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

Percentage Accurate: 84.7% → 93.3%

Time: 6.3s

Alternatives: 16

Speedup: 0.9×

• 49.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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

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

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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: 93.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, \mathsf{fma}\left(-27 \cdot j, k, \left(-4 \cdot x\right) \cdot i\right)\right)\right)\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot \left(18 \cdot x\right)\right) \cdot z, y, \mathsf{fma}\left(a \cdot t, -4, \mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(-4 \cdot x, i, c \cdot b\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1
        (fma
         c
         b
         (fma
          (fma -4.0 a (* z (* y (* 18.0 x))))
          t
          (fma (* -27.0 j) k (* (* -4.0 x) i))))))
  (if (<= t -5.5e-75)
    t_1
    (if (<= t 4e-31)
      (fma
       (* (* t (* 18.0 x)) z)
       y
       (fma
        (* a t)
        -4.0
        (fma (* k j) -27.0 (fma (* -4.0 x) i (* c b)))))
      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(c, b, fma(fma(-4.0, a, (z * (y * (18.0 * x)))), t, fma((-27.0 * j), k, ((-4.0 * x) * i))));
	double tmp;
	if (t <= -5.5e-75) {
		tmp = t_1;
	} else if (t <= 4e-31) {
		tmp = fma(((t * (18.0 * x)) * z), y, fma((a * t), -4.0, fma((k * j), -27.0, fma((-4.0 * x), i, (c * b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(c, b, fma(fma(-4.0, a, Float64(z * Float64(y * Float64(18.0 * x)))), t, fma(Float64(-27.0 * j), k, Float64(Float64(-4.0 * x) * i))))
	tmp = 0.0
	if (t <= -5.5e-75)
		tmp = t_1;
	elseif (t <= 4e-31)
		tmp = fma(Float64(Float64(t * Float64(18.0 * x)) * z), y, fma(Float64(a * t), -4.0, fma(Float64(k * j), -27.0, fma(Float64(-4.0 * x), i, Float64(c * b)))));
	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[(c * b + N[(N[(-4.0 * a + N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t + N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e-75], t$95$1, If[LessEqual[t, 4e-31], N[(N[(N[(t * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * y + N[(N[(a * t), $MachinePrecision] * -4.0 + N[(N[(k * j), $MachinePrecision] * -27.0 + N[(N[(-4.0 * x), $MachinePrecision] * i + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5000000000000003e-75 or 4.0000000000000003e-31 < t

   1. Initial program 84.7%

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

   3. Applied rewrites 89.3%

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

   if -5.5000000000000003e-75 < t < 4.0000000000000003e-31

   1. Initial program 84.7%

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

   3. Applied rewrites 86.8%

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

Alternative 2: 91.7% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (-.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)) < +inf.0

   1. Initial program 84.7%

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

   3. Applied rewrites 89.3%

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

   if +inf.0 < (-.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))

   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. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

   5. Taylor expanded in x around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      7. lower-*.f64 41.7%

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

   7. Applied rewrites 41.7%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. fp-cancel-sub-sign-inv N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. metadata-eval N/A

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

      15. lower-*.f64 41.7%

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 41.7%

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

   9. Applied rewrites 41.7%

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

       1. lift-fma.f64 N/A

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

       2. *-commutative N/A

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

       3. lift-*.f64 N/A

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

       4. +-commutative N/A

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

       5. lift-*.f64 N/A

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

       6. lift-*.f64 N/A

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

       7. lift-*.f64 N/A

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

       8. associate-*l* N/A

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

       9. associate-*r* N/A

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

       10. lower-fma.f64 N/A

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

       11. lower-*.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 42.7%

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

       14. lift-*.f64 N/A

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

       15. *-commutative N/A

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

       16. lower-*.f64 42.7%

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

   11. Applied rewrites 42.7%

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

Alternative 3: 81.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+252}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(-27 \cdot j, k, \left(-4 \cdot x\right) \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot y, t \cdot z, i \cdot -4\right) \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (if (<= x -2.8e+136)
  (- (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))) (* (* j 27.0) k))
  (if (<= x 3.2e+252)
    (fma c b (fma (* -4.0 a) t (fma (* -27.0 j) k (* (* -4.0 x) i))))
    (* (fma (* 18.0 y) (* t z) (* i -4.0)) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -2.8e+136) {
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - ((j * 27.0) * k);
	} else if (x <= 3.2e+252) {
		tmp = fma(c, b, fma((-4.0 * a), t, fma((-27.0 * j), k, ((-4.0 * x) * i))));
	} else {
		tmp = fma((18.0 * y), (t * z), (i * -4.0)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -2.8e+136)
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))) - Float64(Float64(j * 27.0) * k));
	elseif (x <= 3.2e+252)
		tmp = fma(c, b, fma(Float64(-4.0 * a), t, fma(Float64(-27.0 * j), k, Float64(Float64(-4.0 * x) * i))));
	else
		tmp = Float64(fma(Float64(18.0 * y), Float64(t * z), Float64(i * -4.0)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -2.8e+136], N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+252], N[(c * b + N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(18.0 * y), $MachinePrecision] * N[(t * z), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.8000000000000002e136

   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. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      5. lower-*.f64 N/A

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      6. lower-*.f64 58.6%

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

   4. Applied rewrites 58.6%

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

   if -2.8000000000000002e136 < x < 3.2000000000000002e252

   1. Initial program 84.7%

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

   3. Applied rewrites 89.3%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 79.1%

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

   6. Applied rewrites 79.1%

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

   if 3.2000000000000002e252 < x

   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. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

   5. Taylor expanded in x around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      7. lower-*.f64 41.7%

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

   7. Applied rewrites 41.7%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. fp-cancel-sub-sign-inv N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. metadata-eval N/A

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

      15. lower-*.f64 41.7%

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 41.7%

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

   9. Applied rewrites 41.7%

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

       1. lift-fma.f64 N/A

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

       2. *-commutative N/A

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

       3. lift-*.f64 N/A

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

       4. +-commutative N/A

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

       5. lift-*.f64 N/A

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

       6. lift-*.f64 N/A

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

       7. lift-*.f64 N/A

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

       8. associate-*l* N/A

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

       9. associate-*r* N/A

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

       10. lower-fma.f64 N/A

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

       11. lower-*.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 42.7%

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

       14. lift-*.f64 N/A

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

       15. *-commutative N/A

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

       16. lower-*.f64 42.7%

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

   11. Applied rewrites 42.7%

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

Alternative 4: 73.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27, j \cdot k, -4 \cdot \left(a \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot y, t \cdot z, i \cdot -4\right) \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (if (<= x -2.3e+130)
  (- (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))) (* (* j 27.0) k))
  (if (<= x 1.1e+109)
    (fma c b (fma -27.0 (* j k) (* -4.0 (* a t))))
    (* (fma (* 18.0 y) (* t z) (* i -4.0)) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -2.3e+130) {
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - ((j * 27.0) * k);
	} else if (x <= 1.1e+109) {
		tmp = fma(c, b, fma(-27.0, (j * k), (-4.0 * (a * t))));
	} else {
		tmp = fma((18.0 * y), (t * z), (i * -4.0)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -2.3e+130)
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))) - Float64(Float64(j * 27.0) * k));
	elseif (x <= 1.1e+109)
		tmp = fma(c, b, fma(-27.0, Float64(j * k), Float64(-4.0 * Float64(a * t))));
	else
		tmp = Float64(fma(Float64(18.0 * y), Float64(t * z), Float64(i * -4.0)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -2.3e+130], N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+109], N[(c * b + N[(-27.0 * N[(j * k), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(18.0 * y), $MachinePrecision] * N[(t * z), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.3000000000000002e130

   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. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      5. lower-*.f64 N/A

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      6. lower-*.f64 58.6%

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

   4. Applied rewrites 58.6%

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

   if -2.3000000000000002e130 < x < 1.1e109

   1. Initial program 84.7%

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

   3. Applied rewrites 89.3%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 62.3%

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

   6. Applied rewrites 62.3%

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

   if 1.1e109 < x

   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. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

   5. Taylor expanded in x around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      7. lower-*.f64 41.7%

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

   7. Applied rewrites 41.7%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. fp-cancel-sub-sign-inv N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. metadata-eval N/A

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

      15. lower-*.f64 41.7%

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 41.7%

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

   9. Applied rewrites 41.7%

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

       1. lift-fma.f64 N/A

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

       2. *-commutative N/A

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

       3. lift-*.f64 N/A

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

       4. +-commutative N/A

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

       5. lift-*.f64 N/A

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

       6. lift-*.f64 N/A

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

       7. lift-*.f64 N/A

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

       8. associate-*l* N/A

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

       9. associate-*r* N/A

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

       10. lower-fma.f64 N/A

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

       11. lower-*.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 42.7%

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

       14. lift-*.f64 N/A

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

       15. *-commutative N/A

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

       16. lower-*.f64 42.7%

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

   11. Applied rewrites 42.7%

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

Alternative 5: 72.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(18 \cdot y, t \cdot z, i \cdot -4\right) \cdot x\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27, j \cdot k, -4 \cdot \left(a \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* (fma (* 18.0 y) (* t z) (* i -4.0)) x)))
  (if (<= x -2.3e+130)
    t_1
    (if (<= x 1.1e+109)
      (fma c b (fma -27.0 (* j k) (* -4.0 (* a 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 = fma((18.0 * y), (t * z), (i * -4.0)) * x;
	double tmp;
	if (x <= -2.3e+130) {
		tmp = t_1;
	} else if (x <= 1.1e+109) {
		tmp = fma(c, b, fma(-27.0, (j * k), (-4.0 * (a * t))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(Float64(18.0 * y), Float64(t * z), Float64(i * -4.0)) * x)
	tmp = 0.0
	if (x <= -2.3e+130)
		tmp = t_1;
	elseif (x <= 1.1e+109)
		tmp = fma(c, b, fma(-27.0, Float64(j * k), Float64(-4.0 * Float64(a * t))));
	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[(N[(18.0 * y), $MachinePrecision] * N[(t * z), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2.3e+130], t$95$1, If[LessEqual[x, 1.1e+109], N[(c * b + N[(-27.0 * N[(j * k), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3000000000000002e130 or 1.1e109 < x

   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. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

   5. Taylor expanded in x around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      7. lower-*.f64 41.7%

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

   7. Applied rewrites 41.7%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. fp-cancel-sub-sign-inv N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. metadata-eval N/A

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

      15. lower-*.f64 41.7%

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 41.7%

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

   9. Applied rewrites 41.7%

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

       1. lift-fma.f64 N/A

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

       2. *-commutative N/A

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

       3. lift-*.f64 N/A

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

       4. +-commutative N/A

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

       5. lift-*.f64 N/A

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

       6. lift-*.f64 N/A

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

       7. lift-*.f64 N/A

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

       8. associate-*l* N/A

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

       9. associate-*r* N/A

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

       10. lower-fma.f64 N/A

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

       11. lower-*.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 42.7%

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

       14. lift-*.f64 N/A

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

       15. *-commutative N/A

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

       16. lower-*.f64 42.7%

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

   11. Applied rewrites 42.7%

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

   if -2.3000000000000002e130 < x < 1.1e109

   1. Initial program 84.7%

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

   3. Applied rewrites 89.3%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 62.3%

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

   6. Applied rewrites 62.3%

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

Alternative 6: 58.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(c, b, -\left(27 \cdot j\right) \cdot k\right)\\ t_2 := \mathsf{fma}\left(18 \cdot y, t \cdot z, i \cdot -4\right) \cdot x\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-60}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot a, -4, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{elif}\;x \leq 90000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (fma c b (- (* (* 27.0 j) k))))
       (t_2 (* (fma (* 18.0 y) (* t z) (* i -4.0)) x)))
  (if (<= x -4.8e+27)
    t_2
    (if (<= x -2.15e-218)
      t_1
      (if (<= x 3.1e-60)
        (fma (* t a) -4.0 (* (* k j) -27.0))
        (if (<= x 90000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(c, b, -((27.0 * j) * k));
	double t_2 = fma((18.0 * y), (t * z), (i * -4.0)) * x;
	double tmp;
	if (x <= -4.8e+27) {
		tmp = t_2;
	} else if (x <= -2.15e-218) {
		tmp = t_1;
	} else if (x <= 3.1e-60) {
		tmp = fma((t * a), -4.0, ((k * j) * -27.0));
	} else if (x <= 90000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(c, b, Float64(-Float64(Float64(27.0 * j) * k)))
	t_2 = Float64(fma(Float64(18.0 * y), Float64(t * z), Float64(i * -4.0)) * x)
	tmp = 0.0
	if (x <= -4.8e+27)
		tmp = t_2;
	elseif (x <= -2.15e-218)
		tmp = t_1;
	elseif (x <= 3.1e-60)
		tmp = fma(Float64(t * a), -4.0, Float64(Float64(k * j) * -27.0));
	elseif (x <= 90000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(c * b + (-N[(N[(27.0 * j), $MachinePrecision] * k), $MachinePrecision])), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(18.0 * y), $MachinePrecision] * N[(t * z), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -4.8e+27], t$95$2, If[LessEqual[x, -2.15e-218], t$95$1, If[LessEqual[x, 3.1e-60], N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 90000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8e27 or 9e4 < x

   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. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

   5. Taylor expanded in x around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      7. lower-*.f64 41.7%

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

   7. Applied rewrites 41.7%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. fp-cancel-sub-sign-inv N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. metadata-eval N/A

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

      15. lower-*.f64 41.7%

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 41.7%

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

   9. Applied rewrites 41.7%

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

       1. lift-fma.f64 N/A

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

       2. *-commutative N/A

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

       3. lift-*.f64 N/A

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

       4. +-commutative N/A

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

       5. lift-*.f64 N/A

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

       6. lift-*.f64 N/A

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

       7. lift-*.f64 N/A

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

       8. associate-*l* N/A

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

       9. associate-*r* N/A

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

       10. lower-fma.f64 N/A

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

       11. lower-*.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 42.7%

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

       14. lift-*.f64 N/A

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

       15. *-commutative N/A

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

       16. lower-*.f64 42.7%

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

   11. Applied rewrites 42.7%

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

   if -4.8e27 < x < -2.15e-218 or 3.0999999999999999e-60 < x < 9e4

   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. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 61.5%

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.1%

         \[\leadsto b \cdot c - 4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 42.1%

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

   8. Taylor expanded in t around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 45.0%

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot k\right) \]

   10. Applied rewrites 45.0%

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

       1. lift--.f64 N/A

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

       2. sub-flip N/A

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

       3. lift-*.f64 N/A

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

       4. *-commutative N/A

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

       5. lower-fma.f64 N/A

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

       6. lower-neg.f64 45.5%

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

       7. lift-*.f64 N/A

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

       8. lift-*.f64 N/A

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

       9. associate-*r* N/A

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

       10. *-commutative N/A

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

       11. lower-*.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 45.4%

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

   12. Applied rewrites 45.4%

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

   if -2.15e-218 < x < 3.0999999999999999e-60

   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. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 61.5%

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in b around 0

      \[\leadsto -1 \cdot \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(4 \cdot \left(a \cdot t\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot \color{blue}{t}, 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 41.9%

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right) \]

   7. Applied rewrites 41.9%

      \[\leadsto -1 \cdot \color{blue}{\mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right)} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, \color{blue}{a \cdot t}, 27 \cdot \left(j \cdot k\right)\right) \]

      2. mul-1-neg N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-neg-in N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. metadata-eval N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*l* N/A

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

      15. lift-*.f64 N/A

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

      16. lower-fma.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*l* N/A

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 41.9%

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

      25. lift-*.f64 N/A

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

      26. *-commutative N/A

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

      27. lower-*.f64 41.9%

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

   9. Applied rewrites 41.9%

      \[\leadsto \mathsf{fma}\left(t \cdot a, -4, \left(k \cdot j\right) \cdot -27\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 57.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(i, -4, 18 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right) \cdot x\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-218}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -\left(27 \cdot j\right) \cdot k\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot a, -4, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* (fma i -4.0 (* 18.0 (* (* y z) t))) x)))
  (if (<= x -4.8e+27)
    t_1
    (if (<= x -2.15e-218)
      (fma c b (- (* (* 27.0 j) k)))
      (if (<= x 8.5e+96) (fma (* t a) -4.0 (* (* k j) -27.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(i, -4.0, (18.0 * ((y * z) * t))) * x;
	double tmp;
	if (x <= -4.8e+27) {
		tmp = t_1;
	} else if (x <= -2.15e-218) {
		tmp = fma(c, b, -((27.0 * j) * k));
	} else if (x <= 8.5e+96) {
		tmp = fma((t * a), -4.0, ((k * j) * -27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(i, -4.0, Float64(18.0 * Float64(Float64(y * z) * t))) * x)
	tmp = 0.0
	if (x <= -4.8e+27)
		tmp = t_1;
	elseif (x <= -2.15e-218)
		tmp = fma(c, b, Float64(-Float64(Float64(27.0 * j) * k)));
	elseif (x <= 8.5e+96)
		tmp = fma(Float64(t * a), -4.0, Float64(Float64(k * j) * -27.0));
	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[(i * -4.0 + N[(18.0 * N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -4.8e+27], t$95$1, If[LessEqual[x, -2.15e-218], N[(c * b + (-N[(N[(27.0 * j), $MachinePrecision] * k), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 8.5e+96], N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8e27 or 8.5000000000000002e96 < x

   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. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

   5. Taylor expanded in x around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      7. lower-*.f64 41.7%

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

   7. Applied rewrites 41.7%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. fp-cancel-sub-sign-inv N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. metadata-eval N/A

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

      15. lower-*.f64 41.7%

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 41.7%

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

   9. Applied rewrites 41.7%

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

   if -4.8e27 < x < -2.15e-218

   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. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 61.5%

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.1%

         \[\leadsto b \cdot c - 4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 42.1%

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

   8. Taylor expanded in t around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 45.0%

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot k\right) \]

   10. Applied rewrites 45.0%

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

       1. lift--.f64 N/A

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

       2. sub-flip N/A

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

       3. lift-*.f64 N/A

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

       4. *-commutative N/A

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

       5. lower-fma.f64 N/A

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

       6. lower-neg.f64 45.5%

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

       7. lift-*.f64 N/A

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

       8. lift-*.f64 N/A

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

       9. associate-*r* N/A

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

       10. *-commutative N/A

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

       11. lower-*.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 45.4%

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

   12. Applied rewrites 45.4%

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

   if -2.15e-218 < x < 8.5000000000000002e96

   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. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 61.5%

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in b around 0

      \[\leadsto -1 \cdot \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(4 \cdot \left(a \cdot t\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot \color{blue}{t}, 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 41.9%

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right) \]

   7. Applied rewrites 41.9%

      \[\leadsto -1 \cdot \color{blue}{\mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right)} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, \color{blue}{a \cdot t}, 27 \cdot \left(j \cdot k\right)\right) \]

      2. mul-1-neg N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-neg-in N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. metadata-eval N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*l* N/A

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

      15. lift-*.f64 N/A

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

      16. lower-fma.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*l* N/A

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 41.9%

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

      25. lift-*.f64 N/A

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

      26. *-commutative N/A

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

      27. lower-*.f64 41.9%

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

   9. Applied rewrites 41.9%

      \[\leadsto \mathsf{fma}\left(t \cdot a, -4, \left(k \cdot j\right) \cdot -27\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 55.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+152}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-168}:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+87}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot a, -4, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -\left(27 \cdot j\right) \cdot k\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (if (<= (* b c) -2e+152)
  (- (* b c) (* 4.0 (* a t)))
  (if (<= (* b c) -2e-168)
    (- (* -4.0 (* i x)) (* (* j 27.0) k))
    (if (<= (* b c) 2e+87)
      (fma (* t a) -4.0 (* (* k j) -27.0))
      (fma c b (- (* (* 27.0 j) k)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2e+152) {
		tmp = (b * c) - (4.0 * (a * t));
	} else if ((b * c) <= -2e-168) {
		tmp = (-4.0 * (i * x)) - ((j * 27.0) * k);
	} else if ((b * c) <= 2e+87) {
		tmp = fma((t * a), -4.0, ((k * j) * -27.0));
	} else {
		tmp = fma(c, b, -((27.0 * j) * k));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -2e+152)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(a * t)));
	elseif (Float64(b * c) <= -2e-168)
		tmp = Float64(Float64(-4.0 * Float64(i * x)) - Float64(Float64(j * 27.0) * k));
	elseif (Float64(b * c) <= 2e+87)
		tmp = fma(Float64(t * a), -4.0, Float64(Float64(k * j) * -27.0));
	else
		tmp = fma(c, b, Float64(-Float64(Float64(27.0 * j) * k)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -2e+152], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2e-168], N[(N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+87], N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(c * b + (-N[(N[(27.0 * j), $MachinePrecision] * k), $MachinePrecision])), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2.0000000000000001e152

   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. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 61.5%

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.1%

         \[\leadsto b \cdot c - 4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 42.1%

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

   if -2.0000000000000001e152 < (*.f64 b c) < -2.0000000000000001e-168

   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. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 41.6%

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

   4. Applied rewrites 41.6%

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

   if -2.0000000000000001e-168 < (*.f64 b c) < 1.9999999999999999e87

   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. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 61.5%

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in b around 0

      \[\leadsto -1 \cdot \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(4 \cdot \left(a \cdot t\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot \color{blue}{t}, 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 41.9%

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right) \]

   7. Applied rewrites 41.9%

      \[\leadsto -1 \cdot \color{blue}{\mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right)} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, \color{blue}{a \cdot t}, 27 \cdot \left(j \cdot k\right)\right) \]

      2. mul-1-neg N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-neg-in N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. metadata-eval N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*l* N/A

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

      15. lift-*.f64 N/A

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

      16. lower-fma.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*l* N/A

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 41.9%

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

      25. lift-*.f64 N/A

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

      26. *-commutative N/A

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

      27. lower-*.f64 41.9%

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

   9. Applied rewrites 41.9%

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

   if 1.9999999999999999e87 < (*.f64 b c)

   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. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 61.5%

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.1%

         \[\leadsto b \cdot c - 4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 42.1%

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

   8. Taylor expanded in t around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 45.0%

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot k\right) \]

   10. Applied rewrites 45.0%

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

       1. lift--.f64 N/A

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

       2. sub-flip N/A

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

       3. lift-*.f64 N/A

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

       4. *-commutative N/A

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

       5. lower-fma.f64 N/A

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

       6. lower-neg.f64 45.5%

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

       7. lift-*.f64 N/A

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

       8. lift-*.f64 N/A

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

       9. associate-*r* N/A

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

       10. *-commutative N/A

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

       11. lower-*.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 45.4%

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

   12. Applied rewrites 45.4%

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

Alternative 9: 55.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+79}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+87}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot a, -4, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -\left(27 \cdot j\right) \cdot k\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (if (<= (* b c) -2e+79)
  (- (* b c) (* 4.0 (* a t)))
  (if (<= (* b c) 2e+87)
    (fma (* t a) -4.0 (* (* k j) -27.0))
    (fma c b (- (* (* 27.0 j) k))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2e+79) {
		tmp = (b * c) - (4.0 * (a * t));
	} else if ((b * c) <= 2e+87) {
		tmp = fma((t * a), -4.0, ((k * j) * -27.0));
	} else {
		tmp = fma(c, b, -((27.0 * j) * k));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -2e+79)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(a * t)));
	elseif (Float64(b * c) <= 2e+87)
		tmp = fma(Float64(t * a), -4.0, Float64(Float64(k * j) * -27.0));
	else
		tmp = fma(c, b, Float64(-Float64(Float64(27.0 * j) * k)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -2e+79], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+87], N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(c * b + (-N[(N[(27.0 * j), $MachinePrecision] * k), $MachinePrecision])), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.9999999999999999e79

   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. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 61.5%

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.1%

         \[\leadsto b \cdot c - 4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 42.1%

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

   if -1.9999999999999999e79 < (*.f64 b c) < 1.9999999999999999e87

   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. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 61.5%

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in b around 0

      \[\leadsto -1 \cdot \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(4 \cdot \left(a \cdot t\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot \color{blue}{t}, 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 41.9%

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right) \]

   7. Applied rewrites 41.9%

      \[\leadsto -1 \cdot \color{blue}{\mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right)} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, \color{blue}{a \cdot t}, 27 \cdot \left(j \cdot k\right)\right) \]

      2. mul-1-neg N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-neg-in N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. metadata-eval N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*l* N/A

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

      15. lift-*.f64 N/A

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

      16. lower-fma.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*l* N/A

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 41.9%

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

      25. lift-*.f64 N/A

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

      26. *-commutative N/A

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

      27. lower-*.f64 41.9%

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

   9. Applied rewrites 41.9%

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

   if 1.9999999999999999e87 < (*.f64 b c)

   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. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 61.5%

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.1%

         \[\leadsto b \cdot c - 4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 42.1%

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

   8. Taylor expanded in t around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 45.0%

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot k\right) \]

   10. Applied rewrites 45.0%

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

       1. lift--.f64 N/A

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

       2. sub-flip N/A

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

       3. lift-*.f64 N/A

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

       4. *-commutative N/A

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

       5. lower-fma.f64 N/A

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

       6. lower-neg.f64 45.5%

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

       7. lift-*.f64 N/A

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

       8. lift-*.f64 N/A

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

       9. associate-*r* N/A

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

       10. *-commutative N/A

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

       11. lower-*.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 45.4%

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

   12. Applied rewrites 45.4%

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

Alternative 10: 55.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(c, b, -\left(27 \cdot j\right) \cdot k\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+127}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (fma c b (- (* (* 27.0 j) k)))) (t_2 (* (* j 27.0) k)))
  (if (<= t_2 -1e+151)
    t_1
    (if (<= t_2 2e+127) (- (* b c) (* 4.0 (* a 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 = fma(c, b, -((27.0 * j) * k));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -1e+151) {
		tmp = t_1;
	} else if (t_2 <= 2e+127) {
		tmp = (b * c) - (4.0 * (a * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(c, b, Float64(-Float64(Float64(27.0 * j) * k)))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -1e+151)
		tmp = t_1;
	elseif (t_2 <= 2e+127)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(a * t)));
	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[(c * b + (-N[(N[(27.0 * j), $MachinePrecision] * k), $MachinePrecision])), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+151], t$95$1, If[LessEqual[t$95$2, 2e+127], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e151 or 1.9999999999999999e127 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 61.5%

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.1%

         \[\leadsto b \cdot c - 4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 42.1%

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

   8. Taylor expanded in t around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 45.0%

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot k\right) \]

   10. Applied rewrites 45.0%

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

       1. lift--.f64 N/A

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

       2. sub-flip N/A

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

       3. lift-*.f64 N/A

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

       4. *-commutative N/A

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

       5. lower-fma.f64 N/A

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

       6. lower-neg.f64 45.5%

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

       7. lift-*.f64 N/A

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

       8. lift-*.f64 N/A

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

       9. associate-*r* N/A

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

       10. *-commutative N/A

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

       11. lower-*.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 45.4%

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

   12. Applied rewrites 45.4%

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

   if -1e151 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e127

   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. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 61.5%

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.1%

         \[\leadsto b \cdot c - 4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 42.1%

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

Alternative 11: 53.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(j, k\right) \cdot 27\right) \cdot \mathsf{max}\left(j, k\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+151}:\\ \;\;\;\;-27 \cdot \left(\mathsf{min}\left(j, k\right) \cdot \mathsf{max}\left(j, k\right)\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+131}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{max}\left(j, k\right) \cdot -27\right) \cdot \mathsf{min}\left(j, k\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* (* (fmin j k) 27.0) (fmax j k))))
  (if (<= t_1 -1e+151)
    (* -27.0 (* (fmin j k) (fmax j k)))
    (if (<= t_1 2e+131)
      (- (* b c) (* 4.0 (* a t)))
      (* (* (fmax j k) -27.0) (fmin j k))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (fmin(j, k) * 27.0) * fmax(j, k);
	double tmp;
	if (t_1 <= -1e+151) {
		tmp = -27.0 * (fmin(j, k) * fmax(j, k));
	} else if (t_1 <= 2e+131) {
		tmp = (b * c) - (4.0 * (a * t));
	} else {
		tmp = (fmax(j, k) * -27.0) * fmin(j, k);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = (fmin(j, k) * 27.0d0) * fmax(j, k)
    if (t_1 <= (-1d+151)) then
        tmp = (-27.0d0) * (fmin(j, k) * fmax(j, k))
    else if (t_1 <= 2d+131) then
        tmp = (b * c) - (4.0d0 * (a * t))
    else
        tmp = (fmax(j, k) * (-27.0d0)) * fmin(j, k)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (fmin(j, k) * 27.0) * fmax(j, k);
	double tmp;
	if (t_1 <= -1e+151) {
		tmp = -27.0 * (fmin(j, k) * fmax(j, k));
	} else if (t_1 <= 2e+131) {
		tmp = (b * c) - (4.0 * (a * t));
	} else {
		tmp = (fmax(j, k) * -27.0) * fmin(j, k);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (fmin(j, k) * 27.0) * fmax(j, k)
	tmp = 0
	if t_1 <= -1e+151:
		tmp = -27.0 * (fmin(j, k) * fmax(j, k))
	elif t_1 <= 2e+131:
		tmp = (b * c) - (4.0 * (a * t))
	else:
		tmp = (fmax(j, k) * -27.0) * fmin(j, k)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(fmin(j, k) * 27.0) * fmax(j, k))
	tmp = 0.0
	if (t_1 <= -1e+151)
		tmp = Float64(-27.0 * Float64(fmin(j, k) * fmax(j, k)));
	elseif (t_1 <= 2e+131)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(a * t)));
	else
		tmp = Float64(Float64(fmax(j, k) * -27.0) * fmin(j, k));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (min(j, k) * 27.0) * max(j, k);
	tmp = 0.0;
	if (t_1 <= -1e+151)
		tmp = -27.0 * (min(j, k) * max(j, k));
	elseif (t_1 <= 2e+131)
		tmp = (b * c) - (4.0 * (a * t));
	else
		tmp = (max(j, k) * -27.0) * min(j, k);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[Min[j, k], $MachinePrecision] * 27.0), $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+151], N[(-27.0 * N[(N[Min[j, k], $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+131], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Max[j, k], $MachinePrecision] * -27.0), $MachinePrecision] * N[Min[j, k], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e151

   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. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

   if -1e151 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999998e131

   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. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 61.5%

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.1%

         \[\leadsto b \cdot c - 4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 42.1%

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

   if 1.9999999999999998e131 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot k \]

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 24.3%

         \[\leadsto \left(k \cdot -27\right) \cdot j \]

   6. Applied rewrites 24.3%

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

Alternative 12: 35.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ t_2 := \left(\mathsf{min}\left(j, k\right) \cdot 27\right) \cdot \mathsf{max}\left(j, k\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+151}:\\ \;\;\;\;-27 \cdot \left(\mathsf{min}\left(j, k\right) \cdot \mathsf{max}\left(j, k\right)\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-235}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-170}:\\ \;\;\;\;-1 \cdot \left(4 \cdot \left(i \cdot x\right)\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{max}\left(j, k\right) \cdot -27\right) \cdot \mathsf{min}\left(j, k\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* -4.0 (* a t)))
       (t_2 (* (* (fmin j k) 27.0) (fmax j k))))
  (if (<= t_2 -1e+151)
    (* -27.0 (* (fmin j k) (fmax j k)))
    (if (<= t_2 -5e-235)
      t_1
      (if (<= t_2 5e-170)
        (* -1.0 (* 4.0 (* i x)))
        (if (<= t_2 2e+127)
          t_1
          (* (* (fmax j k) -27.0) (fmin j k))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (a * t);
	double t_2 = (fmin(j, k) * 27.0) * fmax(j, k);
	double tmp;
	if (t_2 <= -1e+151) {
		tmp = -27.0 * (fmin(j, k) * fmax(j, k));
	} else if (t_2 <= -5e-235) {
		tmp = t_1;
	} else if (t_2 <= 5e-170) {
		tmp = -1.0 * (4.0 * (i * x));
	} else if (t_2 <= 2e+127) {
		tmp = t_1;
	} else {
		tmp = (fmax(j, k) * -27.0) * fmin(j, k);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = (-4.0d0) * (a * t)
    t_2 = (fmin(j, k) * 27.0d0) * fmax(j, k)
    if (t_2 <= (-1d+151)) then
        tmp = (-27.0d0) * (fmin(j, k) * fmax(j, k))
    else if (t_2 <= (-5d-235)) then
        tmp = t_1
    else if (t_2 <= 5d-170) then
        tmp = (-1.0d0) * (4.0d0 * (i * x))
    else if (t_2 <= 2d+127) then
        tmp = t_1
    else
        tmp = (fmax(j, k) * (-27.0d0)) * fmin(j, k)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (a * t);
	double t_2 = (fmin(j, k) * 27.0) * fmax(j, k);
	double tmp;
	if (t_2 <= -1e+151) {
		tmp = -27.0 * (fmin(j, k) * fmax(j, k));
	} else if (t_2 <= -5e-235) {
		tmp = t_1;
	} else if (t_2 <= 5e-170) {
		tmp = -1.0 * (4.0 * (i * x));
	} else if (t_2 <= 2e+127) {
		tmp = t_1;
	} else {
		tmp = (fmax(j, k) * -27.0) * fmin(j, k);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (a * t)
	t_2 = (fmin(j, k) * 27.0) * fmax(j, k)
	tmp = 0
	if t_2 <= -1e+151:
		tmp = -27.0 * (fmin(j, k) * fmax(j, k))
	elif t_2 <= -5e-235:
		tmp = t_1
	elif t_2 <= 5e-170:
		tmp = -1.0 * (4.0 * (i * x))
	elif t_2 <= 2e+127:
		tmp = t_1
	else:
		tmp = (fmax(j, k) * -27.0) * fmin(j, k)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(a * t))
	t_2 = Float64(Float64(fmin(j, k) * 27.0) * fmax(j, k))
	tmp = 0.0
	if (t_2 <= -1e+151)
		tmp = Float64(-27.0 * Float64(fmin(j, k) * fmax(j, k)));
	elseif (t_2 <= -5e-235)
		tmp = t_1;
	elseif (t_2 <= 5e-170)
		tmp = Float64(-1.0 * Float64(4.0 * Float64(i * x)));
	elseif (t_2 <= 2e+127)
		tmp = t_1;
	else
		tmp = Float64(Float64(fmax(j, k) * -27.0) * fmin(j, k));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (a * t);
	t_2 = (min(j, k) * 27.0) * max(j, k);
	tmp = 0.0;
	if (t_2 <= -1e+151)
		tmp = -27.0 * (min(j, k) * max(j, k));
	elseif (t_2 <= -5e-235)
		tmp = t_1;
	elseif (t_2 <= 5e-170)
		tmp = -1.0 * (4.0 * (i * x));
	elseif (t_2 <= 2e+127)
		tmp = t_1;
	else
		tmp = (max(j, k) * -27.0) * min(j, k);
	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[(a * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Min[j, k], $MachinePrecision] * 27.0), $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+151], N[(-27.0 * N[(N[Min[j, k], $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-235], t$95$1, If[LessEqual[t$95$2, 5e-170], N[(-1.0 * N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+127], t$95$1, N[(N[(N[Max[j, k], $MachinePrecision] * -27.0), $MachinePrecision] * N[Min[j, k], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e151

   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. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

   if -1e151 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.9999999999999998e-235 or 5.0000000000000001e-170 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e127

   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. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 61.5%

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 21.2%

         \[\leadsto -4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 21.2%

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

   if -4.9999999999999998e-235 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.0000000000000001e-170

   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. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

   5. Taylor expanded in x around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      7. lower-*.f64 41.7%

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

   7. Applied rewrites 41.7%

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

   8. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \left(4 \cdot \color{blue}{\left(i \cdot x\right)}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(4 \cdot \left(i \cdot \color{blue}{x}\right)\right) \]

      2. lower-*.f64 20.9%

         \[\leadsto -1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) \]

   10. Applied rewrites 20.9%

       \[\leadsto -1 \cdot \left(4 \cdot \color{blue}{\left(i \cdot x\right)}\right) \]

   if 1.9999999999999999e127 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot k \]

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 24.3%

         \[\leadsto \left(k \cdot -27\right) \cdot j \]

   6. Applied rewrites 24.3%

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

Alternative 13: 35.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(j, k\right) \cdot 27\right) \cdot \mathsf{max}\left(j, k\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+151}:\\ \;\;\;\;-27 \cdot \left(\mathsf{min}\left(j, k\right) \cdot \mathsf{max}\left(j, k\right)\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+127}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{max}\left(j, k\right) \cdot -27\right) \cdot \mathsf{min}\left(j, k\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* (* (fmin j k) 27.0) (fmax j k))))
  (if (<= t_1 -1e+151)
    (* -27.0 (* (fmin j k) (fmax j k)))
    (if (<= t_1 2e+127)
      (* -4.0 (* a t))
      (* (* (fmax j k) -27.0) (fmin j k))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (fmin(j, k) * 27.0) * fmax(j, k);
	double tmp;
	if (t_1 <= -1e+151) {
		tmp = -27.0 * (fmin(j, k) * fmax(j, k));
	} else if (t_1 <= 2e+127) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = (fmax(j, k) * -27.0) * fmin(j, k);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = (fmin(j, k) * 27.0d0) * fmax(j, k)
    if (t_1 <= (-1d+151)) then
        tmp = (-27.0d0) * (fmin(j, k) * fmax(j, k))
    else if (t_1 <= 2d+127) then
        tmp = (-4.0d0) * (a * t)
    else
        tmp = (fmax(j, k) * (-27.0d0)) * fmin(j, k)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (fmin(j, k) * 27.0) * fmax(j, k);
	double tmp;
	if (t_1 <= -1e+151) {
		tmp = -27.0 * (fmin(j, k) * fmax(j, k));
	} else if (t_1 <= 2e+127) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = (fmax(j, k) * -27.0) * fmin(j, k);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (fmin(j, k) * 27.0) * fmax(j, k)
	tmp = 0
	if t_1 <= -1e+151:
		tmp = -27.0 * (fmin(j, k) * fmax(j, k))
	elif t_1 <= 2e+127:
		tmp = -4.0 * (a * t)
	else:
		tmp = (fmax(j, k) * -27.0) * fmin(j, k)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(fmin(j, k) * 27.0) * fmax(j, k))
	tmp = 0.0
	if (t_1 <= -1e+151)
		tmp = Float64(-27.0 * Float64(fmin(j, k) * fmax(j, k)));
	elseif (t_1 <= 2e+127)
		tmp = Float64(-4.0 * Float64(a * t));
	else
		tmp = Float64(Float64(fmax(j, k) * -27.0) * fmin(j, k));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (min(j, k) * 27.0) * max(j, k);
	tmp = 0.0;
	if (t_1 <= -1e+151)
		tmp = -27.0 * (min(j, k) * max(j, k));
	elseif (t_1 <= 2e+127)
		tmp = -4.0 * (a * t);
	else
		tmp = (max(j, k) * -27.0) * min(j, k);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[Min[j, k], $MachinePrecision] * 27.0), $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+151], N[(-27.0 * N[(N[Min[j, k], $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+127], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], N[(N[(N[Max[j, k], $MachinePrecision] * -27.0), $MachinePrecision] * N[Min[j, k], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e151

   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. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

   if -1e151 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e127

   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. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 61.5%

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 21.2%

         \[\leadsto -4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 21.2%

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

   if 1.9999999999999999e127 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot k \]

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 24.3%

         \[\leadsto \left(k \cdot -27\right) \cdot j \]

   6. Applied rewrites 24.3%

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

Alternative 14: 35.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+151}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+127}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* (* j 27.0) k)))
  (if (<= t_1 -1e+151)
    (* -27.0 (* j k))
    (if (<= t_1 2e+127) (* -4.0 (* a t)) (* (* 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) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+151) {
		tmp = -27.0 * (j * k);
	} else if (t_1 <= 2e+127) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = (j * -27.0) * k;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-1d+151)) then
        tmp = (-27.0d0) * (j * k)
    else if (t_1 <= 2d+127) then
        tmp = (-4.0d0) * (a * t)
    else
        tmp = (j * (-27.0d0)) * k
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+151) {
		tmp = -27.0 * (j * k);
	} else if (t_1 <= 2e+127) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = (j * -27.0) * k;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -1e+151:
		tmp = -27.0 * (j * k)
	elif t_1 <= 2e+127:
		tmp = -4.0 * (a * t)
	else:
		tmp = (j * -27.0) * k
	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 <= -1e+151)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (t_1 <= 2e+127)
		tmp = Float64(-4.0 * Float64(a * t));
	else
		tmp = Float64(Float64(j * -27.0) * k);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -1e+151)
		tmp = -27.0 * (j * k);
	elseif (t_1 <= 2e+127)
		tmp = -4.0 * (a * t);
	else
		tmp = (j * -27.0) * k;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+151], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+127], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e151

   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. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

   if -1e151 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e127

   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. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 61.5%

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 21.2%

         \[\leadsto -4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 21.2%

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

   if 1.9999999999999999e127 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot k \]

      5. lower-*.f64 24.2%

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

      6. lift-*.f64 N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot k \]

      7. *-commutative N/A

         \[\leadsto \left(j \cdot -27\right) \cdot k \]

      8. lower-*.f64 24.2%

         \[\leadsto \left(j \cdot -27\right) \cdot k \]

   6. Applied rewrites 24.2%

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

Alternative 15: 35.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+127}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* -27.0 (* j k))) (t_2 (* (* j 27.0) k)))
  (if (<= t_2 -1e+151) t_1 (if (<= t_2 2e+127) (* -4.0 (* a 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 = -27.0 * (j * k);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -1e+151) {
		tmp = t_1;
	} else if (t_2 <= 2e+127) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-1d+151)) then
        tmp = t_1
    else if (t_2 <= 2d+127) then
        tmp = (-4.0d0) * (a * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -1e+151) {
		tmp = t_1;
	} else if (t_2 <= 2e+127) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -1e+151:
		tmp = t_1
	elif t_2 <= 2e+127:
		tmp = -4.0 * (a * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -1e+151)
		tmp = t_1;
	elseif (t_2 <= 2e+127)
		tmp = Float64(-4.0 * Float64(a * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -1e+151)
		tmp = t_1;
	elseif (t_2 <= 2e+127)
		tmp = -4.0 * (a * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+151], t$95$1, If[LessEqual[t$95$2, 2e+127], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e151 or 1.9999999999999999e127 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

   if -1e151 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e127

   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. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 61.5%

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 21.2%

         \[\leadsto -4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 21.2%

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

Alternative 16: 21.2% accurate, 6.3× speedup

Math

\[-4 \cdot \left(a \cdot t\right) \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = (-4.0d0) * (a * t)
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 -4.0 * (a * t);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]

Derivation

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. Taylor expanded in x around 0

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

   1. lower--.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower-fma.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. lower-*.f64 N/A

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

   6. lower-*.f64 61.5%

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

4. Applied rewrites 61.5%

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

5. Taylor expanded in t around inf

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 21.2%

      \[\leadsto -4 \cdot \left(a \cdot t\right) \]

7. Applied rewrites 21.2%

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

Reproduce

herbie shell --seed 2025212 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))