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

Percentage Accurate: 84.5% → 91.9%

Time: 6.8s

Alternatives: 21

Speedup: 0.9×

• 50.8% 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: 84.5% 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: 91.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \left(\left(x \cdot 18\right) \cdot y\right) \cdot z\\ t_2 := \left(\left(-x \cdot \left(i \cdot 4 - \left(\left(y \cdot 18\right) \cdot t\right) \cdot z\right)\right) + \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right)\right) - \left(\mathsf{min}\left(j, k\right) \cdot 27\right) \cdot \mathsf{max}\left(j, k\right)\\ t_3 := \left(\left(t\_1 \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+267}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 10^{+295}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, \mathsf{fma}\left(-27 \cdot \mathsf{min}\left(j, k\right), \mathsf{max}\left(j, k\right), \left(-4 \cdot x\right) \cdot i\right)\right)\right)\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, -4, t\_1\right) \cdot t\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* (* x 18.0) y) z))
        (t_2
         (-
          (+
           (- (* x (- (* i 4.0) (* (* (* y 18.0) t) z))))
           (fma (* a t) -4.0 (* c b)))
          (* (* (fmin j k) 27.0) (fmax j k))))
        (t_3 (- (+ (- (* t_1 t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))))
   (if (<= t_3 -5e+267)
     t_2
     (if (<= t_3 1e+295)
       (fma
        c
        b
        (fma
         (fma -4.0 a (* z (* y (* 18.0 x))))
         t
         (fma (* -27.0 (fmin j k)) (fmax j k) (* (* -4.0 x) i))))
       (if (<= t_3 INFINITY) t_2 (* (fma a -4.0 t_1) t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((x * 18.0) * y) * z;
	double t_2 = (-(x * ((i * 4.0) - (((y * 18.0) * t) * z))) + fma((a * t), -4.0, (c * b))) - ((fmin(j, k) * 27.0) * fmax(j, k));
	double t_3 = (((t_1 * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_3 <= -5e+267) {
		tmp = t_2;
	} else if (t_3 <= 1e+295) {
		tmp = fma(c, b, fma(fma(-4.0, a, (z * (y * (18.0 * x)))), t, fma((-27.0 * fmin(j, k)), fmax(j, k), ((-4.0 * x) * i))));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = fma(a, -4.0, t_1) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(x * 18.0) * y) * z)
	t_2 = Float64(Float64(Float64(-Float64(x * Float64(Float64(i * 4.0) - Float64(Float64(Float64(y * 18.0) * t) * z)))) + fma(Float64(a * t), -4.0, Float64(c * b))) - Float64(Float64(fmin(j, k) * 27.0) * fmax(j, k)))
	t_3 = Float64(Float64(Float64(Float64(t_1 * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i))
	tmp = 0.0
	if (t_3 <= -5e+267)
		tmp = t_2;
	elseif (t_3 <= 1e+295)
		tmp = fma(c, b, fma(fma(-4.0, a, Float64(z * Float64(y * Float64(18.0 * x)))), t, fma(Float64(-27.0 * fmin(j, k)), fmax(j, k), Float64(Float64(-4.0 * x) * i))));
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(fma(a, -4.0, t_1) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-N[(x * N[(N[(i * 4.0), $MachinePrecision] - N[(N[(N[(y * 18.0), $MachinePrecision] * t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]) + N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[Min[j, k], $MachinePrecision] * 27.0), $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(t$95$1 * 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]}, If[LessEqual[t$95$3, -5e+267], t$95$2, If[LessEqual[t$95$3, 1e+295], 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 * N[Min[j, k], $MachinePrecision]), $MachinePrecision] * N[Max[j, k], $MachinePrecision] + N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$2, N[(N[(a * -4.0 + t$95$1), $MachinePrecision] * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 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)) < -4.9999999999999999e267 or 9.9999999999999998e294 < (-.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 84.5%

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

   3. Applied rewrites 86.9%

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

   if -4.9999999999999999e267 < (-.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)) < 9.9999999999999998e294

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   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 84.5%

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

   2. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 42.7

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

   4. Applied rewrites 42.7%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

   6. Applied rewrites 43.2%

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

Alternative 2: 90.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(x * 18.0) * y) * z)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(t_1 * 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 * fmin(j, k)), fmax(j, k), Float64(Float64(-4.0 * x) * i))));
	else
		tmp = Float64(fma(a, -4.0, t_1) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(t$95$1 * 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 * N[Min[j, k], $MachinePrecision]), $MachinePrecision] * N[Max[j, k], $MachinePrecision] + N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * -4.0 + t$95$1), $MachinePrecision] * t), $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 84.5%

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

   3. Applied rewrites 88.9%

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

   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 84.5%

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

   2. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 42.7

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

   4. Applied rewrites 42.7%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

   6. Applied rewrites 43.2%

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

Alternative 3: 90.5% accurate, 0.5× speedup

Math

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

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 84.5%

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

   3. Applied rewrites 87.9%

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

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

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 78.0

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

   6. Applied rewrites 78.0%

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

      1. lift-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 77.3

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 77.2

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

   8. Applied rewrites 77.2%

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

Alternative 4: 84.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-51}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(\left(y \cdot z\right) \cdot 18, x, a \cdot -4\right), t, k \cdot \left(j \cdot -27\right)\right)\right)\\ \mathbf{elif}\;t\_2 \leq 10^{-69}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t\_1, t, -4 \cdot \left(i \cdot x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t\_1, t, -27 \cdot \left(j \cdot k\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma -4.0 a (* z (* y (* 18.0 x))))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -5e-51)
     (fma c b (fma (fma (* (* y z) 18.0) x (* a -4.0)) t (* k (* j -27.0))))
     (if (<= t_2 1e-69)
       (fma c b (fma t_1 t (* -4.0 (* i x))))
       (fma c b (fma t_1 t (* -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 t_1 = fma(-4.0, a, (z * (y * (18.0 * x))));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e-51) {
		tmp = fma(c, b, fma(fma(((y * z) * 18.0), x, (a * -4.0)), t, (k * (j * -27.0))));
	} else if (t_2 <= 1e-69) {
		tmp = fma(c, b, fma(t_1, t, (-4.0 * (i * x))));
	} else {
		tmp = fma(c, b, fma(t_1, t, (-27.0 * (j * k))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(-4.0, a, Float64(z * Float64(y * Float64(18.0 * x))))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -5e-51)
		tmp = fma(c, b, fma(fma(Float64(Float64(y * z) * 18.0), x, Float64(a * -4.0)), t, Float64(k * Float64(j * -27.0))));
	elseif (t_2 <= 1e-69)
		tmp = fma(c, b, fma(t_1, t, Float64(-4.0 * Float64(i * x))));
	else
		tmp = fma(c, b, fma(t_1, t, Float64(-27.0 * Float64(j * k))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * a + N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-51], N[(c * b + N[(N[(N[(N[(y * z), $MachinePrecision] * 18.0), $MachinePrecision] * x + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-69], N[(c * b + N[(t$95$1 * t + N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(t$95$1 * t + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.00000000000000004e-51

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 78.0

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

   6. Applied rewrites 78.0%

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

      1. lift-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 77.3

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 77.2

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

   8. Applied rewrites 77.2%

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

   if -5.00000000000000004e-51 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.9999999999999996e-70

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 78.0

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

   6. Applied rewrites 78.0%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 72.6

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

   9. Applied rewrites 72.6%

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

   if 9.9999999999999996e-70 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 78.0

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

   6. Applied rewrites 78.0%

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

Alternative 5: 84.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right)\\ t_2 := \mathsf{fma}\left(c, b, \mathsf{fma}\left(t\_1, t, -27 \cdot \left(j \cdot k\right)\right)\right)\\ t_3 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{-51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 10^{-69}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t\_1, t, -4 \cdot \left(i \cdot x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma -4.0 a (* z (* y (* 18.0 x)))))
        (t_2 (fma c b (fma t_1 t (* -27.0 (* j k)))))
        (t_3 (* (* j 27.0) k)))
   (if (<= t_3 -5e-51)
     t_2
     (if (<= t_3 1e-69) (fma c b (fma t_1 t (* -4.0 (* i x)))) 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(-4.0, a, (z * (y * (18.0 * x))));
	double t_2 = fma(c, b, fma(t_1, t, (-27.0 * (j * k))));
	double t_3 = (j * 27.0) * k;
	double tmp;
	if (t_3 <= -5e-51) {
		tmp = t_2;
	} else if (t_3 <= 1e-69) {
		tmp = fma(c, b, fma(t_1, t, (-4.0 * (i * x))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(-4.0, a, Float64(z * Float64(y * Float64(18.0 * x))))
	t_2 = fma(c, b, fma(t_1, t, Float64(-27.0 * Float64(j * k))))
	t_3 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_3 <= -5e-51)
		tmp = t_2;
	elseif (t_3 <= 1e-69)
		tmp = fma(c, b, fma(t_1, t, Float64(-4.0 * Float64(i * x))));
	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[(-4.0 * a + N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * b + N[(t$95$1 * t + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$3, -5e-51], t$95$2, If[LessEqual[t$95$3, 1e-69], N[(c * b + N[(t$95$1 * t + N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.00000000000000004e-51 or 9.9999999999999996e-70 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 78.0

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

   6. Applied rewrites 78.0%

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

   if -5.00000000000000004e-51 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.9999999999999996e-70

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 78.0

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

   6. Applied rewrites 78.0%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 72.6

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

   9. Applied rewrites 72.6%

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

Alternative 6: 83.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(-27 \cdot j, k, \left(-4 \cdot x\right) \cdot i\right)\right)\right)\\ \mathbf{if}\;i \leq -1.7 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 9.8 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, -27 \cdot \left(j \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma c b (fma (* -4.0 a) t (fma (* -27.0 j) k (* (* -4.0 x) i))))))
   (if (<= i -1.7e+33)
     t_1
     (if (<= i 9.8e+76)
       (fma c b (fma (fma -4.0 a (* z (* y (* 18.0 x)))) t (* -27.0 (* j k))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(c, b, fma((-4.0 * a), t, fma((-27.0 * j), k, ((-4.0 * x) * i))));
	double tmp;
	if (i <= -1.7e+33) {
		tmp = t_1;
	} else if (i <= 9.8e+76) {
		tmp = fma(c, b, fma(fma(-4.0, a, (z * (y * (18.0 * x)))), t, (-27.0 * (j * k))));
	} 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(Float64(-4.0 * a), t, fma(Float64(-27.0 * j), k, Float64(Float64(-4.0 * x) * i))))
	tmp = 0.0
	if (i <= -1.7e+33)
		tmp = t_1;
	elseif (i <= 9.8e+76)
		tmp = fma(c, b, fma(fma(-4.0, a, Float64(z * Float64(y * Float64(18.0 * x)))), t, Float64(-27.0 * Float64(j * k))));
	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), $MachinePrecision] * t + N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.7e+33], t$95$1, If[LessEqual[i, 9.8e+76], N[(c * b + N[(N[(-4.0 * a + N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if i < -1.7e33 or 9.80000000000000053e76 < i

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   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 78.5

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

   6. Applied rewrites 78.5%

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

   if -1.7e33 < i < 9.80000000000000053e76

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 78.0

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

   6. Applied rewrites 78.0%

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

Alternative 7: 80.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(-27 \cdot \mathsf{min}\left(j, k\right), \mathsf{max}\left(j, k\right), \left(-4 \cdot x\right) \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27, \mathsf{min}\left(j, k\right) \cdot \mathsf{max}\left(j, k\right), t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)\right)\\ \end{array} \]

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))
      5e+276)
   (fma
    c
    b
    (fma (* -4.0 a) t (fma (* -27.0 (fmin j k)) (fmax j k) (* (* -4.0 x) i))))
   (fma
    c
    b
    (fma
     -27.0
     (* (fmin j k) (fmax j k))
     (* t (fma -4.0 a (* 18.0 (* x (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) <= 5e+276) {
		tmp = fma(c, b, fma((-4.0 * a), t, fma((-27.0 * fmin(j, k)), fmax(j, k), ((-4.0 * x) * i))));
	} else {
		tmp = fma(c, b, fma(-27.0, (fmin(j, k) * fmax(j, k)), (t * fma(-4.0, a, (18.0 * (x * (y * z)))))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (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)) <= 5e+276)
		tmp = fma(c, b, fma(Float64(-4.0 * a), t, fma(Float64(-27.0 * fmin(j, k)), fmax(j, k), Float64(Float64(-4.0 * x) * i))));
	else
		tmp = fma(c, b, fma(-27.0, Float64(fmin(j, k) * fmax(j, k)), Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[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], 5e+276], N[(c * b + N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(-27.0 * N[Min[j, k], $MachinePrecision]), $MachinePrecision] * N[Max[j, k], $MachinePrecision] + N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(-27.0 * N[(N[Min[j, k], $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision] + N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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)) < 5.00000000000000001e276

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   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 78.5

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

   6. Applied rewrites 78.5%

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

   if 5.00000000000000001e276 < (-.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 84.5%

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in i around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 76.9

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

   6. Applied rewrites 76.9%

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

Alternative 8: 77.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(-27 \cdot j, k, \left(-4 \cdot x\right) \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right), t, k \cdot \left(j \cdot -27\right)\right)\right)\\ \end{array} \]

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))
      5e+276)
   (fma c b (fma (* -4.0 a) t (fma (* -27.0 j) k (* (* -4.0 x) i))))
   (fma c b (fma (* 18.0 (* x (* y z))) t (* k (* j -27.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) <= 5e+276) {
		tmp = fma(c, b, fma((-4.0 * a), t, fma((-27.0 * j), k, ((-4.0 * x) * i))));
	} else {
		tmp = fma(c, b, fma((18.0 * (x * (y * z))), t, (k * (j * -27.0))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) <= 5e+276)
		tmp = fma(c, b, fma(Float64(-4.0 * a), t, fma(Float64(-27.0 * j), k, Float64(Float64(-4.0 * x) * i))));
	else
		tmp = fma(c, b, fma(Float64(18.0 * Float64(x * Float64(y * z))), t, Float64(k * Float64(j * -27.0))));
	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], 5e+276], 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[(c * b + N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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)) < 5.00000000000000001e276

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   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 78.5

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

   6. Applied rewrites 78.5%

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

   if 5.00000000000000001e276 < (-.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 84.5%

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 78.0

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

   6. Applied rewrites 78.0%

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

      1. lift-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 77.3

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 77.2

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

   8. Applied rewrites 77.2%

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

   9. Taylor expanded in x around inf

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-*.f64 62.2

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

   11. Applied rewrites 62.2%

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

Alternative 9: 77.2% accurate, 0.6× speedup

Math

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

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))
       (* (* j 27.0) k))
      2e+306)
   (fma -27.0 (* j k) (fma -4.0 (* a t) (fma -4.0 (* i x) (* b c))))
   (fma c b (fma (* 18.0 (* x (* y z))) t (* k (* j -27.0))))))

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < 2.00000000000000003e306

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 76.3

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

   6. Applied rewrites 76.3%

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

   if 2.00000000000000003e306 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k))

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 78.0

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

   6. Applied rewrites 78.0%

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

      1. lift-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 77.3

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 77.2

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

   8. Applied rewrites 77.2%

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

   9. Taylor expanded in x around inf

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-*.f64 62.2

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

   11. Applied rewrites 62.2%

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

Alternative 10: 71.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-115}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27, \mathsf{min}\left(j, k\right) \cdot \mathsf{max}\left(j, k\right), -4 \cdot \left(a \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right), t, \mathsf{max}\left(j, k\right) \cdot \left(\mathsf{min}\left(j, k\right) \cdot -27\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -7e+79)
   (* x (fma -4.0 i (* 18.0 (* t (* y z)))))
   (if (<= x 3.5e-115)
     (fma c b (fma -27.0 (* (fmin j k) (fmax j k)) (* -4.0 (* a t))))
     (fma
      c
      b
      (fma (* 18.0 (* x (* y z))) t (* (fmax j k) (* (fmin j k) -27.0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -7e+79) {
		tmp = x * fma(-4.0, i, (18.0 * (t * (y * z))));
	} else if (x <= 3.5e-115) {
		tmp = fma(c, b, fma(-27.0, (fmin(j, k) * fmax(j, k)), (-4.0 * (a * t))));
	} else {
		tmp = fma(c, b, fma((18.0 * (x * (y * z))), t, (fmax(j, k) * (fmin(j, k) * -27.0))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -7e+79)
		tmp = Float64(x * fma(-4.0, i, Float64(18.0 * Float64(t * Float64(y * z)))));
	elseif (x <= 3.5e-115)
		tmp = fma(c, b, fma(-27.0, Float64(fmin(j, k) * fmax(j, k)), Float64(-4.0 * Float64(a * t))));
	else
		tmp = fma(c, b, fma(Float64(18.0 * Float64(x * Float64(y * z))), t, Float64(fmax(j, k) * Float64(fmin(j, k) * -27.0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -7e+79], N[(x * N[(-4.0 * i + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e-115], N[(c * b + N[(-27.0 * N[(N[Min[j, k], $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t + N[(N[Max[j, k], $MachinePrecision] * N[(N[Min[j, k], $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.99999999999999961e79

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.4

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

   6. Applied rewrites 42.4%

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

   if -6.99999999999999961e79 < x < 3.5000000000000002e-115

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   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 61.6

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

   6. Applied rewrites 61.6%

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

   if 3.5000000000000002e-115 < x

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 78.0

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

   6. Applied rewrites 78.0%

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

      1. lift-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 77.3

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 77.2

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

   8. Applied rewrites 77.2%

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

   9. Taylor expanded in x around inf

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-*.f64 62.2

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

   11. Applied rewrites 62.2%

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

Alternative 11: 71.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27, j \cdot k, -4 \cdot \left(a \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (fma -4.0 i (* 18.0 (* t (* y z)))))))
   (if (<= x -7e+79)
     t_1
     (if (<= x 6.6e-9) (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 = x * fma(-4.0, i, (18.0 * (t * (y * z))));
	double tmp;
	if (x <= -7e+79) {
		tmp = t_1;
	} else if (x <= 6.6e-9) {
		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(x * fma(-4.0, i, Float64(18.0 * Float64(t * Float64(y * z)))))
	tmp = 0.0
	if (x <= -7e+79)
		tmp = t_1;
	elseif (x <= 6.6e-9)
		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[(x * N[(-4.0 * i + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e+79], t$95$1, If[LessEqual[x, 6.6e-9], 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 < -6.99999999999999961e79 or 6.60000000000000037e-9 < x

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.4

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

   6. Applied rewrites 42.4%

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

   if -6.99999999999999961e79 < x < 6.60000000000000037e-9

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   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 61.6

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

   6. Applied rewrites 61.6%

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

Alternative 12: 70.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(a, -4, \left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(-4, i \cdot x, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma a -4.0 (* (* (* x 18.0) y) z)) t)))
   (if (<= t -2.5e-39)
     t_1
     (if (<= t 6.6e+40) (fma -27.0 (* j k) (fma -4.0 (* i x) (* b c))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(a, -4.0, (((x * 18.0) * y) * z)) * t;
	double tmp;
	if (t <= -2.5e-39) {
		tmp = t_1;
	} else if (t <= 6.6e+40) {
		tmp = fma(-27.0, (j * k), fma(-4.0, (i * x), (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(a, -4.0, Float64(Float64(Float64(x * 18.0) * y) * z)) * t)
	tmp = 0.0
	if (t <= -2.5e-39)
		tmp = t_1;
	elseif (t <= 6.6e+40)
		tmp = fma(-27.0, Float64(j * k), fma(-4.0, Float64(i * x), Float64(b * c)));
	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[(a * -4.0 + N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2.5e-39], t$95$1, If[LessEqual[t, 6.6e+40], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(-4.0 * N[(i * x), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4999999999999999e-39 or 6.5999999999999997e40 < t

   1. Initial program 84.5%

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

   2. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 42.7

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

   4. Applied rewrites 42.7%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

   6. Applied rewrites 43.2%

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

   if -2.4999999999999999e-39 < t < 6.5999999999999997e40

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in t around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 61.0

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

   6. Applied rewrites 61.0%

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

Alternative 13: 54.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ t_2 := \left(\mathsf{min}\left(j, k\right) \cdot 27\right) \cdot \mathsf{max}\left(j, k\right)\\ t_3 := b \cdot c - 4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot a, -4, \left(\mathsf{max}\left(j, k\right) \cdot -27\right) \cdot \mathsf{min}\left(j, k\right)\right)\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-267}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+61}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{+180}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(\mathsf{min}\left(j, k\right) \cdot \mathsf{max}\left(j, k\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (fma -4.0 i (* 18.0 (* t (* y z))))))
        (t_2 (* (* (fmin j k) 27.0) (fmax j k)))
        (t_3 (- (* b c) (* 4.0 (* a t)))))
   (if (<= t_2 -5e+65)
     (fma (* t a) -4.0 (* (* (fmax j k) -27.0) (fmin j k)))
     (if (<= t_2 -2e-267)
       t_3
       (if (<= t_2 0.0)
         t_1
         (if (<= t_2 4e+61)
           t_3
           (if (<= t_2 1e+180)
             t_1
             (*
              -1.0
              (fma 4.0 (* a t) (* 27.0 (* (fmin j k) (fmax 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 = x * fma(-4.0, i, (18.0 * (t * (y * z))));
	double t_2 = (fmin(j, k) * 27.0) * fmax(j, k);
	double t_3 = (b * c) - (4.0 * (a * t));
	double tmp;
	if (t_2 <= -5e+65) {
		tmp = fma((t * a), -4.0, ((fmax(j, k) * -27.0) * fmin(j, k)));
	} else if (t_2 <= -2e-267) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 4e+61) {
		tmp = t_3;
	} else if (t_2 <= 1e+180) {
		tmp = t_1;
	} else {
		tmp = -1.0 * fma(4.0, (a * t), (27.0 * (fmin(j, k) * fmax(j, k))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * fma(-4.0, i, Float64(18.0 * Float64(t * Float64(y * z)))))
	t_2 = Float64(Float64(fmin(j, k) * 27.0) * fmax(j, k))
	t_3 = Float64(Float64(b * c) - Float64(4.0 * Float64(a * t)))
	tmp = 0.0
	if (t_2 <= -5e+65)
		tmp = fma(Float64(t * a), -4.0, Float64(Float64(fmax(j, k) * -27.0) * fmin(j, k)));
	elseif (t_2 <= -2e-267)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 4e+61)
		tmp = t_3;
	elseif (t_2 <= 1e+180)
		tmp = t_1;
	else
		tmp = Float64(-1.0 * fma(4.0, Float64(a * t), Float64(27.0 * Float64(fmin(j, k) * fmax(j, k)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(-4.0 * i + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Min[j, k], $MachinePrecision] * 27.0), $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+65], N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(N[Max[j, k], $MachinePrecision] * -27.0), $MachinePrecision] * N[Min[j, k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-267], t$95$3, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 4e+61], t$95$3, If[LessEqual[t$95$2, 1e+180], t$95$1, N[(-1.0 * N[(4.0 * N[(a * t), $MachinePrecision] + N[(27.0 * N[(N[Min[j, k], $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999973e65

   1. Initial program 84.5%

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

   2. 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 60.8

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

   4. Applied rewrites 60.8%

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

   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 41.6

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

   7. Applied rewrites 41.6%

      \[\leadsto -1 \cdot \color{blue}{\mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right)} \]
   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. lift-*.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. sub-negate N/A

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

      11. sub-flip-reverse N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

      16. +-commutative N/A

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

   9. Applied rewrites 41.5%

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

   if -4.99999999999999973e65 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e-267 or -0.0 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.9999999999999998e61

   1. Initial program 84.5%

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

   2. 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 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in t around 0

      \[\leadsto b \cdot c - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]
   6. 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 44.5

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

   7. Applied rewrites 44.5%

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

   8. Taylor expanded in t around inf

      \[\leadsto b \cdot c - 4 \cdot \color{blue}{\left(a \cdot t\right)} \]
   9. 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 41.8

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

   10. Applied rewrites 41.8%

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

   if -2e-267 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -0.0 or 3.9999999999999998e61 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1e180

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.4

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

   6. Applied rewrites 42.4%

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

   if 1e180 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.5%

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

   2. 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 60.8

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

   4. Applied rewrites 60.8%

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

   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 41.6

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

   7. Applied rewrites 41.6%

      \[\leadsto -1 \cdot \color{blue}{\mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 14: 54.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t \cdot a, -4, \left(k \cdot -27\right) \cdot j\right)\\ t_2 := x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ t_3 := \left(j \cdot 27\right) \cdot k\\ t_4 := b \cdot c - 4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-267}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{+61}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq 10^{+180}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* t a) -4.0 (* (* k -27.0) j)))
        (t_2 (* x (fma -4.0 i (* 18.0 (* t (* y z))))))
        (t_3 (* (* j 27.0) k))
        (t_4 (- (* b c) (* 4.0 (* a t)))))
   (if (<= t_3 -5e+65)
     t_1
     (if (<= t_3 -2e-267)
       t_4
       (if (<= t_3 0.0)
         t_2
         (if (<= t_3 4e+61) t_4 (if (<= t_3 1e+180) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((t * a), -4.0, ((k * -27.0) * j));
	double t_2 = x * fma(-4.0, i, (18.0 * (t * (y * z))));
	double t_3 = (j * 27.0) * k;
	double t_4 = (b * c) - (4.0 * (a * t));
	double tmp;
	if (t_3 <= -5e+65) {
		tmp = t_1;
	} else if (t_3 <= -2e-267) {
		tmp = t_4;
	} else if (t_3 <= 0.0) {
		tmp = t_2;
	} else if (t_3 <= 4e+61) {
		tmp = t_4;
	} else if (t_3 <= 1e+180) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(t * a), -4.0, Float64(Float64(k * -27.0) * j))
	t_2 = Float64(x * fma(-4.0, i, Float64(18.0 * Float64(t * Float64(y * z)))))
	t_3 = Float64(Float64(j * 27.0) * k)
	t_4 = Float64(Float64(b * c) - Float64(4.0 * Float64(a * t)))
	tmp = 0.0
	if (t_3 <= -5e+65)
		tmp = t_1;
	elseif (t_3 <= -2e-267)
		tmp = t_4;
	elseif (t_3 <= 0.0)
		tmp = t_2;
	elseif (t_3 <= 4e+61)
		tmp = t_4;
	elseif (t_3 <= 1e+180)
		tmp = t_2;
	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[(t * a), $MachinePrecision] * -4.0 + N[(N[(k * -27.0), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(-4.0 * i + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+65], t$95$1, If[LessEqual[t$95$3, -2e-267], t$95$4, If[LessEqual[t$95$3, 0.0], t$95$2, If[LessEqual[t$95$3, 4e+61], t$95$4, If[LessEqual[t$95$3, 1e+180], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999973e65 or 1e180 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.5%

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

   2. 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 60.8

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

   4. Applied rewrites 60.8%

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

   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 41.6

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

   7. Applied rewrites 41.6%

      \[\leadsto -1 \cdot \color{blue}{\mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right)} \]
   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. lift-*.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. sub-negate N/A

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

      11. sub-flip-reverse N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

      16. +-commutative N/A

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

   9. Applied rewrites 41.5%

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

   if -4.99999999999999973e65 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e-267 or -0.0 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.9999999999999998e61

   1. Initial program 84.5%

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

   2. 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 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in t around 0

      \[\leadsto b \cdot c - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]
   6. 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 44.5

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

   7. Applied rewrites 44.5%

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

   8. Taylor expanded in t around inf

      \[\leadsto b \cdot c - 4 \cdot \color{blue}{\left(a \cdot t\right)} \]
   9. 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 41.8

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

   10. Applied rewrites 41.8%

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

   if -2e-267 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -0.0 or 3.9999999999999998e61 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1e180

   1. Initial program 84.5%

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.4

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

   6. Applied rewrites 42.4%

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

Alternative 15: 54.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t \cdot a, -4, \left(k \cdot -27\right) \cdot j\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+81}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* t a) -4.0 (* (* k -27.0) j))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -5e+65)
     t_1
     (if (<= t_2 4e+81) (- (* 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((t * a), -4.0, ((k * -27.0) * j));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+65) {
		tmp = t_1;
	} else if (t_2 <= 4e+81) {
		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(Float64(t * a), -4.0, Float64(Float64(k * -27.0) * j))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -5e+65)
		tmp = t_1;
	elseif (t_2 <= 4e+81)
		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[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(k * -27.0), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+65], t$95$1, If[LessEqual[t$95$2, 4e+81], 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) < -4.99999999999999973e65 or 3.99999999999999969e81 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.5%

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

   2. 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 60.8

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

   4. Applied rewrites 60.8%

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

   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 41.6

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

   7. Applied rewrites 41.6%

      \[\leadsto -1 \cdot \color{blue}{\mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right)} \]
   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. lift-*.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. sub-negate N/A

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

      11. sub-flip-reverse N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

      16. +-commutative N/A

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

   9. Applied rewrites 41.5%

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

   if -4.99999999999999973e65 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.99999999999999969e81

   1. Initial program 84.5%

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

   2. 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 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in t around 0

      \[\leadsto b \cdot c - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]
   6. 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 44.5

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

   7. Applied rewrites 44.5%

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

   8. Taylor expanded in t around inf

      \[\leadsto b \cdot c - 4 \cdot \color{blue}{\left(a \cdot t\right)} \]
   9. 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 41.8

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

   10. Applied rewrites 41.8%

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

Alternative 16: 54.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+61}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+137}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 27.0 (* j k)))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -5e+65)
     t_1
     (if (<= t_2 4e+61)
       (- (* b c) (* 4.0 (* a t)))
       (if (<= t_2 2e+137) (* 18.0 (* t (* x (* y z)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (j * k));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+65) {
		tmp = t_1;
	} else if (t_2 <= 4e+61) {
		tmp = (b * c) - (4.0 * (a * t));
	} else if (t_2 <= 2e+137) {
		tmp = 18.0 * (t * (x * (y * z)));
	} 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 = (b * c) - (27.0d0 * (j * k))
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-5d+65)) then
        tmp = t_1
    else if (t_2 <= 4d+61) then
        tmp = (b * c) - (4.0d0 * (a * t))
    else if (t_2 <= 2d+137) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (j * k));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+65) {
		tmp = t_1;
	} else if (t_2 <= 4e+61) {
		tmp = (b * c) - (4.0 * (a * t));
	} else if (t_2 <= 2e+137) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (27.0 * (j * k))
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -5e+65:
		tmp = t_1
	elif t_2 <= 4e+61:
		tmp = (b * c) - (4.0 * (a * t))
	elif t_2 <= 2e+137:
		tmp = 18.0 * (t * (x * (y * z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -5e+65)
		tmp = t_1;
	elseif (t_2 <= 4e+61)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(a * t)));
	elseif (t_2 <= 2e+137)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (27.0 * (j * k));
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -5e+65)
		tmp = t_1;
	elseif (t_2 <= 4e+61)
		tmp = (b * c) - (4.0 * (a * t));
	elseif (t_2 <= 2e+137)
		tmp = 18.0 * (t * (x * (y * z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+65], t$95$1, If[LessEqual[t$95$2, 4e+61], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+137], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999973e65 or 2.0000000000000001e137 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.5%

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

   2. 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 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in t around 0

      \[\leadsto b \cdot c - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]
   6. 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 44.5

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

   7. Applied rewrites 44.5%

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

   if -4.99999999999999973e65 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.9999999999999998e61

   1. Initial program 84.5%

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

   2. 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 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in t around 0

      \[\leadsto b \cdot c - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]
   6. 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 44.5

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

   7. Applied rewrites 44.5%

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

   8. Taylor expanded in t around inf

      \[\leadsto b \cdot c - 4 \cdot \color{blue}{\left(a \cdot t\right)} \]
   9. 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 41.8

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

   10. Applied rewrites 41.8%

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

   if 3.9999999999999998e61 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000000000000001e137

   1. Initial program 84.5%

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

   2. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 42.7

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

   4. Applied rewrites 42.7%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 26.4

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

   7. Applied rewrites 26.4%

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

Alternative 17: 53.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+60}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 27.0 (* j k)))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -5e+65)
     t_1
     (if (<= t_2 4e+60) (- (* 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 = (b * c) - (27.0 * (j * k));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+65) {
		tmp = t_1;
	} else if (t_2 <= 4e+60) {
		tmp = (b * c) - (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 = (b * c) - (27.0d0 * (j * k))
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-5d+65)) then
        tmp = t_1
    else if (t_2 <= 4d+60) then
        tmp = (b * c) - (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 = (b * c) - (27.0 * (j * k));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+65) {
		tmp = t_1;
	} else if (t_2 <= 4e+60) {
		tmp = (b * c) - (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 = (b * c) - (27.0 * (j * k))
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -5e+65:
		tmp = t_1
	elif t_2 <= 4e+60:
		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 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -5e+65)
		tmp = t_1;
	elseif (t_2 <= 4e+60)
		tmp = Float64(Float64(b * c) - 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 = (b * c) - (27.0 * (j * k));
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -5e+65)
		tmp = t_1;
	elseif (t_2 <= 4e+60)
		tmp = (b * c) - (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[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+65], t$95$1, If[LessEqual[t$95$2, 4e+60], 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) < -4.99999999999999973e65 or 3.9999999999999998e60 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.5%

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

   2. 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 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in t around 0

      \[\leadsto b \cdot c - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]
   6. 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 44.5

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

   7. Applied rewrites 44.5%

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

   if -4.99999999999999973e65 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.9999999999999998e60

   1. Initial program 84.5%

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

   2. 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 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in t around 0

      \[\leadsto b \cdot c - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]
   6. 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 44.5

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

   7. Applied rewrites 44.5%

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

   8. Taylor expanded in t around inf

      \[\leadsto b \cdot c - 4 \cdot \color{blue}{\left(a \cdot t\right)} \]
   9. 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 41.8

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

   10. Applied rewrites 41.8%

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

Alternative 18: 50.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(j, k\right) \cdot 27\right) \cdot \mathsf{max}\left(j, k\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+65}:\\ \;\;\;\;\left(\mathsf{max}\left(j, k\right) \cdot -27\right) \cdot \mathsf{min}\left(j, k\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+61}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(\mathsf{min}\left(j, k\right) \cdot \mathsf{max}\left(j, k\right)\right)\\ \end{array} \]

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 -5e+65)
     (* (* (fmax j k) -27.0) (fmin j k))
     (if (<= t_1 4e+61)
       (- (* b c) (* 4.0 (* a t)))
       (* -27.0 (* (fmin j k) (fmax 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 <= -5e+65) {
		tmp = (fmax(j, k) * -27.0) * fmin(j, k);
	} else if (t_1 <= 4e+61) {
		tmp = (b * c) - (4.0 * (a * t));
	} else {
		tmp = -27.0 * (fmin(j, k) * fmax(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 <= (-5d+65)) then
        tmp = (fmax(j, k) * (-27.0d0)) * fmin(j, k)
    else if (t_1 <= 4d+61) then
        tmp = (b * c) - (4.0d0 * (a * t))
    else
        tmp = (-27.0d0) * (fmin(j, k) * fmax(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 <= -5e+65) {
		tmp = (fmax(j, k) * -27.0) * fmin(j, k);
	} else if (t_1 <= 4e+61) {
		tmp = (b * c) - (4.0 * (a * t));
	} else {
		tmp = -27.0 * (fmin(j, k) * fmax(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 <= -5e+65:
		tmp = (fmax(j, k) * -27.0) * fmin(j, k)
	elif t_1 <= 4e+61:
		tmp = (b * c) - (4.0 * (a * t))
	else:
		tmp = -27.0 * (fmin(j, k) * fmax(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 <= -5e+65)
		tmp = Float64(Float64(fmax(j, k) * -27.0) * fmin(j, k));
	elseif (t_1 <= 4e+61)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(a * t)));
	else
		tmp = Float64(-27.0 * Float64(fmin(j, k) * fmax(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 <= -5e+65)
		tmp = (max(j, k) * -27.0) * min(j, k);
	elseif (t_1 <= 4e+61)
		tmp = (b * c) - (4.0 * (a * t));
	else
		tmp = -27.0 * (min(j, k) * max(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, -5e+65], N[(N[(N[Max[j, k], $MachinePrecision] * -27.0), $MachinePrecision] * N[Min[j, k], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+61], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(N[Min[j, k], $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999973e65

   1. Initial program 84.5%

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

   2. 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 23.9

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

   4. Applied rewrites 23.9%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   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 23.9

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

   6. Applied rewrites 23.9%

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

   if -4.99999999999999973e65 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.9999999999999998e61

   1. Initial program 84.5%

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

   2. 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 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in t around 0

      \[\leadsto b \cdot c - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]
   6. 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 44.5

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

   7. Applied rewrites 44.5%

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

   8. Taylor expanded in t around inf

      \[\leadsto b \cdot c - 4 \cdot \color{blue}{\left(a \cdot t\right)} \]
   9. 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 41.8

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

   10. Applied rewrites 41.8%

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

   if 3.9999999999999998e61 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.5%

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

   2. 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 23.9

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

   4. Applied rewrites 23.9%

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

Alternative 19: 35.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(j, k\right) \cdot 27\right) \cdot \mathsf{max}\left(j, k\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+65}:\\ \;\;\;\;\left(\mathsf{max}\left(j, k\right) \cdot -27\right) \cdot \mathsf{min}\left(j, k\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+60}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(\mathsf{min}\left(j, k\right) \cdot \mathsf{max}\left(j, k\right)\right)\\ \end{array} \]

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 -5e+65)
     (* (* (fmax j k) -27.0) (fmin j k))
     (if (<= t_1 4e+60)
       (* -4.0 (* a t))
       (* -27.0 (* (fmin j k) (fmax 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 <= -5e+65) {
		tmp = (fmax(j, k) * -27.0) * fmin(j, k);
	} else if (t_1 <= 4e+60) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = -27.0 * (fmin(j, k) * fmax(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 <= (-5d+65)) then
        tmp = (fmax(j, k) * (-27.0d0)) * fmin(j, k)
    else if (t_1 <= 4d+60) then
        tmp = (-4.0d0) * (a * t)
    else
        tmp = (-27.0d0) * (fmin(j, k) * fmax(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 <= -5e+65) {
		tmp = (fmax(j, k) * -27.0) * fmin(j, k);
	} else if (t_1 <= 4e+60) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = -27.0 * (fmin(j, k) * fmax(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 <= -5e+65:
		tmp = (fmax(j, k) * -27.0) * fmin(j, k)
	elif t_1 <= 4e+60:
		tmp = -4.0 * (a * t)
	else:
		tmp = -27.0 * (fmin(j, k) * fmax(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 <= -5e+65)
		tmp = Float64(Float64(fmax(j, k) * -27.0) * fmin(j, k));
	elseif (t_1 <= 4e+60)
		tmp = Float64(-4.0 * Float64(a * t));
	else
		tmp = Float64(-27.0 * Float64(fmin(j, k) * fmax(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 <= -5e+65)
		tmp = (max(j, k) * -27.0) * min(j, k);
	elseif (t_1 <= 4e+60)
		tmp = -4.0 * (a * t);
	else
		tmp = -27.0 * (min(j, k) * max(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, -5e+65], N[(N[(N[Max[j, k], $MachinePrecision] * -27.0), $MachinePrecision] * N[Min[j, k], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+60], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(N[Min[j, k], $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999973e65

   1. Initial program 84.5%

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

   2. 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 23.9

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

   4. Applied rewrites 23.9%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   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 23.9

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

   6. Applied rewrites 23.9%

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

   if -4.99999999999999973e65 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.9999999999999998e60

   1. Initial program 84.5%

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

   2. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 42.7

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

   4. Applied rewrites 42.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]
   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 3.9999999999999998e60 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.5%

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

   2. 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 23.9

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

   4. Applied rewrites 23.9%

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

Alternative 20: 35.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+60}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

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 -5e+65) t_1 (if (<= t_2 4e+60) (* -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 <= -5e+65) {
		tmp = t_1;
	} else if (t_2 <= 4e+60) {
		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 <= (-5d+65)) then
        tmp = t_1
    else if (t_2 <= 4d+60) 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 <= -5e+65) {
		tmp = t_1;
	} else if (t_2 <= 4e+60) {
		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 <= -5e+65:
		tmp = t_1
	elif t_2 <= 4e+60:
		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 <= -5e+65)
		tmp = t_1;
	elseif (t_2 <= 4e+60)
		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 <= -5e+65)
		tmp = t_1;
	elseif (t_2 <= 4e+60)
		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, -5e+65], t$95$1, If[LessEqual[t$95$2, 4e+60], 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) < -4.99999999999999973e65 or 3.9999999999999998e60 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.5%

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

   2. 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 23.9

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

   4. Applied rewrites 23.9%

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

   if -4.99999999999999973e65 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.9999999999999998e60

   1. Initial program 84.5%

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

   2. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 42.7

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

   4. Applied rewrites 42.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]
   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 21: 21.2% accurate, 6.4× 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 84.5%

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

2. Taylor expanded in t around -inf

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. lower-*.f64 N/A

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

   6. lower-*.f64 N/A

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

   7. lower-*.f64 42.7

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

4. Applied rewrites 42.7%

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

5. Taylor expanded in x around 0

   \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]
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 2025172 
(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)))