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

Percentage Accurate: 85.8% → 91.3%

Time: 28.4s

Alternatives: 18

Speedup: 0.5×

• 49.6% 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: 85.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.3% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.6%

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

   3. Simplified 95.5%

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

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

   1. Initial program 0.0%

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

   3. Simplified 22.7%

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

   5. Taylor expanded in x around inf 59.3%

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

      1. expm1-log1p-u 41.1%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-udef 41.1%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]

   7. Applied egg-rr 41.1%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]
   8. Step-by-step derivation

      1. expm1-def 41.1%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-log1p 59.3%

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

      3. *-commutative 59.3%

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

      4. associate-*l* 63.8%

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

   9. Simplified 63.8%

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

4. Final simplification 92.8%

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

Alternative 2: 91.3% accurate, 0.5× speedup

Math

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

FPCore

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.6%

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

   3. Simplified 95.5%

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

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

   1. Initial program 0.0%

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

   3. Simplified 22.7%

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

   5. Taylor expanded in x around inf 59.3%

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

      1. expm1-log1p-u 41.1%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-udef 41.1%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]

   7. Applied egg-rr 41.1%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]
   8. Step-by-step derivation

      1. expm1-def 41.1%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-log1p 59.3%

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

      3. *-commutative 59.3%

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

      4. associate-*l* 63.8%

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

   9. Simplified 63.8%

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

4. Final simplification 92.8%

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

Alternative 3: 33.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -1.95 \cdot 10^{+305}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -8.2 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -7.2 \cdot 10^{-144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-324}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 3 \cdot 10^{-117}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 1.02 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 9 \cdot 10^{+130}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))) (t_2 (* -4.0 (* t a))))
   (if (<= (* b c) -1.95e+305)
     (* b c)
     (if (<= (* b c) -8.2e-53)
       t_1
       (if (<= (* b c) -7.2e-144)
         t_2
         (if (<= (* b c) -5e-324)
           t_1
           (if (<= (* b c) 3e-117)
             t_2
             (if (<= (* b c) 1.02e-80)
               t_1
               (if (<= (* b c) 9e+130) 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 = -27.0 * (j * k);
	double t_2 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -1.95e+305) {
		tmp = b * c;
	} else if ((b * c) <= -8.2e-53) {
		tmp = t_1;
	} else if ((b * c) <= -7.2e-144) {
		tmp = t_2;
	} else if ((b * c) <= -5e-324) {
		tmp = t_1;
	} else if ((b * c) <= 3e-117) {
		tmp = t_2;
	} else if ((b * c) <= 1.02e-80) {
		tmp = t_1;
	} else if ((b * c) <= 9e+130) {
		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 = (-27.0d0) * (j * k)
    t_2 = (-4.0d0) * (t * a)
    if ((b * c) <= (-1.95d+305)) then
        tmp = b * c
    else if ((b * c) <= (-8.2d-53)) then
        tmp = t_1
    else if ((b * c) <= (-7.2d-144)) then
        tmp = t_2
    else if ((b * c) <= (-5d-324)) then
        tmp = t_1
    else if ((b * c) <= 3d-117) then
        tmp = t_2
    else if ((b * c) <= 1.02d-80) then
        tmp = t_1
    else if ((b * c) <= 9d+130) 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 = -27.0 * (j * k);
	double t_2 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -1.95e+305) {
		tmp = b * c;
	} else if ((b * c) <= -8.2e-53) {
		tmp = t_1;
	} else if ((b * c) <= -7.2e-144) {
		tmp = t_2;
	} else if ((b * c) <= -5e-324) {
		tmp = t_1;
	} else if ((b * c) <= 3e-117) {
		tmp = t_2;
	} else if ((b * c) <= 1.02e-80) {
		tmp = t_1;
	} else if ((b * c) <= 9e+130) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	t_2 = -4.0 * (t * a)
	tmp = 0
	if (b * c) <= -1.95e+305:
		tmp = b * c
	elif (b * c) <= -8.2e-53:
		tmp = t_1
	elif (b * c) <= -7.2e-144:
		tmp = t_2
	elif (b * c) <= -5e-324:
		tmp = t_1
	elif (b * c) <= 3e-117:
		tmp = t_2
	elif (b * c) <= 1.02e-80:
		tmp = t_1
	elif (b * c) <= 9e+130:
		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(-27.0 * Float64(j * k))
	t_2 = Float64(-4.0 * Float64(t * a))
	tmp = 0.0
	if (Float64(b * c) <= -1.95e+305)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -8.2e-53)
		tmp = t_1;
	elseif (Float64(b * c) <= -7.2e-144)
		tmp = t_2;
	elseif (Float64(b * c) <= -5e-324)
		tmp = t_1;
	elseif (Float64(b * c) <= 3e-117)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.02e-80)
		tmp = t_1;
	elseif (Float64(b * c) <= 9e+130)
		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 = -27.0 * (j * k);
	t_2 = -4.0 * (t * a);
	tmp = 0.0;
	if ((b * c) <= -1.95e+305)
		tmp = b * c;
	elseif ((b * c) <= -8.2e-53)
		tmp = t_1;
	elseif ((b * c) <= -7.2e-144)
		tmp = t_2;
	elseif ((b * c) <= -5e-324)
		tmp = t_1;
	elseif ((b * c) <= 3e-117)
		tmp = t_2;
	elseif ((b * c) <= 1.02e-80)
		tmp = t_1;
	elseif ((b * c) <= 9e+130)
		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[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.95e+305], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -8.2e-53], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -7.2e-144], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -5e-324], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 3e-117], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.02e-80], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 9e+130], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.95e305 or 9.00000000000000078e130 < (*.f64 b c)

   1. Initial program 81.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in x around -inf 81.3%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in b around inf 75.9%

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

   if -1.95e305 < (*.f64 b c) < -8.2000000000000001e-53 or -7.2000000000000001e-144 < (*.f64 b c) < -4.94066e-324 or 2.99999999999999991e-117 < (*.f64 b c) < 1.02000000000000005e-80

   1. Initial program 91.5%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in j around inf 44.3%

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

   if -8.2000000000000001e-53 < (*.f64 b c) < -7.2000000000000001e-144 or -4.94066e-324 < (*.f64 b c) < 2.99999999999999991e-117 or 1.02000000000000005e-80 < (*.f64 b c) < 9.00000000000000078e130

   1. Initial program 87.4%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in x around -inf 88.1%

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

   7. Simplified 88.1%

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

   8. Taylor expanded in a around inf 41.9%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.95 \cdot 10^{+305}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -8.2 \cdot 10^{-53}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -7.2 \cdot 10^{-144}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-324}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 3 \cdot 10^{-117}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.02 \cdot 10^{-80}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 9 \cdot 10^{+130}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 33.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -1.95 \cdot 10^{+305}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.05 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -7.2 \cdot 10^{-144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-324}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.35 \cdot 10^{-111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 3.6 \cdot 10^{-78}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 3.5 \cdot 10^{+127}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (* -4.0 (* t a))))
   (if (<= (* b c) -1.95e+305)
     (* b c)
     (if (<= (* b c) -1.05e-55)
       t_1
       (if (<= (* b c) -7.2e-144)
         t_2
         (if (<= (* b c) -5e-324)
           t_1
           (if (<= (* b c) 1.35e-111)
             t_2
             (if (<= (* b c) 3.6e-78)
               (* -27.0 (* j k))
               (if (<= (* b c) 3.5e+127) 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 = j * (k * -27.0);
	double t_2 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -1.95e+305) {
		tmp = b * c;
	} else if ((b * c) <= -1.05e-55) {
		tmp = t_1;
	} else if ((b * c) <= -7.2e-144) {
		tmp = t_2;
	} else if ((b * c) <= -5e-324) {
		tmp = t_1;
	} else if ((b * c) <= 1.35e-111) {
		tmp = t_2;
	} else if ((b * c) <= 3.6e-78) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 3.5e+127) {
		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 = j * (k * (-27.0d0))
    t_2 = (-4.0d0) * (t * a)
    if ((b * c) <= (-1.95d+305)) then
        tmp = b * c
    else if ((b * c) <= (-1.05d-55)) then
        tmp = t_1
    else if ((b * c) <= (-7.2d-144)) then
        tmp = t_2
    else if ((b * c) <= (-5d-324)) then
        tmp = t_1
    else if ((b * c) <= 1.35d-111) then
        tmp = t_2
    else if ((b * c) <= 3.6d-78) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 3.5d+127) 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 = j * (k * -27.0);
	double t_2 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -1.95e+305) {
		tmp = b * c;
	} else if ((b * c) <= -1.05e-55) {
		tmp = t_1;
	} else if ((b * c) <= -7.2e-144) {
		tmp = t_2;
	} else if ((b * c) <= -5e-324) {
		tmp = t_1;
	} else if ((b * c) <= 1.35e-111) {
		tmp = t_2;
	} else if ((b * c) <= 3.6e-78) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 3.5e+127) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = -4.0 * (t * a)
	tmp = 0
	if (b * c) <= -1.95e+305:
		tmp = b * c
	elif (b * c) <= -1.05e-55:
		tmp = t_1
	elif (b * c) <= -7.2e-144:
		tmp = t_2
	elif (b * c) <= -5e-324:
		tmp = t_1
	elif (b * c) <= 1.35e-111:
		tmp = t_2
	elif (b * c) <= 3.6e-78:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 3.5e+127:
		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(j * Float64(k * -27.0))
	t_2 = Float64(-4.0 * Float64(t * a))
	tmp = 0.0
	if (Float64(b * c) <= -1.95e+305)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.05e-55)
		tmp = t_1;
	elseif (Float64(b * c) <= -7.2e-144)
		tmp = t_2;
	elseif (Float64(b * c) <= -5e-324)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.35e-111)
		tmp = t_2;
	elseif (Float64(b * c) <= 3.6e-78)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 3.5e+127)
		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 = j * (k * -27.0);
	t_2 = -4.0 * (t * a);
	tmp = 0.0;
	if ((b * c) <= -1.95e+305)
		tmp = b * c;
	elseif ((b * c) <= -1.05e-55)
		tmp = t_1;
	elseif ((b * c) <= -7.2e-144)
		tmp = t_2;
	elseif ((b * c) <= -5e-324)
		tmp = t_1;
	elseif ((b * c) <= 1.35e-111)
		tmp = t_2;
	elseif ((b * c) <= 3.6e-78)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 3.5e+127)
		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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.95e+305], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.05e-55], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -7.2e-144], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -5e-324], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.35e-111], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 3.6e-78], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.5e+127], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.95e305 or 3.49999999999999978e127 < (*.f64 b c)

   1. Initial program 81.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in x around -inf 81.3%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in b around inf 75.9%

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

   if -1.95e305 < (*.f64 b c) < -1.0500000000000001e-55 or -7.2000000000000001e-144 < (*.f64 b c) < -4.94066e-324

   1. Initial program 91.6%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in x around -inf 91.6%

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

   7. Simplified 91.6%

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

   8. Taylor expanded in k around inf 40.5%

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

      1. associate-*r* 40.5%

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

      2. *-commutative 40.5%

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

      3. associate-*r* 40.6%

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

   10. Simplified 40.6%

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

   if -1.0500000000000001e-55 < (*.f64 b c) < -7.2000000000000001e-144 or -4.94066e-324 < (*.f64 b c) < 1.34999999999999994e-111 or 3.6000000000000002e-78 < (*.f64 b c) < 3.49999999999999978e127

   1. Initial program 87.4%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in x around -inf 88.1%

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

   7. Simplified 88.1%

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

   8. Taylor expanded in a around inf 41.9%

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

   if 1.34999999999999994e-111 < (*.f64 b c) < 3.6000000000000002e-78

   1. Initial program 90.8%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in j around inf 71.0%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.95 \cdot 10^{+305}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.05 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -7.2 \cdot 10^{-144}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-324}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.35 \cdot 10^{-111}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 3.6 \cdot 10^{-78}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 3.5 \cdot 10^{+127}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 33.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -1.95 \cdot 10^{+305}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.1 \cdot 10^{-48}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -3.3 \cdot 10^{-143}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-324}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 9.6 \cdot 10^{-113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 8.2 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{+125}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j -27.0))) (t_2 (* -4.0 (* t a))))
   (if (<= (* b c) -1.95e+305)
     (* b c)
     (if (<= (* b c) -1.1e-48)
       (* j (* k -27.0))
       (if (<= (* b c) -3.3e-143)
         t_2
         (if (<= (* b c) -5e-324)
           t_1
           (if (<= (* b c) 9.6e-113)
             t_2
             (if (<= (* b c) 8.2e-81)
               t_1
               (if (<= (* b c) 1.6e+125) 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 = k * (j * -27.0);
	double t_2 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -1.95e+305) {
		tmp = b * c;
	} else if ((b * c) <= -1.1e-48) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= -3.3e-143) {
		tmp = t_2;
	} else if ((b * c) <= -5e-324) {
		tmp = t_1;
	} else if ((b * c) <= 9.6e-113) {
		tmp = t_2;
	} else if ((b * c) <= 8.2e-81) {
		tmp = t_1;
	} else if ((b * c) <= 1.6e+125) {
		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 = k * (j * (-27.0d0))
    t_2 = (-4.0d0) * (t * a)
    if ((b * c) <= (-1.95d+305)) then
        tmp = b * c
    else if ((b * c) <= (-1.1d-48)) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= (-3.3d-143)) then
        tmp = t_2
    else if ((b * c) <= (-5d-324)) then
        tmp = t_1
    else if ((b * c) <= 9.6d-113) then
        tmp = t_2
    else if ((b * c) <= 8.2d-81) then
        tmp = t_1
    else if ((b * c) <= 1.6d+125) 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 = k * (j * -27.0);
	double t_2 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -1.95e+305) {
		tmp = b * c;
	} else if ((b * c) <= -1.1e-48) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= -3.3e-143) {
		tmp = t_2;
	} else if ((b * c) <= -5e-324) {
		tmp = t_1;
	} else if ((b * c) <= 9.6e-113) {
		tmp = t_2;
	} else if ((b * c) <= 8.2e-81) {
		tmp = t_1;
	} else if ((b * c) <= 1.6e+125) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * -27.0)
	t_2 = -4.0 * (t * a)
	tmp = 0
	if (b * c) <= -1.95e+305:
		tmp = b * c
	elif (b * c) <= -1.1e-48:
		tmp = j * (k * -27.0)
	elif (b * c) <= -3.3e-143:
		tmp = t_2
	elif (b * c) <= -5e-324:
		tmp = t_1
	elif (b * c) <= 9.6e-113:
		tmp = t_2
	elif (b * c) <= 8.2e-81:
		tmp = t_1
	elif (b * c) <= 1.6e+125:
		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(k * Float64(j * -27.0))
	t_2 = Float64(-4.0 * Float64(t * a))
	tmp = 0.0
	if (Float64(b * c) <= -1.95e+305)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.1e-48)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= -3.3e-143)
		tmp = t_2;
	elseif (Float64(b * c) <= -5e-324)
		tmp = t_1;
	elseif (Float64(b * c) <= 9.6e-113)
		tmp = t_2;
	elseif (Float64(b * c) <= 8.2e-81)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.6e+125)
		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 = k * (j * -27.0);
	t_2 = -4.0 * (t * a);
	tmp = 0.0;
	if ((b * c) <= -1.95e+305)
		tmp = b * c;
	elseif ((b * c) <= -1.1e-48)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= -3.3e-143)
		tmp = t_2;
	elseif ((b * c) <= -5e-324)
		tmp = t_1;
	elseif ((b * c) <= 9.6e-113)
		tmp = t_2;
	elseif ((b * c) <= 8.2e-81)
		tmp = t_1;
	elseif ((b * c) <= 1.6e+125)
		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[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.95e+305], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.1e-48], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.3e-143], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -5e-324], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 9.6e-113], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 8.2e-81], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.6e+125], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.95e305 or 1.59999999999999992e125 < (*.f64 b c)

   1. Initial program 81.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in x around -inf 81.3%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in b around inf 75.9%

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

   if -1.95e305 < (*.f64 b c) < -1.10000000000000006e-48

   1. Initial program 89.6%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in x around -inf 91.5%

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

   7. Simplified 91.5%

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

   8. Taylor expanded in k around inf 36.8%

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

      1. associate-*r* 36.8%

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

      2. *-commutative 36.8%

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

      3. associate-*r* 36.8%

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

   10. Simplified 36.8%

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

   if -1.10000000000000006e-48 < (*.f64 b c) < -3.3000000000000001e-143 or -4.94066e-324 < (*.f64 b c) < 9.60000000000000049e-113 or 8.19999999999999968e-81 < (*.f64 b c) < 1.59999999999999992e125

   1. Initial program 87.4%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in x around -inf 88.1%

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

   7. Simplified 88.1%

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

   8. Taylor expanded in a around inf 41.9%

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

   if -3.3000000000000001e-143 < (*.f64 b c) < -4.94066e-324 or 9.60000000000000049e-113 < (*.f64 b c) < 8.19999999999999968e-81

   1. Initial program 94.1%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in j around inf 54.5%

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

      1. *-commutative 54.5%

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

      2. *-commutative 54.5%

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

      3. associate-*r* 54.5%

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

   7. Simplified 54.5%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.95 \cdot 10^{+305}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.1 \cdot 10^{-48}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -3.3 \cdot 10^{-143}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-324}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 9.6 \cdot 10^{-113}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 8.2 \cdot 10^{-81}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{+125}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 33.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -1.95 \cdot 10^{+305}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.3 \cdot 10^{-58}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -1.3 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-324}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 4.5 \cdot 10^{-113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 4.5 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 2.3 \cdot 10^{+127}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j -27.0))) (t_2 (* -4.0 (* t a))))
   (if (<= (* b c) -1.95e+305)
     (* b c)
     (if (<= (* b c) -1.3e-58)
       (* j (* k -27.0))
       (if (<= (* b c) -1.3e-132)
         (* x (* i -4.0))
         (if (<= (* b c) -5e-324)
           t_1
           (if (<= (* b c) 4.5e-113)
             t_2
             (if (<= (* b c) 4.5e-77)
               t_1
               (if (<= (* b c) 2.3e+127) 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 = k * (j * -27.0);
	double t_2 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -1.95e+305) {
		tmp = b * c;
	} else if ((b * c) <= -1.3e-58) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= -1.3e-132) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= -5e-324) {
		tmp = t_1;
	} else if ((b * c) <= 4.5e-113) {
		tmp = t_2;
	} else if ((b * c) <= 4.5e-77) {
		tmp = t_1;
	} else if ((b * c) <= 2.3e+127) {
		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 = k * (j * (-27.0d0))
    t_2 = (-4.0d0) * (t * a)
    if ((b * c) <= (-1.95d+305)) then
        tmp = b * c
    else if ((b * c) <= (-1.3d-58)) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= (-1.3d-132)) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= (-5d-324)) then
        tmp = t_1
    else if ((b * c) <= 4.5d-113) then
        tmp = t_2
    else if ((b * c) <= 4.5d-77) then
        tmp = t_1
    else if ((b * c) <= 2.3d+127) 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 = k * (j * -27.0);
	double t_2 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -1.95e+305) {
		tmp = b * c;
	} else if ((b * c) <= -1.3e-58) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= -1.3e-132) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= -5e-324) {
		tmp = t_1;
	} else if ((b * c) <= 4.5e-113) {
		tmp = t_2;
	} else if ((b * c) <= 4.5e-77) {
		tmp = t_1;
	} else if ((b * c) <= 2.3e+127) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * -27.0)
	t_2 = -4.0 * (t * a)
	tmp = 0
	if (b * c) <= -1.95e+305:
		tmp = b * c
	elif (b * c) <= -1.3e-58:
		tmp = j * (k * -27.0)
	elif (b * c) <= -1.3e-132:
		tmp = x * (i * -4.0)
	elif (b * c) <= -5e-324:
		tmp = t_1
	elif (b * c) <= 4.5e-113:
		tmp = t_2
	elif (b * c) <= 4.5e-77:
		tmp = t_1
	elif (b * c) <= 2.3e+127:
		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(k * Float64(j * -27.0))
	t_2 = Float64(-4.0 * Float64(t * a))
	tmp = 0.0
	if (Float64(b * c) <= -1.95e+305)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.3e-58)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= -1.3e-132)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= -5e-324)
		tmp = t_1;
	elseif (Float64(b * c) <= 4.5e-113)
		tmp = t_2;
	elseif (Float64(b * c) <= 4.5e-77)
		tmp = t_1;
	elseif (Float64(b * c) <= 2.3e+127)
		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 = k * (j * -27.0);
	t_2 = -4.0 * (t * a);
	tmp = 0.0;
	if ((b * c) <= -1.95e+305)
		tmp = b * c;
	elseif ((b * c) <= -1.3e-58)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= -1.3e-132)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= -5e-324)
		tmp = t_1;
	elseif ((b * c) <= 4.5e-113)
		tmp = t_2;
	elseif ((b * c) <= 4.5e-77)
		tmp = t_1;
	elseif ((b * c) <= 2.3e+127)
		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[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.95e+305], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.3e-58], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.3e-132], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5e-324], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 4.5e-113], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 4.5e-77], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 2.3e+127], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -1.95e305 or 2.3000000000000002e127 < (*.f64 b c)

   1. Initial program 81.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in x around -inf 81.3%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in b around inf 75.9%

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

   if -1.95e305 < (*.f64 b c) < -1.30000000000000003e-58

   1. Initial program 89.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in x around -inf 91.7%

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

   7. Simplified 91.7%

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

   8. Taylor expanded in k around inf 36.1%

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

      1. associate-*r* 36.1%

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

      2. *-commutative 36.1%

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

      3. associate-*r* 36.1%

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

   10. Simplified 36.1%

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

   if -1.30000000000000003e-58 < (*.f64 b c) < -1.3e-132

   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 86.9%

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

   5. Taylor expanded in x around -inf 86.9%

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

   7. Simplified 86.9%

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

   8. Taylor expanded in i around inf 67.8%

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

      1. associate-*r* 67.8%

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

      2. *-commutative 67.8%

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

   10. Simplified 67.8%

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

   if -1.3e-132 < (*.f64 b c) < -4.94066e-324 or 4.5000000000000001e-113 < (*.f64 b c) < 4.5000000000000001e-77

   1. Initial program 94.7%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in j around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. *-commutative 51.5%

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

      3. associate-*r* 51.5%

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

   7. Simplified 51.5%

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

   if -4.94066e-324 < (*.f64 b c) < 4.5000000000000001e-113 or 4.5000000000000001e-77 < (*.f64 b c) < 2.3000000000000002e127

   1. Initial program 86.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in x around -inf 87.7%

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

   7. Simplified 87.8%

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

   8. Taylor expanded in a around inf 43.0%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.95 \cdot 10^{+305}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.3 \cdot 10^{-58}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -1.3 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-324}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 4.5 \cdot 10^{-113}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 4.5 \cdot 10^{-77}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2.3 \cdot 10^{+127}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t\_1\\ \mathbf{if}\;b \cdot c \leq -5.7 \cdot 10^{+209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -7.2 \cdot 10^{+179}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -5.5 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -8.8 \cdot 10^{-110}:\\ \;\;\;\;t\_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.15 \cdot 10^{+124}:\\ \;\;\;\;t\_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ (* b c) t_1)))
   (if (<= (* b c) -5.7e+209)
     t_2
     (if (<= (* b c) -7.2e+179)
       (* t (+ (* 18.0 (* x (* y z))) (* a -4.0)))
       (if (<= (* b c) -5.5e+58)
         t_2
         (if (<= (* b c) -8.8e-110)
           (+ t_1 (* x (* i -4.0)))
           (if (<= (* b c) 1.15e+124) (+ t_1 (* -4.0 (* t a))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if ((b * c) <= -5.7e+209) {
		tmp = t_2;
	} else if ((b * c) <= -7.2e+179) {
		tmp = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	} else if ((b * c) <= -5.5e+58) {
		tmp = t_2;
	} else if ((b * c) <= -8.8e-110) {
		tmp = t_1 + (x * (i * -4.0));
	} else if ((b * c) <= 1.15e+124) {
		tmp = t_1 + (-4.0 * (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    if ((b * c) <= (-5.7d+209)) then
        tmp = t_2
    else if ((b * c) <= (-7.2d+179)) then
        tmp = t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0)))
    else if ((b * c) <= (-5.5d+58)) then
        tmp = t_2
    else if ((b * c) <= (-8.8d-110)) then
        tmp = t_1 + (x * (i * (-4.0d0)))
    else if ((b * c) <= 1.15d+124) then
        tmp = t_1 + ((-4.0d0) * (t * a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if ((b * c) <= -5.7e+209) {
		tmp = t_2;
	} else if ((b * c) <= -7.2e+179) {
		tmp = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	} else if ((b * c) <= -5.5e+58) {
		tmp = t_2;
	} else if ((b * c) <= -8.8e-110) {
		tmp = t_1 + (x * (i * -4.0));
	} else if ((b * c) <= 1.15e+124) {
		tmp = t_1 + (-4.0 * (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	tmp = 0
	if (b * c) <= -5.7e+209:
		tmp = t_2
	elif (b * c) <= -7.2e+179:
		tmp = t * ((18.0 * (x * (y * z))) + (a * -4.0))
	elif (b * c) <= -5.5e+58:
		tmp = t_2
	elif (b * c) <= -8.8e-110:
		tmp = t_1 + (x * (i * -4.0))
	elif (b * c) <= 1.15e+124:
		tmp = t_1 + (-4.0 * (t * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	tmp = 0.0
	if (Float64(b * c) <= -5.7e+209)
		tmp = t_2;
	elseif (Float64(b * c) <= -7.2e+179)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0)));
	elseif (Float64(b * c) <= -5.5e+58)
		tmp = t_2;
	elseif (Float64(b * c) <= -8.8e-110)
		tmp = Float64(t_1 + Float64(x * Float64(i * -4.0)));
	elseif (Float64(b * c) <= 1.15e+124)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	tmp = 0.0;
	if ((b * c) <= -5.7e+209)
		tmp = t_2;
	elseif ((b * c) <= -7.2e+179)
		tmp = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	elseif ((b * c) <= -5.5e+58)
		tmp = t_2;
	elseif ((b * c) <= -8.8e-110)
		tmp = t_1 + (x * (i * -4.0));
	elseif ((b * c) <= 1.15e+124)
		tmp = t_1 + (-4.0 * (t * a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5.7e+209], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -7.2e+179], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5.5e+58], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -8.8e-110], N[(t$95$1 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.15e+124], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -5.7000000000000001e209 or -7.1999999999999995e179 < (*.f64 b c) < -5.4999999999999999e58 or 1.14999999999999992e124 < (*.f64 b c)

   1. Initial program 83.2%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in b around inf 76.4%

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

   if -5.7000000000000001e209 < (*.f64 b c) < -7.1999999999999995e179

   1. Initial program 88.3%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around -inf 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in t around inf 75.5%

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

   if -5.4999999999999999e58 < (*.f64 b c) < -8.7999999999999997e-110

   1. Initial program 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in i around inf 79.5%

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

      1. associate-*r* 79.5%

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

      2. *-commutative 79.5%

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

   7. Simplified 79.5%

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

   if -8.7999999999999997e-110 < (*.f64 b c) < 1.14999999999999992e124

   1. Initial program 89.5%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in a around inf 61.2%

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

      1. *-commutative 61.2%

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

   7. Simplified 61.2%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.7 \cdot 10^{+209}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -7.2 \cdot 10^{+179}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -5.5 \cdot 10^{+58}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -8.8 \cdot 10^{-110}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.15 \cdot 10^{+124}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 41.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ t_3 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;i \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.31 \cdot 10^{-291}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;i \leq 8.8 \cdot 10^{-290}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1650000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 2.9 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a))))
        (t_2 (* -27.0 (* j k)))
        (t_3 (* x (* i -4.0))))
   (if (<= i -2.5e+106)
     t_3
     (if (<= i -2.6e-193)
       t_1
       (if (<= i -1.31e-291)
         (* 18.0 (* x (* z (* y t))))
         (if (<= i 8.8e-290)
           t_2
           (if (<= i 1.45e-41)
             t_1
             (if (<= i 1650000.0) t_2 (if (<= i 2.9e+188) 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 * (t * a));
	double t_2 = -27.0 * (j * k);
	double t_3 = x * (i * -4.0);
	double tmp;
	if (i <= -2.5e+106) {
		tmp = t_3;
	} else if (i <= -2.6e-193) {
		tmp = t_1;
	} else if (i <= -1.31e-291) {
		tmp = 18.0 * (x * (z * (y * t)));
	} else if (i <= 8.8e-290) {
		tmp = t_2;
	} else if (i <= 1.45e-41) {
		tmp = t_1;
	} else if (i <= 1650000.0) {
		tmp = t_2;
	} else if (i <= 2.9e+188) {
		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) * (t * a))
    t_2 = (-27.0d0) * (j * k)
    t_3 = x * (i * (-4.0d0))
    if (i <= (-2.5d+106)) then
        tmp = t_3
    else if (i <= (-2.6d-193)) then
        tmp = t_1
    else if (i <= (-1.31d-291)) then
        tmp = 18.0d0 * (x * (z * (y * t)))
    else if (i <= 8.8d-290) then
        tmp = t_2
    else if (i <= 1.45d-41) then
        tmp = t_1
    else if (i <= 1650000.0d0) then
        tmp = t_2
    else if (i <= 2.9d+188) 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 * (t * a));
	double t_2 = -27.0 * (j * k);
	double t_3 = x * (i * -4.0);
	double tmp;
	if (i <= -2.5e+106) {
		tmp = t_3;
	} else if (i <= -2.6e-193) {
		tmp = t_1;
	} else if (i <= -1.31e-291) {
		tmp = 18.0 * (x * (z * (y * t)));
	} else if (i <= 8.8e-290) {
		tmp = t_2;
	} else if (i <= 1.45e-41) {
		tmp = t_1;
	} else if (i <= 1650000.0) {
		tmp = t_2;
	} else if (i <= 2.9e+188) {
		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 * (t * a))
	t_2 = -27.0 * (j * k)
	t_3 = x * (i * -4.0)
	tmp = 0
	if i <= -2.5e+106:
		tmp = t_3
	elif i <= -2.6e-193:
		tmp = t_1
	elif i <= -1.31e-291:
		tmp = 18.0 * (x * (z * (y * t)))
	elif i <= 8.8e-290:
		tmp = t_2
	elif i <= 1.45e-41:
		tmp = t_1
	elif i <= 1650000.0:
		tmp = t_2
	elif i <= 2.9e+188:
		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(t * a)))
	t_2 = Float64(-27.0 * Float64(j * k))
	t_3 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (i <= -2.5e+106)
		tmp = t_3;
	elseif (i <= -2.6e-193)
		tmp = t_1;
	elseif (i <= -1.31e-291)
		tmp = Float64(18.0 * Float64(x * Float64(z * Float64(y * t))));
	elseif (i <= 8.8e-290)
		tmp = t_2;
	elseif (i <= 1.45e-41)
		tmp = t_1;
	elseif (i <= 1650000.0)
		tmp = t_2;
	elseif (i <= 2.9e+188)
		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 * (t * a));
	t_2 = -27.0 * (j * k);
	t_3 = x * (i * -4.0);
	tmp = 0.0;
	if (i <= -2.5e+106)
		tmp = t_3;
	elseif (i <= -2.6e-193)
		tmp = t_1;
	elseif (i <= -1.31e-291)
		tmp = 18.0 * (x * (z * (y * t)));
	elseif (i <= 8.8e-290)
		tmp = t_2;
	elseif (i <= 1.45e-41)
		tmp = t_1;
	elseif (i <= 1650000.0)
		tmp = t_2;
	elseif (i <= 2.9e+188)
		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[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.5e+106], t$95$3, If[LessEqual[i, -2.6e-193], t$95$1, If[LessEqual[i, -1.31e-291], N[(18.0 * N[(x * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.8e-290], t$95$2, If[LessEqual[i, 1.45e-41], t$95$1, If[LessEqual[i, 1650000.0], t$95$2, If[LessEqual[i, 2.9e+188], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.4999999999999999e106 or 2.8999999999999999e188 < i

   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 87.5%

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

   5. Taylor expanded in x around -inf 87.5%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in i around inf 55.9%

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

      1. associate-*r* 55.9%

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

      2. *-commutative 55.9%

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

   10. Simplified 55.9%

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

   if -2.4999999999999999e106 < i < -2.60000000000000008e-193 or 8.8000000000000004e-290 < i < 1.44999999999999989e-41 or 1.65e6 < i < 2.8999999999999999e188

   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 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. Add Preprocessing

   5. Taylor expanded in x around 0 75.5%

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

      1. associate--l+ 75.5%

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

      2. *-commutative 75.5%

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

      3. associate-*r* 75.5%

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

      4. fma-def 76.2%

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

      5. *-commutative 76.2%

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

      6. *-commutative 76.2%

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

   7. Applied egg-rr 76.2%

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

   8. Taylor expanded in k around 0 60.5%

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

   if -2.60000000000000008e-193 < i < -1.31e-291

   1. Initial program 76.7%

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

   3. Simplified 76.8%

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

   5. Taylor expanded in x around -inf 82.4%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in y around inf 46.3%

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

      1. *-commutative 46.3%

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

      2. associate-*l* 46.4%

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

      3. *-commutative 46.4%

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

      4. associate-*r* 58.0%

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

      5. *-commutative 58.0%

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

   10. Simplified 58.0%

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

   if -1.31e-291 < i < 8.8000000000000004e-290 or 1.44999999999999989e-41 < i < 1.65e6

   1. Initial program 81.8%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in j around inf 75.5%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{-193}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;i \leq -1.31 \cdot 10^{-291}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;i \leq 8.8 \cdot 10^{-290}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{-41}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;i \leq 1650000:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;i \leq 2.9 \cdot 10^{+188}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ t_3 := t\_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;c \leq -6.2 \cdot 10^{-228}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-280}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-265}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-65}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 72000000000000:\\ \;\;\;\;t\_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))
        (t_3 (+ t_1 (* -4.0 (* t a)))))
   (if (<= c -6.2e-228)
     t_2
     (if (<= c -5.2e-280)
       t_3
       (if (<= c 4.6e-265)
         t_2
         (if (<= c 2.8e-65)
           t_3
           (if (<= c 72000000000000.0)
             (+ t_1 (* x (* i -4.0)))
             (if (<= c 4.5e+91)
               (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
               (+ (* b c) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double t_3 = t_1 + (-4.0 * (t * a));
	double tmp;
	if (c <= -6.2e-228) {
		tmp = t_2;
	} else if (c <= -5.2e-280) {
		tmp = t_3;
	} else if (c <= 4.6e-265) {
		tmp = t_2;
	} else if (c <= 2.8e-65) {
		tmp = t_3;
	} else if (c <= 72000000000000.0) {
		tmp = t_1 + (x * (i * -4.0));
	} else if (c <= 4.5e+91) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0)))
    t_3 = t_1 + ((-4.0d0) * (t * a))
    if (c <= (-6.2d-228)) then
        tmp = t_2
    else if (c <= (-5.2d-280)) then
        tmp = t_3
    else if (c <= 4.6d-265) then
        tmp = t_2
    else if (c <= 2.8d-65) then
        tmp = t_3
    else if (c <= 72000000000000.0d0) then
        tmp = t_1 + (x * (i * (-4.0d0)))
    else if (c <= 4.5d+91) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = (b * c) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double t_3 = t_1 + (-4.0 * (t * a));
	double tmp;
	if (c <= -6.2e-228) {
		tmp = t_2;
	} else if (c <= -5.2e-280) {
		tmp = t_3;
	} else if (c <= 4.6e-265) {
		tmp = t_2;
	} else if (c <= 2.8e-65) {
		tmp = t_3;
	} else if (c <= 72000000000000.0) {
		tmp = t_1 + (x * (i * -4.0));
	} else if (c <= 4.5e+91) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t * ((18.0 * (x * (y * z))) + (a * -4.0))
	t_3 = t_1 + (-4.0 * (t * a))
	tmp = 0
	if c <= -6.2e-228:
		tmp = t_2
	elif c <= -5.2e-280:
		tmp = t_3
	elif c <= 4.6e-265:
		tmp = t_2
	elif c <= 2.8e-65:
		tmp = t_3
	elif c <= 72000000000000.0:
		tmp = t_1 + (x * (i * -4.0))
	elif c <= 4.5e+91:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = (b * c) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0)))
	t_3 = Float64(t_1 + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (c <= -6.2e-228)
		tmp = t_2;
	elseif (c <= -5.2e-280)
		tmp = t_3;
	elseif (c <= 4.6e-265)
		tmp = t_2;
	elseif (c <= 2.8e-65)
		tmp = t_3;
	elseif (c <= 72000000000000.0)
		tmp = Float64(t_1 + Float64(x * Float64(i * -4.0)));
	elseif (c <= 4.5e+91)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(b * c) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	t_3 = t_1 + (-4.0 * (t * a));
	tmp = 0.0;
	if (c <= -6.2e-228)
		tmp = t_2;
	elseif (c <= -5.2e-280)
		tmp = t_3;
	elseif (c <= 4.6e-265)
		tmp = t_2;
	elseif (c <= 2.8e-65)
		tmp = t_3;
	elseif (c <= 72000000000000.0)
		tmp = t_1 + (x * (i * -4.0));
	elseif (c <= 4.5e+91)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = (b * c) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.2e-228], t$95$2, If[LessEqual[c, -5.2e-280], t$95$3, If[LessEqual[c, 4.6e-265], t$95$2, If[LessEqual[c, 2.8e-65], t$95$3, If[LessEqual[c, 72000000000000.0], N[(t$95$1 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.5e+91], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -6.1999999999999996e-228 or -5.2e-280 < c < 4.5999999999999998e-265

   1. Initial program 85.4%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in x around -inf 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in t around inf 52.4%

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

   if -6.1999999999999996e-228 < c < -5.2e-280 or 4.5999999999999998e-265 < c < 2.8e-65

   1. Initial program 92.2%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in a around inf 72.5%

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

      1. *-commutative 72.5%

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

   7. Simplified 72.5%

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

   if 2.8e-65 < c < 7.2e13

   1. Initial program 93.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in i around inf 63.6%

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

      1. associate-*r* 63.6%

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

      2. *-commutative 63.6%

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

   7. Simplified 63.6%

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

   if 7.2e13 < c < 4.5e91

   1. Initial program 88.2%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in x around inf 55.4%

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

   if 4.5e91 < c

   1. Initial program 84.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in b around inf 68.4%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{-228}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-280}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-265}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-65}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq 72000000000000:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ t_3 := t\_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;c \leq -5 \cdot 10^{-231}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-281}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-265}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{-64}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 250000000000:\\ \;\;\;\;t\_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))
        (t_3 (+ t_1 (* -4.0 (* t a)))))
   (if (<= c -5e-231)
     t_2
     (if (<= c -1.5e-281)
       t_3
       (if (<= c 3.5e-265)
         t_2
         (if (<= c 5.1e-64)
           t_3
           (if (<= c 250000000000.0)
             (+ t_1 (* x (* i -4.0)))
             (if (<= c 5.5e+92)
               (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))
               (+ (* b c) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double t_3 = t_1 + (-4.0 * (t * a));
	double tmp;
	if (c <= -5e-231) {
		tmp = t_2;
	} else if (c <= -1.5e-281) {
		tmp = t_3;
	} else if (c <= 3.5e-265) {
		tmp = t_2;
	} else if (c <= 5.1e-64) {
		tmp = t_3;
	} else if (c <= 250000000000.0) {
		tmp = t_1 + (x * (i * -4.0));
	} else if (c <= 5.5e+92) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0)))
    t_3 = t_1 + ((-4.0d0) * (t * a))
    if (c <= (-5d-231)) then
        tmp = t_2
    else if (c <= (-1.5d-281)) then
        tmp = t_3
    else if (c <= 3.5d-265) then
        tmp = t_2
    else if (c <= 5.1d-64) then
        tmp = t_3
    else if (c <= 250000000000.0d0) then
        tmp = t_1 + (x * (i * (-4.0d0)))
    else if (c <= 5.5d+92) then
        tmp = x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i))
    else
        tmp = (b * c) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double t_3 = t_1 + (-4.0 * (t * a));
	double tmp;
	if (c <= -5e-231) {
		tmp = t_2;
	} else if (c <= -1.5e-281) {
		tmp = t_3;
	} else if (c <= 3.5e-265) {
		tmp = t_2;
	} else if (c <= 5.1e-64) {
		tmp = t_3;
	} else if (c <= 250000000000.0) {
		tmp = t_1 + (x * (i * -4.0));
	} else if (c <= 5.5e+92) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t * ((18.0 * (x * (y * z))) + (a * -4.0))
	t_3 = t_1 + (-4.0 * (t * a))
	tmp = 0
	if c <= -5e-231:
		tmp = t_2
	elif c <= -1.5e-281:
		tmp = t_3
	elif c <= 3.5e-265:
		tmp = t_2
	elif c <= 5.1e-64:
		tmp = t_3
	elif c <= 250000000000.0:
		tmp = t_1 + (x * (i * -4.0))
	elif c <= 5.5e+92:
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i))
	else:
		tmp = (b * c) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0)))
	t_3 = Float64(t_1 + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (c <= -5e-231)
		tmp = t_2;
	elseif (c <= -1.5e-281)
		tmp = t_3;
	elseif (c <= 3.5e-265)
		tmp = t_2;
	elseif (c <= 5.1e-64)
		tmp = t_3;
	elseif (c <= 250000000000.0)
		tmp = Float64(t_1 + Float64(x * Float64(i * -4.0)));
	elseif (c <= 5.5e+92)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(b * c) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	t_3 = t_1 + (-4.0 * (t * a));
	tmp = 0.0;
	if (c <= -5e-231)
		tmp = t_2;
	elseif (c <= -1.5e-281)
		tmp = t_3;
	elseif (c <= 3.5e-265)
		tmp = t_2;
	elseif (c <= 5.1e-64)
		tmp = t_3;
	elseif (c <= 250000000000.0)
		tmp = t_1 + (x * (i * -4.0));
	elseif (c <= 5.5e+92)
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	else
		tmp = (b * c) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5e-231], t$95$2, If[LessEqual[c, -1.5e-281], t$95$3, If[LessEqual[c, 3.5e-265], t$95$2, If[LessEqual[c, 5.1e-64], t$95$3, If[LessEqual[c, 250000000000.0], N[(t$95$1 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.5e+92], N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -5.00000000000000023e-231 or -1.49999999999999987e-281 < c < 3.50000000000000015e-265

   1. Initial program 85.4%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in x around -inf 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in t around inf 52.4%

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

   if -5.00000000000000023e-231 < c < -1.49999999999999987e-281 or 3.50000000000000015e-265 < c < 5.09999999999999984e-64

   1. Initial program 92.2%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in a around inf 72.5%

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

      1. *-commutative 72.5%

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

   7. Simplified 72.5%

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

   if 5.09999999999999984e-64 < c < 2.5e11

   1. Initial program 93.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in i around inf 63.6%

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

      1. associate-*r* 63.6%

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

      2. *-commutative 63.6%

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

   7. Simplified 63.6%

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

   if 2.5e11 < c < 5.50000000000000053e92

   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 88.3%

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

   5. Taylor expanded in x around inf 53.2%

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

      1. expm1-log1p-u 32.7%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-udef 32.8%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]

   7. Applied egg-rr 32.8%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]
   8. Step-by-step derivation

      1. expm1-def 32.7%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-log1p 53.2%

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

      3. *-commutative 53.2%

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

      4. associate-*l* 56.9%

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

   9. Simplified 56.9%

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

   if 5.50000000000000053e92 < c

   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 94.1%

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

   5. Taylor expanded in b around inf 67.8%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-281}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-265}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{-64}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq 250000000000:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+183} \lor \neg \left(x \leq 6.8 \cdot 10^{-48} \lor \neg \left(x \leq 0.0205\right) \land x \leq 1.18 \cdot 10^{+225}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -9.5e+183)
         (not (or (<= x 6.8e-48) (and (not (<= x 0.0205)) (<= x 1.18e+225)))))
   (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))
   (- (+ (* b c) (* -4.0 (* t a))) (* 27.0 (* j k)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -9.5e+183) || !((x <= 6.8e-48) || (!(x <= 0.0205) && (x <= 1.18e+225)))) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-9.5d+183)) .or. (.not. (x <= 6.8d-48) .or. (.not. (x <= 0.0205d0)) .and. (x <= 1.18d+225))) then
        tmp = x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i))
    else
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -9.5e+183) || !((x <= 6.8e-48) || (!(x <= 0.0205) && (x <= 1.18e+225)))) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -9.5e+183) or not ((x <= 6.8e-48) or (not (x <= 0.0205) and (x <= 1.18e+225))):
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i))
	else:
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -9.5e+183) || !((x <= 6.8e-48) || (!(x <= 0.0205) && (x <= 1.18e+225))))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -9.5e+183) || ~(((x <= 6.8e-48) || (~((x <= 0.0205)) && (x <= 1.18e+225)))))
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	else
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -9.5e+183], N[Not[Or[LessEqual[x, 6.8e-48], And[N[Not[LessEqual[x, 0.0205]], $MachinePrecision], LessEqual[x, 1.18e+225]]]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000003e183 or 6.80000000000000056e-48 < x < 0.0205000000000000009 or 1.17999999999999992e225 < x

   1. Initial program 65.4%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in x around inf 79.0%

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

      1. expm1-log1p-u 59.1%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-udef 57.1%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]

   7. Applied egg-rr 57.1%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]
   8. Step-by-step derivation

      1. expm1-def 59.1%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-log1p 79.0%

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

      3. *-commutative 79.0%

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

      4. associate-*l* 82.7%

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

   9. Simplified 82.7%

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

   if -9.5000000000000003e183 < x < 6.80000000000000056e-48 or 0.0205000000000000009 < x < 1.17999999999999992e225

   1. Initial program 92.8%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in x around 0 75.4%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+183} \lor \neg \left(x \leq 6.8 \cdot 10^{-48} \lor \neg \left(x \leq 0.0205\right) \land x \leq 1.18 \cdot 10^{+225}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 70.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -2.6 \cdot 10^{-29}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{+180}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -2.6e-29)
   (+ (* b c) (* j (* k -27.0)))
   (if (<= k 2.9e+180)
     (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) (* 4.0 (* x i)))
     (- (+ (* b c) (* -4.0 (* t a))) (* 27.0 (* j k))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -2.6e-29) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (k <= 2.9e+180) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (k <= (-2.6d-29)) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (k <= 2.9d+180) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (4.0d0 * (x * i))
    else
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -2.6e-29) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (k <= 2.9e+180) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -2.6e-29:
		tmp = (b * c) + (j * (k * -27.0))
	elif k <= 2.9e+180:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i))
	else:
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -2.6e-29)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (k <= 2.9e+180)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -2.6e-29)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (k <= 2.9e+180)
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	else
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -2.6e-29], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.9e+180], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -2.6000000000000002e-29

   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 85.5%

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

   5. Taylor expanded in b around inf 56.7%

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

   if -2.6000000000000002e-29 < k < 2.90000000000000007e180

   1. Initial program 87.8%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in j around 0 78.9%

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

   if 2.90000000000000007e180 < k

   1. Initial program 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in x around 0 89.8%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.6 \cdot 10^{-29}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{+180}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t\_1\\ \mathbf{if}\;b \cdot c \leq -2.6 \cdot 10^{-59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -1.05 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 3.5 \cdot 10^{+128}:\\ \;\;\;\;t\_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ (* b c) t_1)))
   (if (<= (* b c) -2.6e-59)
     t_2
     (if (<= (* b c) -1.05e-109)
       (* x (* i -4.0))
       (if (<= (* b c) 3.5e+128) (+ t_1 (* -4.0 (* t a))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if ((b * c) <= -2.6e-59) {
		tmp = t_2;
	} else if ((b * c) <= -1.05e-109) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 3.5e+128) {
		tmp = t_1 + (-4.0 * (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    if ((b * c) <= (-2.6d-59)) then
        tmp = t_2
    else if ((b * c) <= (-1.05d-109)) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= 3.5d+128) then
        tmp = t_1 + ((-4.0d0) * (t * a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if ((b * c) <= -2.6e-59) {
		tmp = t_2;
	} else if ((b * c) <= -1.05e-109) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 3.5e+128) {
		tmp = t_1 + (-4.0 * (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	tmp = 0
	if (b * c) <= -2.6e-59:
		tmp = t_2
	elif (b * c) <= -1.05e-109:
		tmp = x * (i * -4.0)
	elif (b * c) <= 3.5e+128:
		tmp = t_1 + (-4.0 * (t * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	tmp = 0.0
	if (Float64(b * c) <= -2.6e-59)
		tmp = t_2;
	elseif (Float64(b * c) <= -1.05e-109)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= 3.5e+128)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	tmp = 0.0;
	if ((b * c) <= -2.6e-59)
		tmp = t_2;
	elseif ((b * c) <= -1.05e-109)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= 3.5e+128)
		tmp = t_1 + (-4.0 * (t * a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.6e-59], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -1.05e-109], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.5e+128], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.59999999999999998e-59 or 3.49999999999999969e128 < (*.f64 b c)

   1. Initial program 85.3%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in b around inf 68.1%

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

   if -2.59999999999999998e-59 < (*.f64 b c) < -1.04999999999999998e-109

   1. Initial program 77.8%

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

   3. Simplified 78.1%

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

   5. Taylor expanded in x around -inf 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in i around inf 89.5%

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

      1. associate-*r* 89.5%

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

      2. *-commutative 89.5%

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

   10. Simplified 89.5%

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

   if -1.04999999999999998e-109 < (*.f64 b c) < 3.49999999999999969e128

   1. Initial program 89.5%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in a around inf 61.2%

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

      1. *-commutative 61.2%

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

   7. Simplified 61.2%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.6 \cdot 10^{-59}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -1.05 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 3.5 \cdot 10^{+128}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t\_1\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -8.5 \cdot 10^{-110}:\\ \;\;\;\;t\_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2.4 \cdot 10^{+130}:\\ \;\;\;\;t\_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ (* b c) t_1)))
   (if (<= (* b c) -5e+54)
     t_2
     (if (<= (* b c) -8.5e-110)
       (+ t_1 (* x (* i -4.0)))
       (if (<= (* b c) 2.4e+130) (+ t_1 (* -4.0 (* t a))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if ((b * c) <= -5e+54) {
		tmp = t_2;
	} else if ((b * c) <= -8.5e-110) {
		tmp = t_1 + (x * (i * -4.0));
	} else if ((b * c) <= 2.4e+130) {
		tmp = t_1 + (-4.0 * (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    if ((b * c) <= (-5d+54)) then
        tmp = t_2
    else if ((b * c) <= (-8.5d-110)) then
        tmp = t_1 + (x * (i * (-4.0d0)))
    else if ((b * c) <= 2.4d+130) then
        tmp = t_1 + ((-4.0d0) * (t * a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if ((b * c) <= -5e+54) {
		tmp = t_2;
	} else if ((b * c) <= -8.5e-110) {
		tmp = t_1 + (x * (i * -4.0));
	} else if ((b * c) <= 2.4e+130) {
		tmp = t_1 + (-4.0 * (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	tmp = 0
	if (b * c) <= -5e+54:
		tmp = t_2
	elif (b * c) <= -8.5e-110:
		tmp = t_1 + (x * (i * -4.0))
	elif (b * c) <= 2.4e+130:
		tmp = t_1 + (-4.0 * (t * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	tmp = 0.0
	if (Float64(b * c) <= -5e+54)
		tmp = t_2;
	elseif (Float64(b * c) <= -8.5e-110)
		tmp = Float64(t_1 + Float64(x * Float64(i * -4.0)));
	elseif (Float64(b * c) <= 2.4e+130)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	tmp = 0.0;
	if ((b * c) <= -5e+54)
		tmp = t_2;
	elseif ((b * c) <= -8.5e-110)
		tmp = t_1 + (x * (i * -4.0));
	elseif ((b * c) <= 2.4e+130)
		tmp = t_1 + (-4.0 * (t * a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5e+54], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -8.5e-110], N[(t$95$1 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.4e+130], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -5.00000000000000005e54 or 2.40000000000000024e130 < (*.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 88.0%

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

   5. Taylor expanded in b around inf 71.1%

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

   if -5.00000000000000005e54 < (*.f64 b c) < -8.50000000000000029e-110

   1. Initial program 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in i around inf 79.5%

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

      1. associate-*r* 79.5%

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

      2. *-commutative 79.5%

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

   7. Simplified 79.5%

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

   if -8.50000000000000029e-110 < (*.f64 b c) < 2.40000000000000024e130

   1. Initial program 89.5%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in a around inf 61.2%

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

      1. *-commutative 61.2%

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

   7. Simplified 61.2%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+54}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -8.5 \cdot 10^{-110}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2.4 \cdot 10^{+130}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 68.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+183}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-114}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -8.5e+183)
   (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))
   (if (<= x 5.4e-114)
     (- (+ (* b c) (* -4.0 (* t a))) (* 27.0 (* j k)))
     (+ (* j (* k -27.0)) (* t (+ (* 18.0 (* x (* y z))) (* a -4.0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -8.5e+183) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else if (x <= 5.4e-114) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	} else {
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-8.5d+183)) then
        tmp = x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i))
    else if (x <= 5.4d-114) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (27.0d0 * (j * k))
    else
        tmp = (j * (k * (-27.0d0))) + (t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -8.5e+183) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else if (x <= 5.4e-114) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	} else {
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -8.5e+183:
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i))
	elif x <= 5.4e-114:
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k))
	else:
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -8.5e+183)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)));
	elseif (x <= 5.4e-114)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -8.5e+183)
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	elseif (x <= 5.4e-114)
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	else
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -8.5e+183], N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.4e-114], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.5000000000000004e183

   1. Initial program 67.7%

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

   3. Simplified 76.1%

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

   5. Taylor expanded in x around inf 79.9%

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

      1. expm1-log1p-u 66.7%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-udef 66.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]

   7. Applied egg-rr 66.5%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]
   8. Step-by-step derivation

      1. expm1-def 66.7%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-log1p 79.9%

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

      3. *-commutative 79.9%

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

      4. associate-*l* 83.7%

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

   9. Simplified 83.7%

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

   if -8.5000000000000004e183 < x < 5.3999999999999999e-114

   1. Initial program 93.0%

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

   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. Add Preprocessing

   5. Taylor expanded in x around 0 78.0%

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

   if 5.3999999999999999e-114 < x

   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 91.3%

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

   5. Taylor expanded in t around inf 68.9%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+183}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-114}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 35.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.95 \cdot 10^{+305} \lor \neg \left(b \cdot c \leq 3.95 \cdot 10^{+62}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -1.95e+305) (not (<= (* b c) 3.95e+62)))
   (* b c)
   (* -27.0 (* j k))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -1.95e+305) || !((b * c) <= 3.95e+62)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-1.95d+305)) .or. (.not. ((b * c) <= 3.95d+62))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (j * k)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -1.95e+305) || !((b * c) <= 3.95e+62)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -1.95e+305) or not ((b * c) <= 3.95e+62):
		tmp = b * c
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -1.95e+305) || !(Float64(b * c) <= 3.95e+62))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -1.95e+305) || ~(((b * c) <= 3.95e+62)))
		tmp = b * c;
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -1.95e+305], N[Not[LessEqual[N[(b * c), $MachinePrecision], 3.95e+62]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.95e305 or 3.9499999999999998e62 < (*.f64 b c)

   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 87.3%

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

   5. Taylor expanded in x around -inf 82.9%

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

   7. Simplified 85.7%

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

   8. Taylor expanded in b around inf 67.0%

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

   if -1.95e305 < (*.f64 b c) < 3.9499999999999998e62

   1. Initial program 88.9%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in j around inf 30.2%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.95 \cdot 10^{+305} \lor \neg \left(b \cdot c \leq 3.95 \cdot 10^{+62}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 52.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{+113} \lor \neg \left(a \leq 6.6 \cdot 10^{+34}\right):\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= a -2.85e+113) (not (<= a 6.6e+34)))
   (+ (* b c) (* -4.0 (* t a)))
   (+ (* b c) (* j (* k -27.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((a <= -2.85e+113) || !(a <= 6.6e+34)) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((a <= (-2.85d+113)) .or. (.not. (a <= 6.6d+34))) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else
        tmp = (b * c) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((a <= -2.85e+113) || !(a <= 6.6e+34)) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (a <= -2.85e+113) or not (a <= 6.6e+34):
		tmp = (b * c) + (-4.0 * (t * a))
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((a <= -2.85e+113) || !(a <= 6.6e+34))
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((a <= -2.85e+113) || ~((a <= 6.6e+34)))
		tmp = (b * c) + (-4.0 * (t * a));
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[a, -2.85e+113], N[Not[LessEqual[a, 6.6e+34]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8499999999999999e113 or 6.59999999999999976e34 < a

   1. Initial program 82.7%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in x around 0 73.2%

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

      1. associate--l+ 73.2%

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

      2. *-commutative 73.2%

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

      3. associate-*r* 73.2%

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

      4. fma-def 75.1%

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

      5. *-commutative 75.1%

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

      6. *-commutative 75.1%

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

   7. Applied egg-rr 75.1%

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

   8. Taylor expanded in k around 0 64.3%

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

   if -2.8499999999999999e113 < a < 6.59999999999999976e34

   1. Initial program 90.8%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in b around inf 56.3%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{+113} \lor \neg \left(a \leq 6.6 \cdot 10^{+34}\right):\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 23.4% 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 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 90.4%

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

5. Taylor expanded in x around -inf 88.0%

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

7. Simplified 88.8%

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

8. Taylor expanded in b around inf 23.7%

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

9. Final simplification 23.7%

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

Developer target: 89.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024040 
(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)))