000000000000001e164

   1. Initial program 89.0%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around 0 77.9%

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

   5. Taylor expanded in j around 0 60.8%

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

   6. Taylor expanded in a around 0 55.7%

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

   if -1.10000000000000005e-259 < a < -1.14999999999999994e-281

   1. Initial program 83.1%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in y around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-*l* 67.5%

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

      3. *-commutative 67.5%

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

      4. associate-*l* 67.7%

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

   6. Simplified 67.7%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+81}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-155}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-236}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-259}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-281}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+164}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \]

Alternative 17: 37.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.4 \cdot 10^{+174}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 5.5 \cdot 10^{+15}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -5.4e+174)
   (* b c)
   (if (<= (* b c) 5.5e+15) (* -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) <= -5.4e+174) {
		tmp = b * c;
	} else if ((b * c) <= 5.5e+15) {
		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) <= (-5.4d+174)) then
        tmp = b * c
    else if ((b * c) <= 5.5d+15) 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) <= -5.4e+174) {
		tmp = b * c;
	} else if ((b * c) <= 5.5e+15) {
		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) <= -5.4e+174:
		tmp = b * c
	elif (b * c) <= 5.5e+15:
		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) <= -5.4e+174)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 5.5e+15)
		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) <= -5.4e+174)
		tmp = b * c;
	elseif ((b * c) <= 5.5e+15)
		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], -5.4e+174], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5.5e+15], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -5.3999999999999998e174 or 5.5e15 < (*.f64 b c)

   1. Initial program 85.1%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in b around inf 52.9%

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

   if -5.3999999999999998e174 < (*.f64 b c) < 5.5e15

   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 92.1%

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

   4. Taylor expanded in j around inf 31.9%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.4 \cdot 10^{+174}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 5.5 \cdot 10^{+15}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 18: 37.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.5 \cdot 10^{+180}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 3 \cdot 10^{+15}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1.5e+180)
   (* b c)
   (if (<= (* b c) 3e+15) (* j (* k -27.0)) (* b c))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1.5e+180) {
		tmp = b * c;
	} else if ((b * c) <= 3e+15) {
		tmp = j * (k * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-1.5d+180)) then
        tmp = b * c
    else if ((b * c) <= 3d+15) then
        tmp = j * (k * (-27.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1.5e+180) {
		tmp = b * c;
	} else if ((b * c) <= 3e+15) {
		tmp = j * (k * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1.5e+180:
		tmp = b * c
	elif (b * c) <= 3e+15:
		tmp = j * (k * -27.0)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1.5e+180)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 3e+15)
		tmp = Float64(j * Float64(k * -27.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1.5e+180)
		tmp = b * c;
	elseif ((b * c) <= 3e+15)
		tmp = j * (k * -27.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -1.5e+180], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3e+15], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.50000000000000001e180 or 3e15 < (*.f64 b c)

   1. Initial program 85.1%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in b around inf 52.9%

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

   if -1.50000000000000001e180 < (*.f64 b c) < 3e15

   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 92.1%

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

   4. Taylor expanded in j around inf 31.9%

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

      1. *-commutative 31.9%

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

      2. associate-*l* 31.9%

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

   6. Simplified 31.9%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.5 \cdot 10^{+180}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 3 \cdot 10^{+15}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 19: 23.8% accurate, 10.3× speedup

Math

\[\begin{array}{l} \\ b \cdot c \end{array} \]

FPCore

(FPCore (x y z t a b c i j k) :precision binary64 (* b c))

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = b * c
end function

Java

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

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(b * c), $MachinePrecision]

Derivation

1. Initial program 88.4%

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

3. Simplified 88.8%

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

4. Taylor expanded in b around inf 22.4%

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

5. Final simplification 22.4%

   \[\leadsto b \cdot c \]

Developer target: 89.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023283 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

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