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

Percentage Accurate: 94.4% → 98.7%

Time: 5.3s

Alternatives: 13

Speedup: 0.4×

• 71.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

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)
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
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.4% accurate, 1.0× speedup

Math

\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

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)
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
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(y, z\right), t\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(y, z\right), t\right)\\ t_3 := \mathsf{max}\left(\mathsf{max}\left(y, z\right), t\_2\right)\\ t_4 := \mathsf{min}\left(\mathsf{max}\left(y, z\right), t\_2\right)\\ \mathbf{if}\;t\_4 \leq 2000000000:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t\_3 \cdot t\_4\right), t\_1, \mathsf{fma}\left(b \cdot a, 27, x + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(t\_1 \cdot 9\right) \cdot t\_4\right) \cdot t\_3\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (fmin (fmin y z) t))
       (t_2 (fmax (fmin y z) t))
       (t_3 (fmax (fmax y z) t_2))
       (t_4 (fmin (fmax y z) t_2)))
  (if (<= t_4 2000000000.0)
    (fma (* -9.0 (* t_3 t_4)) t_1 (fma (* b a) 27.0 (+ x x)))
    (+ (- (* x 2.0) (* (* (* t_1 9.0) t_4) t_3)) (* (* a 27.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fmin(fmin(y, z), t);
	double t_2 = fmax(fmin(y, z), t);
	double t_3 = fmax(fmax(y, z), t_2);
	double t_4 = fmin(fmax(y, z), t_2);
	double tmp;
	if (t_4 <= 2000000000.0) {
		tmp = fma((-9.0 * (t_3 * t_4)), t_1, fma((b * a), 27.0, (x + x)));
	} else {
		tmp = ((x * 2.0) - (((t_1 * 9.0) * t_4) * t_3)) + ((a * 27.0) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fmin(fmin(y, z), t)
	t_2 = fmax(fmin(y, z), t)
	t_3 = fmax(fmax(y, z), t_2)
	t_4 = fmin(fmax(y, z), t_2)
	tmp = 0.0
	if (t_4 <= 2000000000.0)
		tmp = fma(Float64(-9.0 * Float64(t_3 * t_4)), t_1, fma(Float64(b * a), 27.0, Float64(x + x)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(t_1 * 9.0) * t_4) * t_3)) + Float64(Float64(a * 27.0) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Min[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$3 = N[Max[N[Max[y, z], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Max[y, z], $MachinePrecision], t$95$2], $MachinePrecision]}, If[LessEqual[t$95$4, 2000000000.0], N[(N[(-9.0 * N[(t$95$3 * t$95$4), $MachinePrecision]), $MachinePrecision] * t$95$1 + N[(N[(b * a), $MachinePrecision] * 27.0 + N[(x + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(t$95$1 * 9.0), $MachinePrecision] * t$95$4), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if z < 2e9

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{\left(a \cdot 27\right) \cdot b} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      4. associate-*l* N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

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

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right)} \]

      6. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \color{blue}{\left(\left(\mathsf{neg}\left(a\right)\right) \cdot 27\right) \cdot b} \]

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

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \color{blue}{\left(\mathsf{neg}\left(a \cdot 27\right)\right)} \cdot b \]

      12. lift-*.f64 N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \left(\mathsf{neg}\left(\color{blue}{a \cdot 27}\right)\right) \cdot b \]

      13. associate--l+ N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} \]

   3. Applied rewrites 95.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9 \cdot \left(t \cdot z\right), y, \mathsf{fma}\left(b \cdot a, 27, x + x\right)\right)} \]

   if 2e9 < z

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 98.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(y, z\right), t\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(y, z\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(y, z\right), t\_1\right)\\ t_4 := \mathsf{fma}\left(b \cdot a, 27, x + x\right)\\ t_5 := \mathsf{min}\left(\mathsf{min}\left(y, z\right), t\right)\\ \mathbf{if}\;t\_5 \leq -5 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t\_2 \cdot t\_3\right), t\_5, t\_4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t\_2 \cdot t\_5\right), t\_3, t\_4\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (fmax (fmin y z) t))
       (t_2 (fmax (fmax y z) t_1))
       (t_3 (fmin (fmax y z) t_1))
       (t_4 (fma (* b a) 27.0 (+ x x)))
       (t_5 (fmin (fmin y z) t)))
  (if (<= t_5 -5e+23)
    (fma (* -9.0 (* t_2 t_3)) t_5 t_4)
    (fma (* -9.0 (* t_2 t_5)) t_3 t_4))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fmax(fmin(y, z), t);
	double t_2 = fmax(fmax(y, z), t_1);
	double t_3 = fmin(fmax(y, z), t_1);
	double t_4 = fma((b * a), 27.0, (x + x));
	double t_5 = fmin(fmin(y, z), t);
	double tmp;
	if (t_5 <= -5e+23) {
		tmp = fma((-9.0 * (t_2 * t_3)), t_5, t_4);
	} else {
		tmp = fma((-9.0 * (t_2 * t_5)), t_3, t_4);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fmax(fmin(y, z), t)
	t_2 = fmax(fmax(y, z), t_1)
	t_3 = fmin(fmax(y, z), t_1)
	t_4 = fma(Float64(b * a), 27.0, Float64(x + x))
	t_5 = fmin(fmin(y, z), t)
	tmp = 0.0
	if (t_5 <= -5e+23)
		tmp = fma(Float64(-9.0 * Float64(t_2 * t_3)), t_5, t_4);
	else
		tmp = fma(Float64(-9.0 * Float64(t_2 * t_5)), t_3, t_4);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Max[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[y, z], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[y, z], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * a), $MachinePrecision] * 27.0 + N[(x + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[Min[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, If[LessEqual[t$95$5, -5e+23], N[(N[(-9.0 * N[(t$95$2 * t$95$3), $MachinePrecision]), $MachinePrecision] * t$95$5 + t$95$4), $MachinePrecision], N[(N[(-9.0 * N[(t$95$2 * t$95$5), $MachinePrecision]), $MachinePrecision] * t$95$3 + t$95$4), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9999999999999999e23

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{\left(a \cdot 27\right) \cdot b} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      4. associate-*l* N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

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

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right)} \]

      6. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \color{blue}{\left(\left(\mathsf{neg}\left(a\right)\right) \cdot 27\right) \cdot b} \]

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

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \color{blue}{\left(\mathsf{neg}\left(a \cdot 27\right)\right)} \cdot b \]

      12. lift-*.f64 N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \left(\mathsf{neg}\left(\color{blue}{a \cdot 27}\right)\right) \cdot b \]

      13. associate--l+ N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} \]

   3. Applied rewrites 95.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9 \cdot \left(t \cdot z\right), y, \mathsf{fma}\left(b \cdot a, 27, x + x\right)\right)} \]

   if -4.9999999999999999e23 < y

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{\left(a \cdot 27\right) \cdot b} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      4. associate-*l* N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

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

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right)} \]

      6. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \color{blue}{\left(\left(\mathsf{neg}\left(a\right)\right) \cdot 27\right) \cdot b} \]

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

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \color{blue}{\left(\mathsf{neg}\left(a \cdot 27\right)\right)} \cdot b \]

      12. lift-*.f64 N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \left(\mathsf{neg}\left(\color{blue}{a \cdot 27}\right)\right) \cdot b \]

      13. associate--l+ N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} \]

      14. *-commutative N/A

          \[\leadsto \color{blue}{t \cdot \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right)} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

      15. lift-*.f64 N/A

          \[\leadsto t \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot z}\right)\right) + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

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

          \[\leadsto t \cdot \color{blue}{\left(\left(y \cdot 9\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

      17. associate-*r* N/A

          \[\leadsto \color{blue}{\left(t \cdot \left(y \cdot 9\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t \cdot \left(y \cdot 9\right)\right) \cdot z\right)\right)} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(t \cdot \left(y \cdot 9\right)\right)\right) \cdot z} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

   3. Applied rewrites 94.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9 \cdot \left(t \cdot y\right), z, \mathsf{fma}\left(b \cdot a, 27, x + x\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 94.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\mathsf{min}\left(y, t\right) \leq -1.75 \cdot 10^{+204}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, \left(\left(\mathsf{max}\left(y, t\right) \cdot z\right) \cdot -9\right) \cdot \mathsf{min}\left(y, t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(\mathsf{max}\left(y, t\right) \cdot \mathsf{min}\left(y, t\right)\right), z, \mathsf{fma}\left(b \cdot a, 27, x + x\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<= (fmin y t) -1.75e+204)
  (fma (* 27.0 b) a (* (* (* (fmax y t) z) -9.0) (fmin y t)))
  (fma
   (* -9.0 (* (fmax y t) (fmin y t)))
   z
   (fma (* b a) 27.0 (+ x x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (fmin(y, t) <= -1.75e+204) {
		tmp = fma((27.0 * b), a, (((fmax(y, t) * z) * -9.0) * fmin(y, t)));
	} else {
		tmp = fma((-9.0 * (fmax(y, t) * fmin(y, t))), z, fma((b * a), 27.0, (x + x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (fmin(y, t) <= -1.75e+204)
		tmp = fma(Float64(27.0 * b), a, Float64(Float64(Float64(fmax(y, t) * z) * -9.0) * fmin(y, t)));
	else
		tmp = fma(Float64(-9.0 * Float64(fmax(y, t) * fmin(y, t))), z, fma(Float64(b * a), 27.0, Float64(x + x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[Min[y, t], $MachinePrecision], -1.75e+204], N[(N[(27.0 * b), $MachinePrecision] * a + N[(N[(N[(N[Max[y, t], $MachinePrecision] * z), $MachinePrecision] * -9.0), $MachinePrecision] * N[Min[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-9.0 * N[(N[Max[y, t], $MachinePrecision] * N[Min[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + N[(N[(b * a), $MachinePrecision] * 27.0 + N[(x + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7499999999999999e204

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. lower-*.f64 N/A

         \[\leadsto -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      3. lower-*.f64 66.3%

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot \color{blue}{z}\right)\right) + \left(a \cdot 27\right) \cdot b \]

   4. Applied rewrites 66.3%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b} + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\left(27 \cdot b\right) \cdot a} + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      8. lower-*.f64 67.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot b}, a, -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot t\right) \cdot \color{blue}{\left(y \cdot z\right)}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot t\right) \cdot \left(y \cdot \color{blue}{z}\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot t\right) \cdot \left(z \cdot \color{blue}{y}\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(-9 \cdot t\right) \cdot z\right) \cdot \color{blue}{y}\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      17. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      18. lower-*.f64 67.3%

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot \color{blue}{y}\right) \]

      19. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      20. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\right) \]

      21. lower-*.f64 67.3%

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\right) \]

   6. Applied rewrites 67.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\right)} \]

   if -1.7499999999999999e204 < y

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{\left(a \cdot 27\right) \cdot b} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      4. associate-*l* N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

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

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right)} \]

      6. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \color{blue}{\left(\left(\mathsf{neg}\left(a\right)\right) \cdot 27\right) \cdot b} \]

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

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \color{blue}{\left(\mathsf{neg}\left(a \cdot 27\right)\right)} \cdot b \]

      12. lift-*.f64 N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \left(\mathsf{neg}\left(\color{blue}{a \cdot 27}\right)\right) \cdot b \]

      13. associate--l+ N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} \]

      14. *-commutative N/A

          \[\leadsto \color{blue}{t \cdot \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right)} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

      15. lift-*.f64 N/A

          \[\leadsto t \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot z}\right)\right) + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

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

          \[\leadsto t \cdot \color{blue}{\left(\left(y \cdot 9\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

      17. associate-*r* N/A

          \[\leadsto \color{blue}{\left(t \cdot \left(y \cdot 9\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t \cdot \left(y \cdot 9\right)\right) \cdot z\right)\right)} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(t \cdot \left(y \cdot 9\right)\right)\right) \cdot z} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

   3. Applied rewrites 94.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9 \cdot \left(t \cdot y\right), z, \mathsf{fma}\left(b \cdot a, 27, x + x\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 87.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(y, z\right), t\right)\\ t_2 := \mathsf{min}\left(\mathsf{max}\left(y, z\right), t\_1\right)\\ t_3 := \mathsf{max}\left(\mathsf{max}\left(y, z\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(y, z\right), t\right)\\ t_5 := \left(\left(t\_4 \cdot 9\right) \cdot t\_2\right) \cdot t\_3\\ \mathbf{if}\;t\_5 \leq -5 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, \left(\left(t\_3 \cdot t\_2\right) \cdot -9\right) \cdot t\_4\right)\\ \mathbf{elif}\;t\_5 \leq 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, \left(\left(-9 \cdot t\_4\right) \cdot t\_2\right) \cdot t\_3\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (fmax (fmin y z) t))
       (t_2 (fmin (fmax y z) t_1))
       (t_3 (fmax (fmax y z) t_1))
       (t_4 (fmin (fmin y z) t))
       (t_5 (* (* (* t_4 9.0) t_2) t_3)))
  (if (<= t_5 -5e+52)
    (fma (* 27.0 b) a (* (* (* t_3 t_2) -9.0) t_4))
    (if (<= t_5 1e-8)
      (fma (* a 27.0) b (+ x x))
      (fma (* b 27.0) a (* (* (* -9.0 t_4) t_2) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fmax(fmin(y, z), t);
	double t_2 = fmin(fmax(y, z), t_1);
	double t_3 = fmax(fmax(y, z), t_1);
	double t_4 = fmin(fmin(y, z), t);
	double t_5 = ((t_4 * 9.0) * t_2) * t_3;
	double tmp;
	if (t_5 <= -5e+52) {
		tmp = fma((27.0 * b), a, (((t_3 * t_2) * -9.0) * t_4));
	} else if (t_5 <= 1e-8) {
		tmp = fma((a * 27.0), b, (x + x));
	} else {
		tmp = fma((b * 27.0), a, (((-9.0 * t_4) * t_2) * t_3));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fmax(fmin(y, z), t)
	t_2 = fmin(fmax(y, z), t_1)
	t_3 = fmax(fmax(y, z), t_1)
	t_4 = fmin(fmin(y, z), t)
	t_5 = Float64(Float64(Float64(t_4 * 9.0) * t_2) * t_3)
	tmp = 0.0
	if (t_5 <= -5e+52)
		tmp = fma(Float64(27.0 * b), a, Float64(Float64(Float64(t_3 * t_2) * -9.0) * t_4));
	elseif (t_5 <= 1e-8)
		tmp = fma(Float64(a * 27.0), b, Float64(x + x));
	else
		tmp = fma(Float64(b * 27.0), a, Float64(Float64(Float64(-9.0 * t_4) * t_2) * t_3));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Max[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$2 = N[Min[N[Max[y, z], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Max[N[Max[y, z], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$4 * 9.0), $MachinePrecision] * t$95$2), $MachinePrecision] * t$95$3), $MachinePrecision]}, If[LessEqual[t$95$5, -5e+52], N[(N[(27.0 * b), $MachinePrecision] * a + N[(N[(N[(t$95$3 * t$95$2), $MachinePrecision] * -9.0), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 1e-8], N[(N[(a * 27.0), $MachinePrecision] * b + N[(x + x), $MachinePrecision]), $MachinePrecision], N[(N[(b * 27.0), $MachinePrecision] * a + N[(N[(N[(-9.0 * t$95$4), $MachinePrecision] * t$95$2), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5e52

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. lower-*.f64 N/A

         \[\leadsto -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      3. lower-*.f64 66.3%

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot \color{blue}{z}\right)\right) + \left(a \cdot 27\right) \cdot b \]

   4. Applied rewrites 66.3%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b} + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\left(27 \cdot b\right) \cdot a} + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      8. lower-*.f64 67.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot b}, a, -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot t\right) \cdot \color{blue}{\left(y \cdot z\right)}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot t\right) \cdot \left(y \cdot \color{blue}{z}\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot t\right) \cdot \left(z \cdot \color{blue}{y}\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(-9 \cdot t\right) \cdot z\right) \cdot \color{blue}{y}\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      17. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      18. lower-*.f64 67.3%

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot \color{blue}{y}\right) \]

      19. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      20. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\right) \]

      21. lower-*.f64 67.3%

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\right) \]

   6. Applied rewrites 67.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\right)} \]

   if -5e52 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 1e-8

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{x}, 27 \cdot \left(a \cdot b\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 64.2%

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   4. Applied rewrites 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. +-commutative N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2 \cdot x} \]

      3. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2} \cdot x \]

      4. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + 2 \cdot x \]

      5. *-commutative N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      6. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{2} \cdot x \]

      8. count-2-rev N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + x\right) \]

      11. associate-*l* N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

      12. lift-*.f64 N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

      13. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

      17. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

      22. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      23. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\color{blue}{x}\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      24. associate-*l* N/A

          \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      25. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \cdot \color{blue}{2} \]

      28. remove-double-neg N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + x \cdot 2 \]

      29. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + 2 \cdot \color{blue}{x} \]

   6. Applied rewrites 64.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, x + x\right)} \]
   7. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(x + x\right)} \]

      2. lift-+.f64 N/A

         \[\leadsto \left(27 \cdot b\right) \cdot a + \left(x + \color{blue}{x}\right) \]

      3. associate-+r+ N/A

         \[\leadsto \left(\left(27 \cdot b\right) \cdot a + x\right) + \color{blue}{x} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(27 \cdot b\right) \cdot a + x\right) + x \]

      5. *-commutative N/A

         \[\leadsto \left(\left(b \cdot 27\right) \cdot a + x\right) + x \]

      6. associate-*l* N/A

         \[\leadsto \left(b \cdot \left(27 \cdot a\right) + x\right) + x \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot \left(a \cdot 27\right) + x\right) + x \]

      8. associate-*l* N/A

         \[\leadsto \left(\left(b \cdot a\right) \cdot 27 + x\right) + x \]

      9. associate-+r+ N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{\left(x + x\right)} \]

      10. associate-*l* N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

      11. lift-*.f64 N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

      12. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      14. count-2 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

      15. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

      20. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

      22. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(2 \cdot \left(\mathsf{neg}\left(x\right)\right)\right)\right) \]

      23. count-2-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right) \]

      24. sub-flip-reverse N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) - x\right)\right)\right) \]

      25. sub-negate-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x - \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      26. add-flip N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      27. lift-+.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      28. lower-fma.f64 64.2%

          \[\leadsto \mathsf{fma}\left(a \cdot 27, \color{blue}{b}, x + x\right) \]

   8. Applied rewrites 64.2%

      \[\leadsto \mathsf{fma}\left(a \cdot 27, \color{blue}{b}, x + x\right) \]

   if 1e-8 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. lower-*.f64 N/A

         \[\leadsto -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      3. lower-*.f64 66.3%

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot \color{blue}{z}\right)\right) + \left(a \cdot 27\right) \cdot b \]

   4. Applied rewrites 66.3%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b} + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\left(27 \cdot b\right) \cdot a} + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      8. lower-*.f64 67.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot b}, a, -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot t\right) \cdot \color{blue}{\left(y \cdot z\right)}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot t\right) \cdot \left(y \cdot \color{blue}{z}\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot t\right) \cdot \left(z \cdot \color{blue}{y}\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(-9 \cdot t\right) \cdot z\right) \cdot \color{blue}{y}\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      17. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      18. lower-*.f64 67.3%

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot \color{blue}{y}\right) \]

      19. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      20. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\right) \]

      21. lower-*.f64 67.3%

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\right) \]

   6. Applied rewrites 67.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot -9\right) \cdot \color{blue}{y}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, y \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot -9\right)}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, y \cdot \left(\left(t \cdot z\right) \cdot \color{blue}{-9}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(y \cdot \left(t \cdot z\right)\right) \cdot \color{blue}{-9}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot y\right) \cdot -9\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot y\right) \cdot -9\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(t \cdot \left(z \cdot y\right)\right) \cdot -9\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(t \cdot \left(y \cdot z\right)\right) \cdot -9\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(t \cdot \left(y \cdot z\right)\right) \cdot -9\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(t \cdot \left(y \cdot z\right)\right) \cdot -9\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot t\right) \cdot \color{blue}{\left(y \cdot z\right)}\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot t\right) \cdot \left(y \cdot \color{blue}{z}\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(-9 \cdot t\right) \cdot y\right) \cdot \color{blue}{z}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(-9 \cdot t\right) \cdot y\right) \cdot \color{blue}{z}\right) \]

      17. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot y\right)\right) \cdot z\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(y \cdot t\right)\right) \cdot z\right) \]

      19. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(-9 \cdot y\right) \cdot t\right) \cdot z\right) \]

      20. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(y \cdot -9\right) \cdot t\right) \cdot z\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(y \cdot \left(\mathsf{neg}\left(9\right)\right)\right) \cdot t\right) \cdot z\right) \]

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

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t\right) \cdot z\right) \]

      23. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t\right) \cdot z\right) \]

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

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(y \cdot \left(\mathsf{neg}\left(9\right)\right)\right) \cdot t\right) \cdot z\right) \]

      25. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(y \cdot -9\right) \cdot t\right) \cdot z\right) \]

      26. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(-9 \cdot y\right) \cdot t\right) \cdot z\right) \]

      27. lower-*.f64 67.0%

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(-9 \cdot y\right) \cdot t\right) \cdot z\right) \]

   8. Applied rewrites 67.0%

      \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(-9 \cdot y\right) \cdot t\right) \cdot \color{blue}{z}\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot b}, a, \left(\left(-9 \cdot y\right) \cdot t\right) \cdot z\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot 27}, a, \left(\left(-9 \cdot y\right) \cdot t\right) \cdot z\right) \]

      3. lower-*.f64 67.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot 27}, a, \left(\left(-9 \cdot y\right) \cdot t\right) \cdot z\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \left(\left(-9 \cdot y\right) \cdot t\right) \cdot \color{blue}{z}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \left(\left(-9 \cdot y\right) \cdot t\right) \cdot z\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \left(-9 \cdot y\right) \cdot \color{blue}{\left(t \cdot z\right)}\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \left(-9 \cdot y\right) \cdot \left(\color{blue}{t} \cdot z\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(b \cdot 27, a, -9 \cdot \color{blue}{\left(y \cdot \left(t \cdot z\right)\right)}\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \left(\mathsf{neg}\left(9\right)\right) \cdot \left(\color{blue}{y} \cdot \left(t \cdot z\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot \color{blue}{t}\right)\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \mathsf{neg}\left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      12. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \mathsf{neg}\left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \mathsf{neg}\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot \color{blue}{t}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot \color{blue}{t}\right) \]

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

          \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \left(\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot z\right) \cdot t\right) \]

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

          \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \left(\left(y \cdot \left(\mathsf{neg}\left(9\right)\right)\right) \cdot z\right) \cdot t\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \left(\left(y \cdot -9\right) \cdot z\right) \cdot t\right) \]

      20. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \left(\left(-9 \cdot y\right) \cdot z\right) \cdot t\right) \]

      21. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \left(\left(-9 \cdot y\right) \cdot z\right) \cdot t\right) \]

      22. lower-*.f64 67.0%

          \[\leadsto \mathsf{fma}\left(b \cdot 27, a, \left(\left(-9 \cdot y\right) \cdot z\right) \cdot t\right) \]

   10. Applied rewrites 67.0%

       \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot 27, a, \left(\left(-9 \cdot y\right) \cdot z\right) \cdot t\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 87.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(y, z\right), t\right)\\ t_2 := \mathsf{min}\left(\mathsf{max}\left(y, z\right), t\_1\right)\\ t_3 := \mathsf{max}\left(\mathsf{max}\left(y, z\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(y, z\right), t\right)\\ t_5 := \left(\left(t\_4 \cdot 9\right) \cdot t\_2\right) \cdot t\_3\\ \mathbf{if}\;t\_5 \leq -5 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, \left(\left(t\_3 \cdot t\_2\right) \cdot -9\right) \cdot t\_4\right)\\ \mathbf{elif}\;t\_5 \leq 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t\_2 \cdot t\_4\right), t\_3, 27 \cdot \left(a \cdot b\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (fmax (fmin y z) t))
       (t_2 (fmin (fmax y z) t_1))
       (t_3 (fmax (fmax y z) t_1))
       (t_4 (fmin (fmin y z) t))
       (t_5 (* (* (* t_4 9.0) t_2) t_3)))
  (if (<= t_5 -5e+52)
    (fma (* 27.0 b) a (* (* (* t_3 t_2) -9.0) t_4))
    (if (<= t_5 1e-8)
      (fma (* a 27.0) b (+ x x))
      (fma (* -9.0 (* t_2 t_4)) t_3 (* 27.0 (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fmax(fmin(y, z), t);
	double t_2 = fmin(fmax(y, z), t_1);
	double t_3 = fmax(fmax(y, z), t_1);
	double t_4 = fmin(fmin(y, z), t);
	double t_5 = ((t_4 * 9.0) * t_2) * t_3;
	double tmp;
	if (t_5 <= -5e+52) {
		tmp = fma((27.0 * b), a, (((t_3 * t_2) * -9.0) * t_4));
	} else if (t_5 <= 1e-8) {
		tmp = fma((a * 27.0), b, (x + x));
	} else {
		tmp = fma((-9.0 * (t_2 * t_4)), t_3, (27.0 * (a * b)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fmax(fmin(y, z), t)
	t_2 = fmin(fmax(y, z), t_1)
	t_3 = fmax(fmax(y, z), t_1)
	t_4 = fmin(fmin(y, z), t)
	t_5 = Float64(Float64(Float64(t_4 * 9.0) * t_2) * t_3)
	tmp = 0.0
	if (t_5 <= -5e+52)
		tmp = fma(Float64(27.0 * b), a, Float64(Float64(Float64(t_3 * t_2) * -9.0) * t_4));
	elseif (t_5 <= 1e-8)
		tmp = fma(Float64(a * 27.0), b, Float64(x + x));
	else
		tmp = fma(Float64(-9.0 * Float64(t_2 * t_4)), t_3, Float64(27.0 * Float64(a * b)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Max[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$2 = N[Min[N[Max[y, z], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Max[N[Max[y, z], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$4 * 9.0), $MachinePrecision] * t$95$2), $MachinePrecision] * t$95$3), $MachinePrecision]}, If[LessEqual[t$95$5, -5e+52], N[(N[(27.0 * b), $MachinePrecision] * a + N[(N[(N[(t$95$3 * t$95$2), $MachinePrecision] * -9.0), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 1e-8], N[(N[(a * 27.0), $MachinePrecision] * b + N[(x + x), $MachinePrecision]), $MachinePrecision], N[(N[(-9.0 * N[(t$95$2 * t$95$4), $MachinePrecision]), $MachinePrecision] * t$95$3 + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5e52

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. lower-*.f64 N/A

         \[\leadsto -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      3. lower-*.f64 66.3%

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot \color{blue}{z}\right)\right) + \left(a \cdot 27\right) \cdot b \]

   4. Applied rewrites 66.3%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b} + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\left(27 \cdot b\right) \cdot a} + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      8. lower-*.f64 67.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot b}, a, -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot t\right) \cdot \color{blue}{\left(y \cdot z\right)}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot t\right) \cdot \left(y \cdot \color{blue}{z}\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot t\right) \cdot \left(z \cdot \color{blue}{y}\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(-9 \cdot t\right) \cdot z\right) \cdot \color{blue}{y}\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      17. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      18. lower-*.f64 67.3%

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot \color{blue}{y}\right) \]

      19. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      20. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\right) \]

      21. lower-*.f64 67.3%

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\right) \]

   6. Applied rewrites 67.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\right)} \]

   if -5e52 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 1e-8

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{x}, 27 \cdot \left(a \cdot b\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 64.2%

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   4. Applied rewrites 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. +-commutative N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2 \cdot x} \]

      3. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2} \cdot x \]

      4. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + 2 \cdot x \]

      5. *-commutative N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      6. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{2} \cdot x \]

      8. count-2-rev N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + x\right) \]

      11. associate-*l* N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

      12. lift-*.f64 N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

      13. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

      17. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

      22. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      23. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\color{blue}{x}\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      24. associate-*l* N/A

          \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      25. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \cdot \color{blue}{2} \]

      28. remove-double-neg N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + x \cdot 2 \]

      29. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + 2 \cdot \color{blue}{x} \]

   6. Applied rewrites 64.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, x + x\right)} \]
   7. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(x + x\right)} \]

      2. lift-+.f64 N/A

         \[\leadsto \left(27 \cdot b\right) \cdot a + \left(x + \color{blue}{x}\right) \]

      3. associate-+r+ N/A

         \[\leadsto \left(\left(27 \cdot b\right) \cdot a + x\right) + \color{blue}{x} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(27 \cdot b\right) \cdot a + x\right) + x \]

      5. *-commutative N/A

         \[\leadsto \left(\left(b \cdot 27\right) \cdot a + x\right) + x \]

      6. associate-*l* N/A

         \[\leadsto \left(b \cdot \left(27 \cdot a\right) + x\right) + x \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot \left(a \cdot 27\right) + x\right) + x \]

      8. associate-*l* N/A

         \[\leadsto \left(\left(b \cdot a\right) \cdot 27 + x\right) + x \]

      9. associate-+r+ N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{\left(x + x\right)} \]

      10. associate-*l* N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

      11. lift-*.f64 N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

      12. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      14. count-2 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

      15. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

      20. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

      22. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(2 \cdot \left(\mathsf{neg}\left(x\right)\right)\right)\right) \]

      23. count-2-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right) \]

      24. sub-flip-reverse N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) - x\right)\right)\right) \]

      25. sub-negate-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x - \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      26. add-flip N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      27. lift-+.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      28. lower-fma.f64 64.2%

          \[\leadsto \mathsf{fma}\left(a \cdot 27, \color{blue}{b}, x + x\right) \]

   8. Applied rewrites 64.2%

      \[\leadsto \mathsf{fma}\left(a \cdot 27, \color{blue}{b}, x + x\right) \]

   if 1e-8 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right) \]

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

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t\right)} \]

      6. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t} \]

      7. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot z}\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(9 \cdot y\right)} \cdot z\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      12. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{9 \cdot \left(y \cdot z\right)}\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot z\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(\mathsf{neg}\left(9\right)\right) \cdot \color{blue}{\left(z \cdot y\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(z \cdot y\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-9} \cdot \left(z \cdot y\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-9 \cdot \color{blue}{\left(z \cdot y\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      18. add-flip N/A

          \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \color{blue}{\left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right)}\right) \]

      19. sub-flip N/A

          \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \color{blue}{\left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x \cdot 2\right)\right)\right)\right)}\right) \]

   3. Applied rewrites 95.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \mathsf{fma}\left(b \cdot a, 27, x + x\right)\right)} \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \color{blue}{27 \cdot \left(a \cdot b\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, 27 \cdot \color{blue}{\left(a \cdot b\right)}\right) \]

      2. lower-*.f64 66.8%

         \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, 27 \cdot \left(a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 66.8%

      \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \color{blue}{27 \cdot \left(a \cdot b\right)}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 86.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{max}\left(y, z\right), t\right)\\ t_2 := \mathsf{min}\left(\mathsf{max}\left(y, z\right), t\right)\\ t_3 := \left(\left(\mathsf{min}\left(y, z\right) \cdot 9\right) \cdot t\_2\right) \cdot t\_1\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, \left(\left(-9 \cdot t\_1\right) \cdot t\_2\right) \cdot \mathsf{min}\left(y, z\right)\right)\\ \mathbf{elif}\;t\_3 \leq 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t\_2 \cdot \mathsf{min}\left(y, z\right)\right), t\_1, 27 \cdot \left(a \cdot b\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (fmax (fmax y z) t))
       (t_2 (fmin (fmax y z) t))
       (t_3 (* (* (* (fmin y z) 9.0) t_2) t_1)))
  (if (<= t_3 -5e+52)
    (fma (* 27.0 b) a (* (* (* -9.0 t_1) t_2) (fmin y z)))
    (if (<= t_3 1e-8)
      (fma (* a 27.0) b (+ x x))
      (fma (* -9.0 (* t_2 (fmin y z))) t_1 (* 27.0 (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fmax(fmax(y, z), t);
	double t_2 = fmin(fmax(y, z), t);
	double t_3 = ((fmin(y, z) * 9.0) * t_2) * t_1;
	double tmp;
	if (t_3 <= -5e+52) {
		tmp = fma((27.0 * b), a, (((-9.0 * t_1) * t_2) * fmin(y, z)));
	} else if (t_3 <= 1e-8) {
		tmp = fma((a * 27.0), b, (x + x));
	} else {
		tmp = fma((-9.0 * (t_2 * fmin(y, z))), t_1, (27.0 * (a * b)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fmax(fmax(y, z), t)
	t_2 = fmin(fmax(y, z), t)
	t_3 = Float64(Float64(Float64(fmin(y, z) * 9.0) * t_2) * t_1)
	tmp = 0.0
	if (t_3 <= -5e+52)
		tmp = fma(Float64(27.0 * b), a, Float64(Float64(Float64(-9.0 * t_1) * t_2) * fmin(y, z)));
	elseif (t_3 <= 1e-8)
		tmp = fma(Float64(a * 27.0), b, Float64(x + x));
	else
		tmp = fma(Float64(-9.0 * Float64(t_2 * fmin(y, z))), t_1, Float64(27.0 * Float64(a * b)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Max[N[Max[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$2 = N[Min[N[Max[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[Min[y, z], $MachinePrecision] * 9.0), $MachinePrecision] * t$95$2), $MachinePrecision] * t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+52], N[(N[(27.0 * b), $MachinePrecision] * a + N[(N[(N[(-9.0 * t$95$1), $MachinePrecision] * t$95$2), $MachinePrecision] * N[Min[y, z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e-8], N[(N[(a * 27.0), $MachinePrecision] * b + N[(x + x), $MachinePrecision]), $MachinePrecision], N[(N[(-9.0 * N[(t$95$2 * N[Min[y, z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1 + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5e52

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. lower-*.f64 N/A

         \[\leadsto -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      3. lower-*.f64 66.3%

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot \color{blue}{z}\right)\right) + \left(a \cdot 27\right) \cdot b \]

   4. Applied rewrites 66.3%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b} + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\left(27 \cdot b\right) \cdot a} + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      8. lower-*.f64 67.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot b}, a, -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot t\right) \cdot \color{blue}{\left(y \cdot z\right)}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot t\right) \cdot \left(y \cdot \color{blue}{z}\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot t\right) \cdot \left(z \cdot \color{blue}{y}\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(-9 \cdot t\right) \cdot z\right) \cdot \color{blue}{y}\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      17. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      18. lower-*.f64 67.3%

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot \color{blue}{y}\right) \]

      19. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      20. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\right) \]

      21. lower-*.f64 67.3%

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\right) \]

   6. Applied rewrites 67.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\right) \]

      6. lower-*.f64 67.3%

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\right) \]

   8. Applied rewrites 67.3%

      \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\right) \]

   if -5e52 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 1e-8

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{x}, 27 \cdot \left(a \cdot b\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 64.2%

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   4. Applied rewrites 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. +-commutative N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2 \cdot x} \]

      3. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2} \cdot x \]

      4. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + 2 \cdot x \]

      5. *-commutative N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      6. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{2} \cdot x \]

      8. count-2-rev N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + x\right) \]

      11. associate-*l* N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

      12. lift-*.f64 N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

      13. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

      17. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

      22. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      23. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\color{blue}{x}\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      24. associate-*l* N/A

          \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      25. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \cdot \color{blue}{2} \]

      28. remove-double-neg N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + x \cdot 2 \]

      29. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + 2 \cdot \color{blue}{x} \]

   6. Applied rewrites 64.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, x + x\right)} \]
   7. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(x + x\right)} \]

      2. lift-+.f64 N/A

         \[\leadsto \left(27 \cdot b\right) \cdot a + \left(x + \color{blue}{x}\right) \]

      3. associate-+r+ N/A

         \[\leadsto \left(\left(27 \cdot b\right) \cdot a + x\right) + \color{blue}{x} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(27 \cdot b\right) \cdot a + x\right) + x \]

      5. *-commutative N/A

         \[\leadsto \left(\left(b \cdot 27\right) \cdot a + x\right) + x \]

      6. associate-*l* N/A

         \[\leadsto \left(b \cdot \left(27 \cdot a\right) + x\right) + x \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot \left(a \cdot 27\right) + x\right) + x \]

      8. associate-*l* N/A

         \[\leadsto \left(\left(b \cdot a\right) \cdot 27 + x\right) + x \]

      9. associate-+r+ N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{\left(x + x\right)} \]

      10. associate-*l* N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

      11. lift-*.f64 N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

      12. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      14. count-2 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

      15. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

      20. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

      22. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(2 \cdot \left(\mathsf{neg}\left(x\right)\right)\right)\right) \]

      23. count-2-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right) \]

      24. sub-flip-reverse N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) - x\right)\right)\right) \]

      25. sub-negate-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x - \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      26. add-flip N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      27. lift-+.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      28. lower-fma.f64 64.2%

          \[\leadsto \mathsf{fma}\left(a \cdot 27, \color{blue}{b}, x + x\right) \]

   8. Applied rewrites 64.2%

      \[\leadsto \mathsf{fma}\left(a \cdot 27, \color{blue}{b}, x + x\right) \]

   if 1e-8 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right) \]

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

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t\right)} \]

      6. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t} \]

      7. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot z}\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(9 \cdot y\right)} \cdot z\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      12. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{9 \cdot \left(y \cdot z\right)}\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot z\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(\mathsf{neg}\left(9\right)\right) \cdot \color{blue}{\left(z \cdot y\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(z \cdot y\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-9} \cdot \left(z \cdot y\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-9 \cdot \color{blue}{\left(z \cdot y\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      18. add-flip N/A

          \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \color{blue}{\left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right)}\right) \]

      19. sub-flip N/A

          \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \color{blue}{\left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x \cdot 2\right)\right)\right)\right)}\right) \]

   3. Applied rewrites 95.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \mathsf{fma}\left(b \cdot a, 27, x + x\right)\right)} \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \color{blue}{27 \cdot \left(a \cdot b\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, 27 \cdot \color{blue}{\left(a \cdot b\right)}\right) \]

      2. lower-*.f64 66.8%

         \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, 27 \cdot \left(a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 66.8%

      \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \color{blue}{27 \cdot \left(a \cdot b\right)}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 85.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(y, z\right), t\right)\\ t_2 := \mathsf{min}\left(\mathsf{max}\left(y, z\right), t\_1\right)\\ t_3 := \mathsf{max}\left(\mathsf{max}\left(y, z\right), t\_1\right)\\ t_4 := 27 \cdot \left(a \cdot b\right)\\ t_5 := \mathsf{min}\left(\mathsf{min}\left(y, z\right), t\right)\\ t_6 := \left(\left(t\_5 \cdot 9\right) \cdot t\_2\right) \cdot t\_3\\ \mathbf{if}\;t\_6 \leq -5 \cdot 10^{+181}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t\_3 \cdot t\_5\right), t\_2, t\_4\right)\\ \mathbf{elif}\;t\_6 \leq 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t\_2 \cdot t\_5\right), t\_3, t\_4\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (fmax (fmin y z) t))
       (t_2 (fmin (fmax y z) t_1))
       (t_3 (fmax (fmax y z) t_1))
       (t_4 (* 27.0 (* a b)))
       (t_5 (fmin (fmin y z) t))
       (t_6 (* (* (* t_5 9.0) t_2) t_3)))
  (if (<= t_6 -5e+181)
    (fma (* -9.0 (* t_3 t_5)) t_2 t_4)
    (if (<= t_6 1e-8)
      (fma (* a 27.0) b (+ x x))
      (fma (* -9.0 (* t_2 t_5)) t_3 t_4)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fmax(fmin(y, z), t);
	double t_2 = fmin(fmax(y, z), t_1);
	double t_3 = fmax(fmax(y, z), t_1);
	double t_4 = 27.0 * (a * b);
	double t_5 = fmin(fmin(y, z), t);
	double t_6 = ((t_5 * 9.0) * t_2) * t_3;
	double tmp;
	if (t_6 <= -5e+181) {
		tmp = fma((-9.0 * (t_3 * t_5)), t_2, t_4);
	} else if (t_6 <= 1e-8) {
		tmp = fma((a * 27.0), b, (x + x));
	} else {
		tmp = fma((-9.0 * (t_2 * t_5)), t_3, t_4);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fmax(fmin(y, z), t)
	t_2 = fmin(fmax(y, z), t_1)
	t_3 = fmax(fmax(y, z), t_1)
	t_4 = Float64(27.0 * Float64(a * b))
	t_5 = fmin(fmin(y, z), t)
	t_6 = Float64(Float64(Float64(t_5 * 9.0) * t_2) * t_3)
	tmp = 0.0
	if (t_6 <= -5e+181)
		tmp = fma(Float64(-9.0 * Float64(t_3 * t_5)), t_2, t_4);
	elseif (t_6 <= 1e-8)
		tmp = fma(Float64(a * 27.0), b, Float64(x + x));
	else
		tmp = fma(Float64(-9.0 * Float64(t_2 * t_5)), t_3, t_4);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Max[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$2 = N[Min[N[Max[y, z], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Max[N[Max[y, z], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[Min[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$5 * 9.0), $MachinePrecision] * t$95$2), $MachinePrecision] * t$95$3), $MachinePrecision]}, If[LessEqual[t$95$6, -5e+181], N[(N[(-9.0 * N[(t$95$3 * t$95$5), $MachinePrecision]), $MachinePrecision] * t$95$2 + t$95$4), $MachinePrecision], If[LessEqual[t$95$6, 1e-8], N[(N[(a * 27.0), $MachinePrecision] * b + N[(x + x), $MachinePrecision]), $MachinePrecision], N[(N[(-9.0 * N[(t$95$2 * t$95$5), $MachinePrecision]), $MachinePrecision] * t$95$3 + t$95$4), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000003e181

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{\left(a \cdot 27\right) \cdot b} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      4. associate-*l* N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

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

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right)} \]

      6. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \color{blue}{\left(\left(\mathsf{neg}\left(a\right)\right) \cdot 27\right) \cdot b} \]

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

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \color{blue}{\left(\mathsf{neg}\left(a \cdot 27\right)\right)} \cdot b \]

      12. lift-*.f64 N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \left(\mathsf{neg}\left(\color{blue}{a \cdot 27}\right)\right) \cdot b \]

      13. associate--l+ N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} \]

      14. *-commutative N/A

          \[\leadsto \color{blue}{t \cdot \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right)} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

      15. lift-*.f64 N/A

          \[\leadsto t \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot z}\right)\right) + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

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

          \[\leadsto t \cdot \color{blue}{\left(\left(y \cdot 9\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

      17. associate-*r* N/A

          \[\leadsto \color{blue}{\left(t \cdot \left(y \cdot 9\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t \cdot \left(y \cdot 9\right)\right) \cdot z\right)\right)} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(t \cdot \left(y \cdot 9\right)\right)\right) \cdot z} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

   3. Applied rewrites 94.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9 \cdot \left(t \cdot y\right), z, \mathsf{fma}\left(b \cdot a, 27, x + x\right)\right)} \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(-9 \cdot \left(t \cdot y\right), z, \color{blue}{27 \cdot \left(a \cdot b\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-9 \cdot \left(t \cdot y\right), z, 27 \cdot \color{blue}{\left(a \cdot b\right)}\right) \]

      2. lower-*.f64 66.8%

         \[\leadsto \mathsf{fma}\left(-9 \cdot \left(t \cdot y\right), z, 27 \cdot \left(a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 66.8%

      \[\leadsto \mathsf{fma}\left(-9 \cdot \left(t \cdot y\right), z, \color{blue}{27 \cdot \left(a \cdot b\right)}\right) \]

   if -5.0000000000000003e181 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 1e-8

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{x}, 27 \cdot \left(a \cdot b\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 64.2%

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   4. Applied rewrites 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. +-commutative N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2 \cdot x} \]

      3. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2} \cdot x \]

      4. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + 2 \cdot x \]

      5. *-commutative N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      6. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{2} \cdot x \]

      8. count-2-rev N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + x\right) \]

      11. associate-*l* N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

      12. lift-*.f64 N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

      13. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

      17. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

      22. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      23. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\color{blue}{x}\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      24. associate-*l* N/A

          \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      25. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \cdot \color{blue}{2} \]

      28. remove-double-neg N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + x \cdot 2 \]

      29. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + 2 \cdot \color{blue}{x} \]

   6. Applied rewrites 64.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, x + x\right)} \]
   7. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(x + x\right)} \]

      2. lift-+.f64 N/A

         \[\leadsto \left(27 \cdot b\right) \cdot a + \left(x + \color{blue}{x}\right) \]

      3. associate-+r+ N/A

         \[\leadsto \left(\left(27 \cdot b\right) \cdot a + x\right) + \color{blue}{x} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(27 \cdot b\right) \cdot a + x\right) + x \]

      5. *-commutative N/A

         \[\leadsto \left(\left(b \cdot 27\right) \cdot a + x\right) + x \]

      6. associate-*l* N/A

         \[\leadsto \left(b \cdot \left(27 \cdot a\right) + x\right) + x \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot \left(a \cdot 27\right) + x\right) + x \]

      8. associate-*l* N/A

         \[\leadsto \left(\left(b \cdot a\right) \cdot 27 + x\right) + x \]

      9. associate-+r+ N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{\left(x + x\right)} \]

      10. associate-*l* N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

      11. lift-*.f64 N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

      12. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      14. count-2 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

      15. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

      20. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

      22. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(2 \cdot \left(\mathsf{neg}\left(x\right)\right)\right)\right) \]

      23. count-2-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right) \]

      24. sub-flip-reverse N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) - x\right)\right)\right) \]

      25. sub-negate-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x - \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      26. add-flip N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      27. lift-+.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      28. lower-fma.f64 64.2%

          \[\leadsto \mathsf{fma}\left(a \cdot 27, \color{blue}{b}, x + x\right) \]

   8. Applied rewrites 64.2%

      \[\leadsto \mathsf{fma}\left(a \cdot 27, \color{blue}{b}, x + x\right) \]

   if 1e-8 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right) \]

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

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t\right)} \]

      6. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t} \]

      7. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot z}\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(9 \cdot y\right)} \cdot z\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      12. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{9 \cdot \left(y \cdot z\right)}\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot z\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(\mathsf{neg}\left(9\right)\right) \cdot \color{blue}{\left(z \cdot y\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(z \cdot y\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-9} \cdot \left(z \cdot y\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-9 \cdot \color{blue}{\left(z \cdot y\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      18. add-flip N/A

          \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \color{blue}{\left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right)}\right) \]

      19. sub-flip N/A

          \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \color{blue}{\left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x \cdot 2\right)\right)\right)\right)}\right) \]

   3. Applied rewrites 95.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \mathsf{fma}\left(b \cdot a, 27, x + x\right)\right)} \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \color{blue}{27 \cdot \left(a \cdot b\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, 27 \cdot \color{blue}{\left(a \cdot b\right)}\right) \]

      2. lower-*.f64 66.8%

         \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, 27 \cdot \left(a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 66.8%

      \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \color{blue}{27 \cdot \left(a \cdot b\right)}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 85.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(y, z\right), t\right)\\ t_2 := \mathsf{min}\left(\mathsf{max}\left(y, z\right), t\_1\right)\\ t_3 := \mathsf{max}\left(\mathsf{max}\left(y, z\right), t\_1\right)\\ t_4 := 27 \cdot \left(a \cdot b\right)\\ t_5 := \mathsf{min}\left(\mathsf{min}\left(y, z\right), t\right)\\ t_6 := \left(\left(t\_5 \cdot 9\right) \cdot t\_2\right) \cdot t\_3\\ \mathbf{if}\;t\_6 \leq -5 \cdot 10^{+181}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t\_3 \cdot t\_5\right), t\_2, t\_4\right)\\ \mathbf{elif}\;t\_6 \leq 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9, t\_3 \cdot \left(t\_5 \cdot t\_2\right), t\_4\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (fmax (fmin y z) t))
       (t_2 (fmin (fmax y z) t_1))
       (t_3 (fmax (fmax y z) t_1))
       (t_4 (* 27.0 (* a b)))
       (t_5 (fmin (fmin y z) t))
       (t_6 (* (* (* t_5 9.0) t_2) t_3)))
  (if (<= t_6 -5e+181)
    (fma (* -9.0 (* t_3 t_5)) t_2 t_4)
    (if (<= t_6 1e-8)
      (fma (* a 27.0) b (+ x x))
      (fma -9.0 (* t_3 (* t_5 t_2)) t_4)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fmax(fmin(y, z), t);
	double t_2 = fmin(fmax(y, z), t_1);
	double t_3 = fmax(fmax(y, z), t_1);
	double t_4 = 27.0 * (a * b);
	double t_5 = fmin(fmin(y, z), t);
	double t_6 = ((t_5 * 9.0) * t_2) * t_3;
	double tmp;
	if (t_6 <= -5e+181) {
		tmp = fma((-9.0 * (t_3 * t_5)), t_2, t_4);
	} else if (t_6 <= 1e-8) {
		tmp = fma((a * 27.0), b, (x + x));
	} else {
		tmp = fma(-9.0, (t_3 * (t_5 * t_2)), t_4);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fmax(fmin(y, z), t)
	t_2 = fmin(fmax(y, z), t_1)
	t_3 = fmax(fmax(y, z), t_1)
	t_4 = Float64(27.0 * Float64(a * b))
	t_5 = fmin(fmin(y, z), t)
	t_6 = Float64(Float64(Float64(t_5 * 9.0) * t_2) * t_3)
	tmp = 0.0
	if (t_6 <= -5e+181)
		tmp = fma(Float64(-9.0 * Float64(t_3 * t_5)), t_2, t_4);
	elseif (t_6 <= 1e-8)
		tmp = fma(Float64(a * 27.0), b, Float64(x + x));
	else
		tmp = fma(-9.0, Float64(t_3 * Float64(t_5 * t_2)), t_4);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Max[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$2 = N[Min[N[Max[y, z], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Max[N[Max[y, z], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[Min[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$5 * 9.0), $MachinePrecision] * t$95$2), $MachinePrecision] * t$95$3), $MachinePrecision]}, If[LessEqual[t$95$6, -5e+181], N[(N[(-9.0 * N[(t$95$3 * t$95$5), $MachinePrecision]), $MachinePrecision] * t$95$2 + t$95$4), $MachinePrecision], If[LessEqual[t$95$6, 1e-8], N[(N[(a * 27.0), $MachinePrecision] * b + N[(x + x), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(t$95$3 * N[(t$95$5 * t$95$2), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000003e181

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{\left(a \cdot 27\right) \cdot b} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      4. associate-*l* N/A

         \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

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

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right)} \]

      6. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(27 \cdot b\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \color{blue}{\left(\left(\mathsf{neg}\left(a\right)\right) \cdot 27\right) \cdot b} \]

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

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \color{blue}{\left(\mathsf{neg}\left(a \cdot 27\right)\right)} \cdot b \]

      12. lift-*.f64 N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + x \cdot 2\right) - \left(\mathsf{neg}\left(\color{blue}{a \cdot 27}\right)\right) \cdot b \]

      13. associate--l+ N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} \]

      14. *-commutative N/A

          \[\leadsto \color{blue}{t \cdot \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right)} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

      15. lift-*.f64 N/A

          \[\leadsto t \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot z}\right)\right) + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

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

          \[\leadsto t \cdot \color{blue}{\left(\left(y \cdot 9\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

      17. associate-*r* N/A

          \[\leadsto \color{blue}{\left(t \cdot \left(y \cdot 9\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t \cdot \left(y \cdot 9\right)\right) \cdot z\right)\right)} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(t \cdot \left(y \cdot 9\right)\right)\right) \cdot z} + \left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) \]

   3. Applied rewrites 94.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9 \cdot \left(t \cdot y\right), z, \mathsf{fma}\left(b \cdot a, 27, x + x\right)\right)} \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(-9 \cdot \left(t \cdot y\right), z, \color{blue}{27 \cdot \left(a \cdot b\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-9 \cdot \left(t \cdot y\right), z, 27 \cdot \color{blue}{\left(a \cdot b\right)}\right) \]

      2. lower-*.f64 66.8%

         \[\leadsto \mathsf{fma}\left(-9 \cdot \left(t \cdot y\right), z, 27 \cdot \left(a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 66.8%

      \[\leadsto \mathsf{fma}\left(-9 \cdot \left(t \cdot y\right), z, \color{blue}{27 \cdot \left(a \cdot b\right)}\right) \]

   if -5.0000000000000003e181 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 1e-8

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{x}, 27 \cdot \left(a \cdot b\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 64.2%

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   4. Applied rewrites 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. +-commutative N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2 \cdot x} \]

      3. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2} \cdot x \]

      4. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + 2 \cdot x \]

      5. *-commutative N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      6. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{2} \cdot x \]

      8. count-2-rev N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + x\right) \]

      11. associate-*l* N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

      12. lift-*.f64 N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

      13. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

      17. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

      22. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      23. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\color{blue}{x}\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      24. associate-*l* N/A

          \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      25. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \cdot \color{blue}{2} \]

      28. remove-double-neg N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + x \cdot 2 \]

      29. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + 2 \cdot \color{blue}{x} \]

   6. Applied rewrites 64.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, x + x\right)} \]
   7. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(x + x\right)} \]

      2. lift-+.f64 N/A

         \[\leadsto \left(27 \cdot b\right) \cdot a + \left(x + \color{blue}{x}\right) \]

      3. associate-+r+ N/A

         \[\leadsto \left(\left(27 \cdot b\right) \cdot a + x\right) + \color{blue}{x} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(27 \cdot b\right) \cdot a + x\right) + x \]

      5. *-commutative N/A

         \[\leadsto \left(\left(b \cdot 27\right) \cdot a + x\right) + x \]

      6. associate-*l* N/A

         \[\leadsto \left(b \cdot \left(27 \cdot a\right) + x\right) + x \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot \left(a \cdot 27\right) + x\right) + x \]

      8. associate-*l* N/A

         \[\leadsto \left(\left(b \cdot a\right) \cdot 27 + x\right) + x \]

      9. associate-+r+ N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{\left(x + x\right)} \]

      10. associate-*l* N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

      11. lift-*.f64 N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

      12. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      14. count-2 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

      15. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

      20. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

      22. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(2 \cdot \left(\mathsf{neg}\left(x\right)\right)\right)\right) \]

      23. count-2-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right) \]

      24. sub-flip-reverse N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) - x\right)\right)\right) \]

      25. sub-negate-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x - \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      26. add-flip N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      27. lift-+.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      28. lower-fma.f64 64.2%

          \[\leadsto \mathsf{fma}\left(a \cdot 27, \color{blue}{b}, x + x\right) \]

   8. Applied rewrites 64.2%

      \[\leadsto \mathsf{fma}\left(a \cdot 27, \color{blue}{b}, x + x\right) \]

   if 1e-8 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right) \]

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

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t\right)} \]

      6. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t} \]

      7. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot z}\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(9 \cdot y\right)} \cdot z\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      12. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{9 \cdot \left(y \cdot z\right)}\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot z\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(\mathsf{neg}\left(9\right)\right) \cdot \color{blue}{\left(z \cdot y\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(z \cdot y\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-9} \cdot \left(z \cdot y\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-9 \cdot \color{blue}{\left(z \cdot y\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      18. add-flip N/A

          \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \color{blue}{\left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right)}\right) \]

      19. sub-flip N/A

          \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \color{blue}{\left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x \cdot 2\right)\right)\right)\right)}\right) \]

   3. Applied rewrites 95.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \mathsf{fma}\left(b \cdot a, 27, x + x\right)\right)} \]

   4. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + 27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-9, \color{blue}{t \cdot \left(y \cdot z\right)}, 27 \cdot \left(a \cdot b\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-9, t \cdot \color{blue}{\left(y \cdot z\right)}, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-9, t \cdot \left(y \cdot \color{blue}{z}\right), 27 \cdot \left(a \cdot b\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-9, t \cdot \left(y \cdot z\right), 27 \cdot \left(a \cdot b\right)\right) \]

      5. lower-*.f64 66.4%

         \[\leadsto \mathsf{fma}\left(-9, t \cdot \left(y \cdot z\right), 27 \cdot \left(a \cdot b\right)\right) \]

   6. Applied rewrites 66.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9, t \cdot \left(y \cdot z\right), 27 \cdot \left(a \cdot b\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(-9, t \cdot \left(y \cdot z\right), 27 \cdot \left(a \cdot b\right)\right)\\ t_2 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (fma -9.0 (* t (* y z)) (* 27.0 (* a b))))
       (t_2 (* (* (* y 9.0) z) t)))
  (if (<= t_2 -5e+52)
    t_1
    (if (<= t_2 1e-8) (fma (* a 27.0) b (+ x x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-9.0, (t * (y * z)), (27.0 * (a * b)));
	double t_2 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_2 <= -5e+52) {
		tmp = t_1;
	} else if (t_2 <= 1e-8) {
		tmp = fma((a * 27.0), b, (x + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(-9.0, Float64(t * Float64(y * z)), Float64(27.0 * Float64(a * b)))
	t_2 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_2 <= -5e+52)
		tmp = t_1;
	elseif (t_2 <= 1e-8)
		tmp = fma(Float64(a * 27.0), b, Float64(x + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+52], t$95$1, If[LessEqual[t$95$2, 1e-8], N[(N[(a * 27.0), $MachinePrecision] * b + N[(x + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5e52 or 1e-8 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right) \]

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

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t\right)} \]

      6. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t} \]

      7. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right) \cdot t + \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot z}\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(9 \cdot y\right)} \cdot z\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      12. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{9 \cdot \left(y \cdot z\right)}\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot z\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(\mathsf{neg}\left(9\right)\right) \cdot \color{blue}{\left(z \cdot y\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(z \cdot y\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-9} \cdot \left(z \cdot y\right), t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-9 \cdot \color{blue}{\left(z \cdot y\right)}, t, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      18. add-flip N/A

          \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \color{blue}{\left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right)}\right) \]

      19. sub-flip N/A

          \[\leadsto \mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \color{blue}{\left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x \cdot 2\right)\right)\right)\right)}\right) \]

   3. Applied rewrites 95.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \mathsf{fma}\left(b \cdot a, 27, x + x\right)\right)} \]

   4. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + 27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-9, \color{blue}{t \cdot \left(y \cdot z\right)}, 27 \cdot \left(a \cdot b\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-9, t \cdot \color{blue}{\left(y \cdot z\right)}, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-9, t \cdot \left(y \cdot \color{blue}{z}\right), 27 \cdot \left(a \cdot b\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-9, t \cdot \left(y \cdot z\right), 27 \cdot \left(a \cdot b\right)\right) \]

      5. lower-*.f64 66.4%

         \[\leadsto \mathsf{fma}\left(-9, t \cdot \left(y \cdot z\right), 27 \cdot \left(a \cdot b\right)\right) \]

   6. Applied rewrites 66.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9, t \cdot \left(y \cdot z\right), 27 \cdot \left(a \cdot b\right)\right)} \]

   if -5e52 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 1e-8

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{x}, 27 \cdot \left(a \cdot b\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 64.2%

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   4. Applied rewrites 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. +-commutative N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2 \cdot x} \]

      3. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2} \cdot x \]

      4. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + 2 \cdot x \]

      5. *-commutative N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      6. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{2} \cdot x \]

      8. count-2-rev N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + x\right) \]

      11. associate-*l* N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

      12. lift-*.f64 N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

      13. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

      17. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

      22. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      23. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\color{blue}{x}\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      24. associate-*l* N/A

          \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      25. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \cdot \color{blue}{2} \]

      28. remove-double-neg N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + x \cdot 2 \]

      29. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + 2 \cdot \color{blue}{x} \]

   6. Applied rewrites 64.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, x + x\right)} \]
   7. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(x + x\right)} \]

      2. lift-+.f64 N/A

         \[\leadsto \left(27 \cdot b\right) \cdot a + \left(x + \color{blue}{x}\right) \]

      3. associate-+r+ N/A

         \[\leadsto \left(\left(27 \cdot b\right) \cdot a + x\right) + \color{blue}{x} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(27 \cdot b\right) \cdot a + x\right) + x \]

      5. *-commutative N/A

         \[\leadsto \left(\left(b \cdot 27\right) \cdot a + x\right) + x \]

      6. associate-*l* N/A

         \[\leadsto \left(b \cdot \left(27 \cdot a\right) + x\right) + x \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot \left(a \cdot 27\right) + x\right) + x \]

      8. associate-*l* N/A

         \[\leadsto \left(\left(b \cdot a\right) \cdot 27 + x\right) + x \]

      9. associate-+r+ N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{\left(x + x\right)} \]

      10. associate-*l* N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

      11. lift-*.f64 N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

      12. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      14. count-2 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

      15. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

      20. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

      22. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(2 \cdot \left(\mathsf{neg}\left(x\right)\right)\right)\right) \]

      23. count-2-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right) \]

      24. sub-flip-reverse N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) - x\right)\right)\right) \]

      25. sub-negate-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x - \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      26. add-flip N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      27. lift-+.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      28. lower-fma.f64 64.2%

          \[\leadsto \mathsf{fma}\left(a \cdot 27, \color{blue}{b}, x + x\right) \]

   8. Applied rewrites 64.2%

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

Alternative 10: 64.2% accurate, 2.1× speedup

Math

\[\mathsf{fma}\left(a \cdot 27, b, x + x\right) \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (fma (* a 27.0) b (+ x x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma((a * 27.0), b, (x + x));
}

Julia

function code(x, y, z, t, a, b)
	return fma(Float64(a * 27.0), b, Float64(x + x))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(a * 27.0), $MachinePrecision] * b + N[(x + x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.4%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

2. Taylor expanded in y around 0

   \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
3. Step-by-step derivation

   1. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(2, \color{blue}{x}, 27 \cdot \left(a \cdot b\right)\right) \]

   2. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   3. lower-*.f64 64.2%

      \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

4. Applied rewrites 64.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)} \]
5. Step-by-step derivation

   1. lift-fma.f64 N/A

      \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   2. +-commutative N/A

      \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2 \cdot x} \]

   3. lift-*.f64 N/A

      \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2} \cdot x \]

   4. lift-*.f64 N/A

      \[\leadsto 27 \cdot \left(a \cdot b\right) + 2 \cdot x \]

   5. *-commutative N/A

      \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

   6. lift-*.f64 N/A

      \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

   7. *-commutative N/A

      \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{2} \cdot x \]

   8. count-2-rev N/A

      \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

   9. lift-+.f64 N/A

      \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

   10. lift-*.f64 N/A

       \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + x\right) \]

   11. associate-*l* N/A

       \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

   12. lift-*.f64 N/A

       \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

   13. *-commutative N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

   14. lift-*.f64 N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

   15. lift-+.f64 N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

   16. count-2-rev N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

   17. *-commutative N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

       \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

       \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

       \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

       \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

   22. lift-*.f64 N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

   23. lift-*.f64 N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\color{blue}{x}\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right) \]

   24. associate-*l* N/A

       \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

   25. *-commutative N/A

       \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

       \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

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

       \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \cdot \color{blue}{2} \]

   28. remove-double-neg N/A

       \[\leadsto \left(27 \cdot b\right) \cdot a + x \cdot 2 \]

   29. *-commutative N/A

       \[\leadsto \left(27 \cdot b\right) \cdot a + 2 \cdot \color{blue}{x} \]

6. Applied rewrites 64.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, x + x\right)} \]
7. Step-by-step derivation

   1. lift-fma.f64 N/A

      \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(x + x\right)} \]

   2. lift-+.f64 N/A

      \[\leadsto \left(27 \cdot b\right) \cdot a + \left(x + \color{blue}{x}\right) \]

   3. associate-+r+ N/A

      \[\leadsto \left(\left(27 \cdot b\right) \cdot a + x\right) + \color{blue}{x} \]

   4. lift-*.f64 N/A

      \[\leadsto \left(\left(27 \cdot b\right) \cdot a + x\right) + x \]

   5. *-commutative N/A

      \[\leadsto \left(\left(b \cdot 27\right) \cdot a + x\right) + x \]

   6. associate-*l* N/A

      \[\leadsto \left(b \cdot \left(27 \cdot a\right) + x\right) + x \]

   7. *-commutative N/A

      \[\leadsto \left(b \cdot \left(a \cdot 27\right) + x\right) + x \]

   8. associate-*l* N/A

      \[\leadsto \left(\left(b \cdot a\right) \cdot 27 + x\right) + x \]

   9. associate-+r+ N/A

      \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{\left(x + x\right)} \]

   10. associate-*l* N/A

       \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

   11. lift-*.f64 N/A

       \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

   12. *-commutative N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

   13. lift-*.f64 N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

   14. count-2 N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

   15. *-commutative N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

       \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

       \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

       \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

       \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

   20. lift-*.f64 N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

   22. *-commutative N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(2 \cdot \left(\mathsf{neg}\left(x\right)\right)\right)\right) \]

   23. count-2-rev N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right) \]

   24. sub-flip-reverse N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) - x\right)\right)\right) \]

   25. sub-negate-rev N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x - \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

   26. add-flip N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

   27. lift-+.f64 N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

   28. lower-fma.f64 64.2%

       \[\leadsto \mathsf{fma}\left(a \cdot 27, \color{blue}{b}, x + x\right) \]

8. Applied rewrites 64.2%

   \[\leadsto \mathsf{fma}\left(a \cdot 27, \color{blue}{b}, x + x\right) \]
9. Add Preprocessing

Alternative 11: 64.2% accurate, 1.4× speedup

Math

\[\mathsf{fma}\left(\mathsf{min}\left(a, b\right) \cdot 27, \mathsf{max}\left(a, b\right), x\right) + x \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (+ (fma (* (fmin a b) 27.0) (fmax a b) x) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma((fmin(a, b) * 27.0), fmax(a, b), x) + x;
}

Julia

function code(x, y, z, t, a, b)
	return Float64(fma(Float64(fmin(a, b) * 27.0), fmax(a, b), x) + x)
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[Min[a, b], $MachinePrecision] * 27.0), $MachinePrecision] * N[Max[a, b], $MachinePrecision] + x), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 94.4%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

2. Taylor expanded in y around 0

   \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
3. Step-by-step derivation

   1. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(2, \color{blue}{x}, 27 \cdot \left(a \cdot b\right)\right) \]

   2. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   3. lower-*.f64 64.2%

      \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

4. Applied rewrites 64.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)} \]
5. Step-by-step derivation

   1. lift-fma.f64 N/A

      \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   2. +-commutative N/A

      \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2 \cdot x} \]

   3. lift-*.f64 N/A

      \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2} \cdot x \]

   4. lift-*.f64 N/A

      \[\leadsto 27 \cdot \left(a \cdot b\right) + 2 \cdot x \]

   5. *-commutative N/A

      \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

   6. lift-*.f64 N/A

      \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

   7. *-commutative N/A

      \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{2} \cdot x \]

   8. count-2-rev N/A

      \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

   9. lift-+.f64 N/A

      \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

   10. lift-*.f64 N/A

       \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + x\right) \]

   11. associate-*l* N/A

       \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

   12. lift-*.f64 N/A

       \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

   13. *-commutative N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

   14. lift-*.f64 N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

   15. lift-+.f64 N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

   16. count-2-rev N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

   17. *-commutative N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

       \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

       \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

       \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

       \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

   22. lift-*.f64 N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

   23. lift-*.f64 N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\color{blue}{x}\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right) \]

   24. associate-*l* N/A

       \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

   25. *-commutative N/A

       \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

       \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

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

       \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \cdot \color{blue}{2} \]

   28. remove-double-neg N/A

       \[\leadsto \left(27 \cdot b\right) \cdot a + x \cdot 2 \]

   29. *-commutative N/A

       \[\leadsto \left(27 \cdot b\right) \cdot a + 2 \cdot \color{blue}{x} \]

6. Applied rewrites 64.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, x + x\right)} \]
7. Step-by-step derivation

   1. lift-fma.f64 N/A

      \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(x + x\right)} \]

   2. lift-+.f64 N/A

      \[\leadsto \left(27 \cdot b\right) \cdot a + \left(x + \color{blue}{x}\right) \]

   3. associate-+r+ N/A

      \[\leadsto \left(\left(27 \cdot b\right) \cdot a + x\right) + \color{blue}{x} \]

   4. lower-+.f64 N/A

      \[\leadsto \left(\left(27 \cdot b\right) \cdot a + x\right) + \color{blue}{x} \]

   5. *-commutative N/A

      \[\leadsto \left(a \cdot \left(27 \cdot b\right) + x\right) + x \]

   6. lift-*.f64 N/A

      \[\leadsto \left(a \cdot \left(27 \cdot b\right) + x\right) + x \]

   7. associate-*l* N/A

      \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x\right) + x \]

   8. lift-*.f64 N/A

      \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x\right) + x \]

   9. lower-fma.f64 64.2%

      \[\leadsto \mathsf{fma}\left(a \cdot 27, b, x\right) + x \]

8. Applied rewrites 64.2%

   \[\leadsto \mathsf{fma}\left(a \cdot 27, b, x\right) + \color{blue}{x} \]
9. Add Preprocessing

Alternative 12: 46.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(a, b\right) \cdot 27\right) \cdot \mathsf{max}\left(a, b\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{-54}:\\ \;\;\;\;\mathsf{max}\left(a, b\right) \cdot \left(2 \cdot \frac{x}{\mathsf{max}\left(a, b\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(\mathsf{min}\left(a, b\right) \cdot \mathsf{max}\left(a, b\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* (* (fmin a b) 27.0) (fmax a b))))
  (if (<= t_1 -5e+78)
    t_1
    (if (<= t_1 1e-54)
      (* (fmax a b) (* 2.0 (/ x (fmax a b))))
      (* 27.0 (* (fmin a b) (fmax a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (fmin(a, b) * 27.0) * fmax(a, b);
	double tmp;
	if (t_1 <= -5e+78) {
		tmp = t_1;
	} else if (t_1 <= 1e-54) {
		tmp = fmax(a, b) * (2.0 * (x / fmax(a, b)));
	} else {
		tmp = 27.0 * (fmin(a, b) * fmax(a, b));
	}
	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)
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) :: t_1
    real(8) :: tmp
    t_1 = (fmin(a, b) * 27.0d0) * fmax(a, b)
    if (t_1 <= (-5d+78)) then
        tmp = t_1
    else if (t_1 <= 1d-54) then
        tmp = fmax(a, b) * (2.0d0 * (x / fmax(a, b)))
    else
        tmp = 27.0d0 * (fmin(a, b) * fmax(a, b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (fmin(a, b) * 27.0) * fmax(a, b);
	double tmp;
	if (t_1 <= -5e+78) {
		tmp = t_1;
	} else if (t_1 <= 1e-54) {
		tmp = fmax(a, b) * (2.0 * (x / fmax(a, b)));
	} else {
		tmp = 27.0 * (fmin(a, b) * fmax(a, b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (fmin(a, b) * 27.0) * fmax(a, b)
	tmp = 0
	if t_1 <= -5e+78:
		tmp = t_1
	elif t_1 <= 1e-54:
		tmp = fmax(a, b) * (2.0 * (x / fmax(a, b)))
	else:
		tmp = 27.0 * (fmin(a, b) * fmax(a, b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(fmin(a, b) * 27.0) * fmax(a, b))
	tmp = 0.0
	if (t_1 <= -5e+78)
		tmp = t_1;
	elseif (t_1 <= 1e-54)
		tmp = Float64(fmax(a, b) * Float64(2.0 * Float64(x / fmax(a, b))));
	else
		tmp = Float64(27.0 * Float64(fmin(a, b) * fmax(a, b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (min(a, b) * 27.0) * max(a, b);
	tmp = 0.0;
	if (t_1 <= -5e+78)
		tmp = t_1;
	elseif (t_1 <= 1e-54)
		tmp = max(a, b) * (2.0 * (x / max(a, b)));
	else
		tmp = 27.0 * (min(a, b) * max(a, b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Min[a, b], $MachinePrecision] * 27.0), $MachinePrecision] * N[Max[a, b], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+78], t$95$1, If[LessEqual[t$95$1, 1e-54], N[(N[Max[a, b], $MachinePrecision] * N[(2.0 * N[(x / N[Max[a, b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(27.0 * N[(N[Min[a, b], $MachinePrecision] * N[Max[a, b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.9999999999999998e78

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{x}, 27 \cdot \left(a \cdot b\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 64.2%

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   4. Applied rewrites 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. +-commutative N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2 \cdot x} \]

      3. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2} \cdot x \]

      4. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + 2 \cdot x \]

      5. *-commutative N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      6. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{2} \cdot x \]

      8. count-2-rev N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + x\right) \]

      11. associate-*l* N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

      12. lift-*.f64 N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

      13. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

      17. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

      22. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      23. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\color{blue}{x}\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      24. associate-*l* N/A

          \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      25. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \cdot \color{blue}{2} \]

      28. remove-double-neg N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + x \cdot 2 \]

      29. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + 2 \cdot \color{blue}{x} \]

   6. Applied rewrites 64.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, x + x\right)} \]

   7. Taylor expanded in x around 0

      \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot \color{blue}{b}\right) \]

      2. lower-*.f64 35.8%

         \[\leadsto 27 \cdot \left(a \cdot b\right) \]

   9. Applied rewrites 35.8%

      \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto 27 \cdot \left(a \cdot \color{blue}{b}\right) \]

       2. lift-*.f64 N/A

          \[\leadsto 27 \cdot \left(a \cdot b\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(27 \cdot a\right) \cdot b \]

       4. lift-*.f64 N/A

          \[\leadsto \left(27 \cdot a\right) \cdot b \]

       5. lower-*.f64 35.8%

          \[\leadsto \left(27 \cdot a\right) \cdot b \]

       6. lift-*.f64 N/A

          \[\leadsto \left(27 \cdot a\right) \cdot b \]

       7. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b \]

       8. lift-*.f64 35.8%

          \[\leadsto \left(a \cdot 27\right) \cdot b \]

   11. Applied rewrites 35.8%

       \[\leadsto \left(a \cdot 27\right) \cdot b \]

   if -4.9999999999999998e78 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1e-54

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{x}, 27 \cdot \left(a \cdot b\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 64.2%

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   4. Applied rewrites 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. +-commutative N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2 \cdot x} \]

      3. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2} \cdot x \]

      4. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + 2 \cdot x \]

      5. *-commutative N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      6. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{2} \cdot x \]

      8. count-2-rev N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + x\right) \]

      11. associate-*l* N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

      12. lift-*.f64 N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

      13. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

      17. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

      22. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      23. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\color{blue}{x}\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      24. associate-*l* N/A

          \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      25. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \cdot \color{blue}{2} \]

      28. remove-double-neg N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + x \cdot 2 \]

      29. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + 2 \cdot \color{blue}{x} \]

   6. Applied rewrites 64.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, x + x\right)} \]

   7. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(2 \cdot \frac{x}{b} + 27 \cdot a\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(2 \cdot \frac{x}{b} + \color{blue}{27 \cdot a}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto b \cdot \mathsf{fma}\left(2, \frac{x}{\color{blue}{b}}, 27 \cdot a\right) \]

      3. lower-/.f64 N/A

         \[\leadsto b \cdot \mathsf{fma}\left(2, \frac{x}{b}, 27 \cdot a\right) \]

      4. lower-*.f64 56.8%

         \[\leadsto b \cdot \mathsf{fma}\left(2, \frac{x}{b}, 27 \cdot a\right) \]

   9. Applied rewrites 56.8%

      \[\leadsto b \cdot \color{blue}{\mathsf{fma}\left(2, \frac{x}{b}, 27 \cdot a\right)} \]

   10. Taylor expanded in x around inf

       \[\leadsto b \cdot \left(2 \cdot \frac{x}{\color{blue}{b}}\right) \]
   11. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto b \cdot \left(2 \cdot \frac{x}{b}\right) \]

       2. lower-/.f64 23.0%

          \[\leadsto b \cdot \left(2 \cdot \frac{x}{b}\right) \]

   12. Applied rewrites 23.0%

       \[\leadsto b \cdot \left(2 \cdot \frac{x}{\color{blue}{b}}\right) \]

   if 1e-54 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{x}, 27 \cdot \left(a \cdot b\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 64.2%

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   4. Applied rewrites 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. +-commutative N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2 \cdot x} \]

      3. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2} \cdot x \]

      4. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + 2 \cdot x \]

      5. *-commutative N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      6. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{2} \cdot x \]

      8. count-2-rev N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + x\right) \]

      11. associate-*l* N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

      12. lift-*.f64 N/A

          \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

      13. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

      17. *-commutative N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

      22. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      23. lift-*.f64 N/A

          \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\color{blue}{x}\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      24. associate-*l* N/A

          \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

      25. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

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

          \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \cdot \color{blue}{2} \]

      28. remove-double-neg N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + x \cdot 2 \]

      29. *-commutative N/A

          \[\leadsto \left(27 \cdot b\right) \cdot a + 2 \cdot \color{blue}{x} \]

   6. Applied rewrites 64.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, x + x\right)} \]

   7. Taylor expanded in x around 0

      \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot \color{blue}{b}\right) \]

      2. lower-*.f64 35.8%

         \[\leadsto 27 \cdot \left(a \cdot b\right) \]

   9. Applied rewrites 35.8%

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

Alternative 13: 35.8% accurate, 3.5× speedup

Math

\[27 \cdot \left(a \cdot b\right) \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (* 27.0 (* a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return 27.0 * (a * b);
}

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)
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
    code = 27.0d0 * (a * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return 27.0 * (a * b);
}

Python

def code(x, y, z, t, a, b):
	return 27.0 * (a * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(27.0 * Float64(a * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = 27.0 * (a * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.4%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

2. Taylor expanded in y around 0

   \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
3. Step-by-step derivation

   1. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(2, \color{blue}{x}, 27 \cdot \left(a \cdot b\right)\right) \]

   2. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   3. lower-*.f64 64.2%

      \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

4. Applied rewrites 64.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)} \]
5. Step-by-step derivation

   1. lift-fma.f64 N/A

      \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   2. +-commutative N/A

      \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2 \cdot x} \]

   3. lift-*.f64 N/A

      \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{2} \cdot x \]

   4. lift-*.f64 N/A

      \[\leadsto 27 \cdot \left(a \cdot b\right) + 2 \cdot x \]

   5. *-commutative N/A

      \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

   6. lift-*.f64 N/A

      \[\leadsto 27 \cdot \left(b \cdot a\right) + 2 \cdot x \]

   7. *-commutative N/A

      \[\leadsto \left(b \cdot a\right) \cdot 27 + \color{blue}{2} \cdot x \]

   8. count-2-rev N/A

      \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

   9. lift-+.f64 N/A

      \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + \color{blue}{x}\right) \]

   10. lift-*.f64 N/A

       \[\leadsto \left(b \cdot a\right) \cdot 27 + \left(x + x\right) \]

   11. associate-*l* N/A

       \[\leadsto b \cdot \left(a \cdot 27\right) + \left(\color{blue}{x} + x\right) \]

   12. lift-*.f64 N/A

       \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x + x\right) \]

   13. *-commutative N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

   14. lift-*.f64 N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\color{blue}{x} + x\right) \]

   15. lift-+.f64 N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x + \color{blue}{x}\right) \]

   16. count-2-rev N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + 2 \cdot \color{blue}{x} \]

   17. *-commutative N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot \color{blue}{2} \]

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

       \[\leadsto \left(a \cdot 27\right) \cdot b - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot 2} \]

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

       \[\leadsto \left(a \cdot 27\right) \cdot b - \left(\mathsf{neg}\left(x \cdot 2\right)\right) \]

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

       \[\leadsto \left(a \cdot 27\right) \cdot b - x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \]

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

       \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right)} \]

   22. lift-*.f64 N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

   23. lift-*.f64 N/A

       \[\leadsto \left(a \cdot 27\right) \cdot b + \left(\mathsf{neg}\left(\color{blue}{x}\right)\right) \cdot \left(\mathsf{neg}\left(2\right)\right) \]

   24. associate-*l* N/A

       \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

   25. *-commutative N/A

       \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(2\right)\right) \]

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

       \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 2\right)\right) \]

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

       \[\leadsto \left(27 \cdot b\right) \cdot a + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \cdot \color{blue}{2} \]

   28. remove-double-neg N/A

       \[\leadsto \left(27 \cdot b\right) \cdot a + x \cdot 2 \]

   29. *-commutative N/A

       \[\leadsto \left(27 \cdot b\right) \cdot a + 2 \cdot \color{blue}{x} \]

6. Applied rewrites 64.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, x + x\right)} \]

7. Taylor expanded in x around 0

   \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} \]
8. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto 27 \cdot \left(a \cdot \color{blue}{b}\right) \]

   2. lower-*.f64 35.8%

      \[\leadsto 27 \cdot \left(a \cdot b\right) \]

9. Applied rewrites 35.8%

   \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2025212 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64
  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))