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

Percentage Accurate: 84.7% → 90.4%

Time: 30.2s

Alternatives: 18

Speedup: 0.5×

• 51.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 18 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, t\_1, a \cdot -4\right), b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.9%

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

   4. Applied rewrites 97.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 70.9

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

   5. Applied rewrites 70.9%

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

4. Final simplification 95.3%

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

Alternative 2: 35.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -3.3 \cdot 10^{+193}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -2.25 \cdot 10^{-132}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 4.8 \cdot 10^{-308}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.14 \cdot 10^{+79}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 6.5 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= (* b c) -3.3e+193)
     (* b c)
     (if (<= (* b c) -2.1e-22)
       t_1
       (if (<= (* b c) -2.25e-132)
         (* -4.0 (* t a))
         (if (<= (* b c) 4.8e-308)
           t_1
           (if (<= (* b c) 1.14e+79)
             (* j (* k -27.0))
             (if (<= (* b c) 6.5e+162) t_1 (* b c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if ((b * c) <= -3.3e+193) {
		tmp = b * c;
	} else if ((b * c) <= -2.1e-22) {
		tmp = t_1;
	} else if ((b * c) <= -2.25e-132) {
		tmp = -4.0 * (t * a);
	} else if ((b * c) <= 4.8e-308) {
		tmp = t_1;
	} else if ((b * c) <= 1.14e+79) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 6.5e+162) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (x * i)
    if ((b * c) <= (-3.3d+193)) then
        tmp = b * c
    else if ((b * c) <= (-2.1d-22)) then
        tmp = t_1
    else if ((b * c) <= (-2.25d-132)) then
        tmp = (-4.0d0) * (t * a)
    else if ((b * c) <= 4.8d-308) then
        tmp = t_1
    else if ((b * c) <= 1.14d+79) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 6.5d+162) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if ((b * c) <= -3.3e+193) {
		tmp = b * c;
	} else if ((b * c) <= -2.1e-22) {
		tmp = t_1;
	} else if ((b * c) <= -2.25e-132) {
		tmp = -4.0 * (t * a);
	} else if ((b * c) <= 4.8e-308) {
		tmp = t_1;
	} else if ((b * c) <= 1.14e+79) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 6.5e+162) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	tmp = 0
	if (b * c) <= -3.3e+193:
		tmp = b * c
	elif (b * c) <= -2.1e-22:
		tmp = t_1
	elif (b * c) <= -2.25e-132:
		tmp = -4.0 * (t * a)
	elif (b * c) <= 4.8e-308:
		tmp = t_1
	elif (b * c) <= 1.14e+79:
		tmp = j * (k * -27.0)
	elif (b * c) <= 6.5e+162:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (Float64(b * c) <= -3.3e+193)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2.1e-22)
		tmp = t_1;
	elseif (Float64(b * c) <= -2.25e-132)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (Float64(b * c) <= 4.8e-308)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.14e+79)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 6.5e+162)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	tmp = 0.0;
	if ((b * c) <= -3.3e+193)
		tmp = b * c;
	elseif ((b * c) <= -2.1e-22)
		tmp = t_1;
	elseif ((b * c) <= -2.25e-132)
		tmp = -4.0 * (t * a);
	elseif ((b * c) <= 4.8e-308)
		tmp = t_1;
	elseif ((b * c) <= 1.14e+79)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 6.5e+162)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -3.3e+193], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.1e-22], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -2.25e-132], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.8e-308], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.14e+79], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 6.5e+162], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -3.3e193 or 6.5000000000000004e162 < (*.f64 b c)

   1. Initial program 79.5%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. lower-*.f64 72.6

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

   5. Applied rewrites 72.6%

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

   if -3.3e193 < (*.f64 b c) < -2.10000000000000008e-22 or -2.25e-132 < (*.f64 b c) < 4.80000000000000016e-308 or 1.13999999999999997e79 < (*.f64 b c) < 6.5000000000000004e162

   1. Initial program 89.4%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 42.3

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

   5. Applied rewrites 42.3%

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

   if -2.10000000000000008e-22 < (*.f64 b c) < -2.25e-132

   1. Initial program 93.4%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 41.1

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

   5. Applied rewrites 41.1%

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

   if 4.80000000000000016e-308 < (*.f64 b c) < 1.13999999999999997e79

   1. Initial program 94.8%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 36.1

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

   5. Applied rewrites 36.1%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.3 \cdot 10^{+193}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -2.25 \cdot 10^{-132}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 4.8 \cdot 10^{-308}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.14 \cdot 10^{+79}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 6.5 \cdot 10^{+162}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \mathsf{fma}\left(x, i \cdot -4, a \cdot \left(t \cdot -4\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+152}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma b c (fma -4.0 (* t a) (* j (* k -27.0))))))
   (if (<= (* b c) -1e+195)
     t_1
     (if (<= (* b c) 2e+74)
       (fma (* j k) -27.0 (fma x (* i -4.0) (* a (* t -4.0))))
       (if (<= (* b c) 1e+152)
         (* x (fma -4.0 i (* t (* 18.0 (* y z)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(b, c, fma(-4.0, (t * a), (j * (k * -27.0))));
	double tmp;
	if ((b * c) <= -1e+195) {
		tmp = t_1;
	} else if ((b * c) <= 2e+74) {
		tmp = fma((j * k), -27.0, fma(x, (i * -4.0), (a * (t * -4.0))));
	} else if ((b * c) <= 1e+152) {
		tmp = x * fma(-4.0, i, (t * (18.0 * (y * z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(b, c, fma(-4.0, Float64(t * a), Float64(j * Float64(k * -27.0))))
	tmp = 0.0
	if (Float64(b * c) <= -1e+195)
		tmp = t_1;
	elseif (Float64(b * c) <= 2e+74)
		tmp = fma(Float64(j * k), -27.0, fma(x, Float64(i * -4.0), Float64(a * Float64(t * -4.0))));
	elseif (Float64(b * c) <= 1e+152)
		tmp = Float64(x * fma(-4.0, i, Float64(t * Float64(18.0 * Float64(y * z)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1e+195], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 2e+74], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(x * N[(i * -4.0), $MachinePrecision] + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+152], N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -9.99999999999999977e194 or 1e152 < (*.f64 b c)

   1. Initial program 80.1%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

      4. distribute-lft-neg-in N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 89.6

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

   5. Applied rewrites 89.6%

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

   if -9.99999999999999977e194 < (*.f64 b c) < 1.9999999999999999e74

   1. Initial program 91.1%

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 73.5

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

   7. Applied rewrites 73.5%

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

   if 1.9999999999999999e74 < (*.f64 b c) < 1e152

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 99.9

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

   5. Applied rewrites 99.9%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+195}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \mathsf{fma}\left(x, i \cdot -4, a \cdot \left(t \cdot -4\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+152}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 34.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -3.3 \cdot 10^{+193}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -2.25 \cdot 10^{-132}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 6.5 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= (* b c) -3.3e+193)
     (* b c)
     (if (<= (* b c) -2.1e-22)
       t_1
       (if (<= (* b c) -2.25e-132)
         (* -4.0 (* t a))
         (if (<= (* b c) 6.5e+162) t_1 (* b c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if ((b * c) <= -3.3e+193) {
		tmp = b * c;
	} else if ((b * c) <= -2.1e-22) {
		tmp = t_1;
	} else if ((b * c) <= -2.25e-132) {
		tmp = -4.0 * (t * a);
	} else if ((b * c) <= 6.5e+162) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (x * i)
    if ((b * c) <= (-3.3d+193)) then
        tmp = b * c
    else if ((b * c) <= (-2.1d-22)) then
        tmp = t_1
    else if ((b * c) <= (-2.25d-132)) then
        tmp = (-4.0d0) * (t * a)
    else if ((b * c) <= 6.5d+162) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if ((b * c) <= -3.3e+193) {
		tmp = b * c;
	} else if ((b * c) <= -2.1e-22) {
		tmp = t_1;
	} else if ((b * c) <= -2.25e-132) {
		tmp = -4.0 * (t * a);
	} else if ((b * c) <= 6.5e+162) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	tmp = 0
	if (b * c) <= -3.3e+193:
		tmp = b * c
	elif (b * c) <= -2.1e-22:
		tmp = t_1
	elif (b * c) <= -2.25e-132:
		tmp = -4.0 * (t * a)
	elif (b * c) <= 6.5e+162:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (Float64(b * c) <= -3.3e+193)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2.1e-22)
		tmp = t_1;
	elseif (Float64(b * c) <= -2.25e-132)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (Float64(b * c) <= 6.5e+162)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	tmp = 0.0;
	if ((b * c) <= -3.3e+193)
		tmp = b * c;
	elseif ((b * c) <= -2.1e-22)
		tmp = t_1;
	elseif ((b * c) <= -2.25e-132)
		tmp = -4.0 * (t * a);
	elseif ((b * c) <= 6.5e+162)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -3.3e+193], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.1e-22], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -2.25e-132], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 6.5e+162], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -3.3e193 or 6.5000000000000004e162 < (*.f64 b c)

   1. Initial program 79.5%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. lower-*.f64 72.6

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

   5. Applied rewrites 72.6%

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

   if -3.3e193 < (*.f64 b c) < -2.10000000000000008e-22 or -2.25e-132 < (*.f64 b c) < 6.5000000000000004e162

   1. Initial program 91.4%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 32.8

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

   5. Applied rewrites 32.8%

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

   if -2.10000000000000008e-22 < (*.f64 b c) < -2.25e-132

   1. Initial program 93.4%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 41.1

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

   5. Applied rewrites 41.1%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.3 \cdot 10^{+193}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -2.25 \cdot 10^{-132}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 6.5 \cdot 10^{+162}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;z \leq 3.2 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right), \mathsf{fma}\left(b, c, t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= z 3.2e+74)
     (fma b c (fma -4.0 (fma a t (* x i)) t_1))
     (fma x (fma -4.0 i (* t (* 18.0 (* y z)))) (fma 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 tmp;
	if (z <= 3.2e+74) {
		tmp = fma(b, c, fma(-4.0, fma(a, t, (x * i)), t_1));
	} else {
		tmp = fma(x, fma(-4.0, i, (t * (18.0 * (y * z)))), fma(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))
	tmp = 0.0
	if (z <= 3.2e+74)
		tmp = fma(b, c, fma(-4.0, fma(a, t, Float64(x * i)), t_1));
	else
		tmp = fma(x, fma(-4.0, i, Float64(t * Float64(18.0 * Float64(y * z)))), fma(b, c, t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 3.2e+74], N[(b * c + N[(-4.0 * N[(a * t + N[(x * i), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 3.19999999999999995e74

   1. Initial program 89.7%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. lower-fma.f64 N/A

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

      3. associate-+r+ N/A

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

      4. distribute-neg-in N/A

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

      5. distribute-lft-out N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-neg-in N/A

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 85.8

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

   5. Applied rewrites 85.8%

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

   if 3.19999999999999995e74 < z

   1. Initial program 83.6%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 79.1%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.2 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right), \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -200000000000:\\ \;\;\;\;b \cdot c - t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{+93}:\\ \;\;\;\;-4 \cdot \mathsf{fma}\left(a, t, x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -200000000000.0)
     (- (* b c) t_1)
     (if (<= t_1 1e+93)
       (* -4.0 (fma a t (* x i)))
       (fma (* j k) -27.0 (* b c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -200000000000.0) {
		tmp = (b * c) - t_1;
	} else if (t_1 <= 1e+93) {
		tmp = -4.0 * fma(a, t, (x * i));
	} else {
		tmp = fma((j * k), -27.0, (b * c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -200000000000.0)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (t_1 <= 1e+93)
		tmp = Float64(-4.0 * fma(a, t, Float64(x * i)));
	else
		tmp = fma(Float64(j * k), -27.0, Float64(b * c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -200000000000.0], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 1e+93], N[(-4.0 * N[(a * t + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e11

   1. Initial program 85.4%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 60.6

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

   5. Applied rewrites 60.6%

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

   if -2e11 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000004e93

   1. Initial program 89.0%

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

   4. Applied rewrites 94.1%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 59.7

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

   7. Applied rewrites 59.7%

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

   8. Taylor expanded in k around 0

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

      1. distribute-lft-out N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 55.6

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

   10. Applied rewrites 55.6%

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

   if 1.00000000000000004e93 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 92.6%

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

   4. Applied rewrites 92.6%

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

   5. Taylor expanded in b around inf

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

      1. lower-*.f64 71.8

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

   7. Applied rewrites 71.8%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -200000000000:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+93}:\\ \;\;\;\;-4 \cdot \mathsf{fma}\left(a, t, x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(j \cdot k, -27, b \cdot c\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -200000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+93}:\\ \;\;\;\;-4 \cdot \mathsf{fma}\left(a, t, x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* j k) -27.0 (* b c))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -200000000000.0)
     t_1
     (if (<= t_2 1e+93) (* -4.0 (fma a t (* x i))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((j * k), -27.0, (b * c));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -200000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+93) {
		tmp = -4.0 * fma(a, t, (x * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(j * k), -27.0, Float64(b * c))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -200000000000.0)
		tmp = t_1;
	elseif (t_2 <= 1e+93)
		tmp = Float64(-4.0 * fma(a, t, Float64(x * i)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * k), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -200000000000.0], t$95$1, If[LessEqual[t$95$2, 1e+93], N[(-4.0 * N[(a * t + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e11 or 1.00000000000000004e93 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 88.2%

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

   4. Applied rewrites 91.2%

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

   5. Taylor expanded in b around inf

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

      1. lower-*.f64 64.9

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

   7. Applied rewrites 64.9%

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

   if -2e11 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000004e93

   1. Initial program 89.0%

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

   4. Applied rewrites 94.1%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 59.7

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

   7. Applied rewrites 59.7%

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

   8. Taylor expanded in k around 0

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

      1. distribute-lft-out N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 55.6

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

   10. Applied rewrites 55.6%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -200000000000:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, b \cdot c\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+93}:\\ \;\;\;\;-4 \cdot \mathsf{fma}\left(a, t, x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+47}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+243}:\\ \;\;\;\;-4 \cdot \mathsf{fma}\left(a, t, x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+47)
     (* k (* j -27.0))
     (if (<= t_1 2e+243) (* -4.0 (fma a t (* x i))) (* j (* k -27.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+47) {
		tmp = k * (j * -27.0);
	} else if (t_1 <= 2e+243) {
		tmp = -4.0 * fma(a, t, (x * i));
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+47)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (t_1 <= 2e+243)
		tmp = Float64(-4.0 * fma(a, t, Float64(x * i)));
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+47], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+243], N[(-4.0 * N[(a * t + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.0000000000000001e47

   1. Initial program 85.5%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 54.3

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

   5. Applied rewrites 54.3%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 54.3

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

   7. Applied rewrites 54.3%

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

   if -2.0000000000000001e47 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000000000000001e243

   1. Initial program 89.3%

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

   4. Applied rewrites 94.1%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 59.4

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

   7. Applied rewrites 59.4%

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

   8. Taylor expanded in k around 0

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

      1. distribute-lft-out N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 53.2

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

   10. Applied rewrites 53.2%

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

   if 2.0000000000000001e243 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 90.7%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 91.0

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

   5. Applied rewrites 91.0%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+47}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+243}:\\ \;\;\;\;-4 \cdot \mathsf{fma}\left(a, t, x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-150}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, i \cdot \left(x \cdot -4\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+36}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a \cdot \left(t \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -2.3e+18)
   (* t (fma -4.0 a (* 18.0 (* x (* y z)))))
   (if (<= t 1.85e-150)
     (fma (* j -27.0) k (* i (* x -4.0)))
     (if (<= t 1.15e+36)
       (fma b c (* a (* t -4.0)))
       (* t (fma x (* 18.0 (* 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 (t <= -2.3e+18) {
		tmp = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	} else if (t <= 1.85e-150) {
		tmp = fma((j * -27.0), k, (i * (x * -4.0)));
	} else if (t <= 1.15e+36) {
		tmp = fma(b, c, (a * (t * -4.0)));
	} else {
		tmp = t * fma(x, (18.0 * (y * z)), (a * -4.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -2.3e+18)
		tmp = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))));
	elseif (t <= 1.85e-150)
		tmp = fma(Float64(j * -27.0), k, Float64(i * Float64(x * -4.0)));
	elseif (t <= 1.15e+36)
		tmp = fma(b, c, Float64(a * Float64(t * -4.0)));
	else
		tmp = Float64(t * fma(x, Float64(18.0 * Float64(y * z)), Float64(a * -4.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -2.3e+18], N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e-150], N[(N[(j * -27.0), $MachinePrecision] * k + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+36], N[(b * c + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.3e18

   1. Initial program 84.7%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 59.2

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

   5. Applied rewrites 59.2%

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

   if -2.3e18 < t < 1.85e-150

   1. Initial program 90.3%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 70.1

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

   5. Applied rewrites 70.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-*.f64 70.1

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

      19. lift-*.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

      24. *-commutative N/A

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

      25. lower-*.f64 70.1

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

   7. Applied rewrites 70.1%

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

   if 1.85e-150 < t < 1.14999999999999998e36

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

      4. distribute-lft-neg-in N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 65.3

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

   5. Applied rewrites 65.3%

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

   6. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 58.3

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

   8. Applied rewrites 58.3%

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

   if 1.14999999999999998e36 < t

   1. Initial program 89.5%

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

   4. Applied rewrites 97.0%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 69.5

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

   7. Applied rewrites 69.5%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-150}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, i \cdot \left(x \cdot -4\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+36}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a \cdot \left(t \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-150}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, i \cdot \left(x \cdot -4\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+36}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a \cdot \left(t \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (fma -4.0 a (* 18.0 (* x (* y z)))))))
   (if (<= t -2.3e+18)
     t_1
     (if (<= t 1.85e-150)
       (fma (* j -27.0) k (* i (* x -4.0)))
       (if (<= t 1.15e+36) (fma b c (* a (* t -4.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -2.3e+18) {
		tmp = t_1;
	} else if (t <= 1.85e-150) {
		tmp = fma((j * -27.0), k, (i * (x * -4.0)));
	} else if (t <= 1.15e+36) {
		tmp = fma(b, c, (a * (t * -4.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))))
	tmp = 0.0
	if (t <= -2.3e+18)
		tmp = t_1;
	elseif (t <= 1.85e-150)
		tmp = fma(Float64(j * -27.0), k, Float64(i * Float64(x * -4.0)));
	elseif (t <= 1.15e+36)
		tmp = fma(b, c, Float64(a * Float64(t * -4.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e+18], t$95$1, If[LessEqual[t, 1.85e-150], N[(N[(j * -27.0), $MachinePrecision] * k + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+36], N[(b * c + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3e18 or 1.14999999999999998e36 < t

   1. Initial program 87.3%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 64.7

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

   5. Applied rewrites 64.7%

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

   if -2.3e18 < t < 1.85e-150

   1. Initial program 90.3%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 70.1

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

   5. Applied rewrites 70.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-*.f64 70.1

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

      19. lift-*.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

      24. *-commutative N/A

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

      25. lower-*.f64 70.1

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

   7. Applied rewrites 70.1%

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

   if 1.85e-150 < t < 1.14999999999999998e36

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

      4. distribute-lft-neg-in N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 65.3

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

   5. Applied rewrites 65.3%

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

   6. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 58.3

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

   8. Applied rewrites 58.3%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-150}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, i \cdot \left(x \cdot -4\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+36}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a \cdot \left(t \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -56000000000000:\\ \;\;\;\;\mathsf{fma}\left(x \cdot -4, i, \left(j \cdot k\right) \cdot -27\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+122}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(-27, \frac{j \cdot k}{i}, x \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= i -56000000000000.0)
   (fma (* x -4.0) i (* (* j k) -27.0))
   (if (<= i 3.5e+122)
     (fma b c (fma -4.0 (* t a) (* j (* k -27.0))))
     (* i (fma -27.0 (/ (* j k) i) (* x -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 (i <= -56000000000000.0) {
		tmp = fma((x * -4.0), i, ((j * k) * -27.0));
	} else if (i <= 3.5e+122) {
		tmp = fma(b, c, fma(-4.0, (t * a), (j * (k * -27.0))));
	} else {
		tmp = i * fma(-27.0, ((j * k) / i), (x * -4.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (i <= -56000000000000.0)
		tmp = fma(Float64(x * -4.0), i, Float64(Float64(j * k) * -27.0));
	elseif (i <= 3.5e+122)
		tmp = fma(b, c, fma(-4.0, Float64(t * a), Float64(j * Float64(k * -27.0))));
	else
		tmp = Float64(i * fma(-27.0, Float64(Float64(j * k) / i), Float64(x * -4.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[i, -56000000000000.0], N[(N[(x * -4.0), $MachinePrecision] * i + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.5e+122], N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(-27.0 * N[(N[(j * k), $MachinePrecision] / i), $MachinePrecision] + N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -5.6e13

   1. Initial program 82.2%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 73.8

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

   5. Applied rewrites 73.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. metadata-eval N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*r* N/A

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 73.8

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*r* N/A

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

      21. *-commutative N/A

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

      22. lift-*.f64 N/A

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

      23. lower-*.f64 73.8

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

   7. Applied rewrites 73.8%

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

   if -5.6e13 < i < 3.50000000000000014e122

   1. Initial program 93.0%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

      4. distribute-lft-neg-in N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 73.7

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

   5. Applied rewrites 73.7%

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

   if 3.50000000000000014e122 < i

   1. Initial program 80.7%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 66.7

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

   5. Applied rewrites 66.7%

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

   6. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 71.6

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

   8. Applied rewrites 71.6%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -56000000000000:\\ \;\;\;\;\mathsf{fma}\left(x \cdot -4, i, \left(j \cdot k\right) \cdot -27\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+122}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(-27, \frac{j \cdot k}{i}, x \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x \cdot -4, i, j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{if}\;i \leq -1.9 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-225}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, b \cdot c\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+121}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a \cdot \left(t \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* x -4.0) i (* j (* k -27.0)))))
   (if (<= i -1.9e-28)
     t_1
     (if (<= i 2.2e-225)
       (fma (* j k) -27.0 (* b c))
       (if (<= i 5.2e+121) (fma b c (* a (* t -4.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((x * -4.0), i, (j * (k * -27.0)));
	double tmp;
	if (i <= -1.9e-28) {
		tmp = t_1;
	} else if (i <= 2.2e-225) {
		tmp = fma((j * k), -27.0, (b * c));
	} else if (i <= 5.2e+121) {
		tmp = fma(b, c, (a * (t * -4.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(x * -4.0), i, Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (i <= -1.9e-28)
		tmp = t_1;
	elseif (i <= 2.2e-225)
		tmp = fma(Float64(j * k), -27.0, Float64(b * c));
	elseif (i <= 5.2e+121)
		tmp = fma(b, c, Float64(a * Float64(t * -4.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * -4.0), $MachinePrecision] * i + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.9e-28], t$95$1, If[LessEqual[i, 2.2e-225], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.2e+121], N[(b * c + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.90000000000000005e-28 or 5.1999999999999998e121 < i

   1. Initial program 83.3%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 69.0

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

   5. Applied rewrites 69.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. metadata-eval N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*r* N/A

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 70.9

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*r* N/A

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

      21. *-commutative N/A

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

      22. lift-*.f64 N/A

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

      23. lower-*.f64 70.9

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

   7. Applied rewrites 70.9%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 70.9

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

   9. Applied rewrites 70.9%

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

   if -1.90000000000000005e-28 < i < 2.2e-225

   1. Initial program 93.3%

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

   4. Applied rewrites 94.7%

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

   5. Taylor expanded in b around inf

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

      1. lower-*.f64 53.7

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

   7. Applied rewrites 53.7%

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

   if 2.2e-225 < i < 5.1999999999999998e121

   1. Initial program 91.8%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

      4. distribute-lft-neg-in N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 78.9

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 62.7

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

   8. Applied rewrites 62.7%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.9 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot -4, i, j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-225}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, b \cdot c\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+121}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a \cdot \left(t \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot -4, i, j \cdot \left(k \cdot -27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(j \cdot -27, k, i \cdot \left(x \cdot -4\right)\right)\\ \mathbf{if}\;i \leq -1.9 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-225}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, b \cdot c\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+121}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a \cdot \left(t \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* j -27.0) k (* i (* x -4.0)))))
   (if (<= i -1.9e-28)
     t_1
     (if (<= i 2.2e-225)
       (fma (* j k) -27.0 (* b c))
       (if (<= i 5.2e+121) (fma b c (* a (* t -4.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((j * -27.0), k, (i * (x * -4.0)));
	double tmp;
	if (i <= -1.9e-28) {
		tmp = t_1;
	} else if (i <= 2.2e-225) {
		tmp = fma((j * k), -27.0, (b * c));
	} else if (i <= 5.2e+121) {
		tmp = fma(b, c, (a * (t * -4.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(j * -27.0), k, Float64(i * Float64(x * -4.0)))
	tmp = 0.0
	if (i <= -1.9e-28)
		tmp = t_1;
	elseif (i <= 2.2e-225)
		tmp = fma(Float64(j * k), -27.0, Float64(b * c));
	elseif (i <= 5.2e+121)
		tmp = fma(b, c, Float64(a * Float64(t * -4.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * -27.0), $MachinePrecision] * k + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.9e-28], t$95$1, If[LessEqual[i, 2.2e-225], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.2e+121], N[(b * c + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.90000000000000005e-28 or 5.1999999999999998e121 < i

   1. Initial program 83.3%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 69.0

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

   5. Applied rewrites 69.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-*.f64 69.0

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

      19. lift-*.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

      24. *-commutative N/A

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

      25. lower-*.f64 69.0

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

   7. Applied rewrites 69.0%

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

   if -1.90000000000000005e-28 < i < 2.2e-225

   1. Initial program 93.3%

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

   4. Applied rewrites 94.7%

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

   5. Taylor expanded in b around inf

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

      1. lower-*.f64 53.7

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

   7. Applied rewrites 53.7%

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

   if 2.2e-225 < i < 5.1999999999999998e121

   1. Initial program 91.8%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

      4. distribute-lft-neg-in N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 78.9

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 62.7

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

   8. Applied rewrites 62.7%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.9 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, i \cdot \left(x \cdot -4\right)\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-225}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, b \cdot c\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+121}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a \cdot \left(t \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, i \cdot \left(x \cdot -4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;i \leq -56000000000000:\\ \;\;\;\;\mathsf{fma}\left(x \cdot -4, i, \left(j \cdot k\right) \cdot -27\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+122}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot -4, i, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= i -56000000000000.0)
     (fma (* x -4.0) i (* (* j k) -27.0))
     (if (<= i 3.5e+122)
       (fma b c (fma -4.0 (* t a) t_1))
       (fma (* x -4.0) i t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (i <= -56000000000000.0) {
		tmp = fma((x * -4.0), i, ((j * k) * -27.0));
	} else if (i <= 3.5e+122) {
		tmp = fma(b, c, fma(-4.0, (t * a), t_1));
	} else {
		tmp = fma((x * -4.0), i, 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))
	tmp = 0.0
	if (i <= -56000000000000.0)
		tmp = fma(Float64(x * -4.0), i, Float64(Float64(j * k) * -27.0));
	elseif (i <= 3.5e+122)
		tmp = fma(b, c, fma(-4.0, Float64(t * a), t_1));
	else
		tmp = fma(Float64(x * -4.0), i, t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -56000000000000.0], N[(N[(x * -4.0), $MachinePrecision] * i + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.5e+122], N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x * -4.0), $MachinePrecision] * i + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if i < -5.6e13

   1. Initial program 82.2%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 73.8

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

   5. Applied rewrites 73.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. metadata-eval N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*r* N/A

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 73.8

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*r* N/A

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

      21. *-commutative N/A

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

      22. lift-*.f64 N/A

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

      23. lower-*.f64 73.8

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

   7. Applied rewrites 73.8%

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

   if -5.6e13 < i < 3.50000000000000014e122

   1. Initial program 93.0%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

      4. distribute-lft-neg-in N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 73.7

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

   5. Applied rewrites 73.7%

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

   if 3.50000000000000014e122 < i

   1. Initial program 80.7%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 66.7

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

   5. Applied rewrites 66.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. metadata-eval N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*r* N/A

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 71.7

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*r* N/A

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

      21. *-commutative N/A

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

      22. lift-*.f64 N/A

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

      23. lower-*.f64 71.6

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

   7. Applied rewrites 71.6%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 71.7

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

   9. Applied rewrites 71.7%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -56000000000000:\\ \;\;\;\;\mathsf{fma}\left(x \cdot -4, i, \left(j \cdot k\right) \cdot -27\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+122}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot -4, i, j \cdot \left(k \cdot -27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 78.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 5.9 \cdot 10^{+183}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t 5.9e+183)
   (fma b c (fma -4.0 (fma a t (* x i)) (* j (* k -27.0))))
   (* t (fma -4.0 a (* 18.0 (* x (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= 5.9e+183) {
		tmp = fma(b, c, fma(-4.0, fma(a, t, (x * i)), (j * (k * -27.0))));
	} else {
		tmp = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= 5.9e+183)
		tmp = fma(b, c, fma(-4.0, fma(a, t, Float64(x * i)), Float64(j * Float64(k * -27.0))));
	else
		tmp = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, 5.9e+183], N[(b * c + N[(-4.0 * N[(a * t + N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.89999999999999956e183

   1. Initial program 89.1%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. lower-fma.f64 N/A

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

      3. associate-+r+ N/A

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

      4. distribute-neg-in N/A

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

      5. distribute-lft-out N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-neg-in N/A

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 84.1

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

   5. Applied rewrites 84.1%

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

   if 5.89999999999999956e183 < t

   1. Initial program 84.9%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 88.4

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

   5. Applied rewrites 88.4%

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

Alternative 16: 51.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, c, a \cdot \left(t \cdot -4\right)\right)\\ \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 6 \cdot 10^{+162}:\\ \;\;\;\;-4 \cdot \mathsf{fma}\left(a, t, x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma b c (* a (* t -4.0)))))
   (if (<= (* b c) -1e+195)
     t_1
     (if (<= (* b c) 6e+162) (* -4.0 (fma a t (* x i))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(b, c, (a * (t * -4.0)));
	double tmp;
	if ((b * c) <= -1e+195) {
		tmp = t_1;
	} else if ((b * c) <= 6e+162) {
		tmp = -4.0 * fma(a, t, (x * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(b, c, Float64(a * Float64(t * -4.0)))
	tmp = 0.0
	if (Float64(b * c) <= -1e+195)
		tmp = t_1;
	elseif (Float64(b * c) <= 6e+162)
		tmp = Float64(-4.0 * fma(a, t, Float64(x * i)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(b * c + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1e+195], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 6e+162], N[(-4.0 * N[(a * t + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -9.99999999999999977e194 or 5.9999999999999996e162 < (*.f64 b c)

   1. Initial program 79.5%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

      4. distribute-lft-neg-in N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 90.8

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

   5. Applied rewrites 90.8%

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

   6. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 81.5

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

   8. Applied rewrites 81.5%

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

   if -9.99999999999999977e194 < (*.f64 b c) < 5.9999999999999996e162

   1. Initial program 91.7%

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

   4. Applied rewrites 96.3%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 72.4

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

   7. Applied rewrites 72.4%

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

   8. Taylor expanded in k around 0

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

      1. distribute-lft-out N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 49.0

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

   10. Applied rewrites 49.0%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+195}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a \cdot \left(t \cdot -4\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 6 \cdot 10^{+162}:\\ \;\;\;\;-4 \cdot \mathsf{fma}\left(a, t, x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a \cdot \left(t \cdot -4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 35.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.2 \cdot 10^{-20}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{+143}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -3.2e-20)
   (* b c)
   (if (<= (* b c) 1.6e+143) (* -4.0 (* t a)) (* b c))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -3.2e-20) {
		tmp = b * c;
	} else if ((b * c) <= 1.6e+143) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-3.2d-20)) then
        tmp = b * c
    else if ((b * c) <= 1.6d+143) then
        tmp = (-4.0d0) * (t * a)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -3.2e-20) {
		tmp = b * c;
	} else if ((b * c) <= 1.6e+143) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -3.2e-20:
		tmp = b * c
	elif (b * c) <= 1.6e+143:
		tmp = -4.0 * (t * a)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -3.2e-20)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 1.6e+143)
		tmp = Float64(-4.0 * Float64(t * a));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -3.2e-20)
		tmp = b * c;
	elseif ((b * c) <= 1.6e+143)
		tmp = -4.0 * (t * a);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -3.2e-20], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.6e+143], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -3.1999999999999997e-20 or 1.60000000000000008e143 < (*.f64 b c)

   1. Initial program 81.4%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. lower-*.f64 49.8

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

   5. Applied rewrites 49.8%

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

   if -3.1999999999999997e-20 < (*.f64 b c) < 1.60000000000000008e143

   1. Initial program 93.9%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 26.3

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

   5. Applied rewrites 26.3%

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

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.2 \cdot 10^{-20}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{+143}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 24.5% accurate, 11.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.7%

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

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot c} \]
4. Step-by-step derivation

   1. lower-*.f64 23.2

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

5. Applied rewrites 23.2%

   \[\leadsto \color{blue}{b \cdot c} \]
6. Add Preprocessing

Developer Target 1: 88.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024216 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8105407698770699/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 8284013971902611/50000000000000) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))))))

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