ab-angle->ABCF D

Percentage Accurate: 81.9% → 99.7%

Time: 1.2s

Alternatives: 3

Speedup: 1.0×

• 27.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ -\left(\left(a \cdot a\right) \cdot b\right) \cdot b \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (- (* (* (* a a) b) b)))

C

double code(double a, double b) {
	return -(((a * a) * b) * 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(a, b)
use fmin_fmax_functions
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = -(((a * a) * b) * b)
end function

Java

public static double code(double a, double b) {
	return -(((a * a) * b) * b);
}

Python

def code(a, b):
	return -(((a * a) * b) * b)

Julia

function code(a, b)
	return Float64(-Float64(Float64(Float64(a * a) * b) * b))
end

MATLAB

function tmp = code(a, b)
	tmp = -(((a * a) * b) * b);
end

Wolfram

code[a_, b_] := (-N[(N[(N[(a * a), $MachinePrecision] * b), $MachinePrecision] * b), $MachinePrecision])

Initial Program: 81.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ -\left(\left(a \cdot a\right) \cdot b\right) \cdot b \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (- (* (* (* a a) b) b)))

C

double code(double a, double b) {
	return -(((a * a) * b) * 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(a, b)
use fmin_fmax_functions
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = -(((a * a) * b) * b)
end function

Java

public static double code(double a, double b) {
	return -(((a * a) * b) * b);
}

Python

def code(a, b):
	return -(((a * a) * b) * b)

Julia

function code(a, b)
	return Float64(-Float64(Float64(Float64(a * a) * b) * b))
end

MATLAB

function tmp = code(a, b)
	tmp = -(((a * a) * b) * b);
end

Wolfram

code[a_, b_] := (-N[(N[(N[(a * a), $MachinePrecision] * b), $MachinePrecision] * b), $MachinePrecision])

Alternative 1: 99.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ [a_m, b_m] = \mathsf{sort}([a_m, b_m])\\ \\ \begin{array}{l} \mathbf{if}\;a\_m \leq 3.35 \cdot 10^{-155}:\\ \;\;\;\;\left(-a\_m\right) \cdot \left(\left(b\_m \cdot a\_m\right) \cdot b\_m\right)\\ \mathbf{else}:\\ \;\;\;\;-\left(\left(a\_m \cdot a\_m\right) \cdot b\_m\right) \cdot b\_m\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
NOTE: a_m and b_m should be sorted in increasing order before calling this function.
(FPCore (a_m b_m)
 :precision binary64
 (if (<= a_m 3.35e-155)
   (* (- a_m) (* (* b_m a_m) b_m))
   (- (* (* (* a_m a_m) b_m) b_m))))

C

a_m = fabs(a);
b_m = fabs(b);
assert(a_m < b_m);
double code(double a_m, double b_m) {
	double tmp;
	if (a_m <= 3.35e-155) {
		tmp = -a_m * ((b_m * a_m) * b_m);
	} else {
		tmp = -(((a_m * a_m) * b_m) * b_m);
	}
	return tmp;
}

Fortran

a_m =     private
b_m =     private
NOTE: a_m and b_m should be sorted in increasing order before calling this function.
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(a_m, b_m)
use fmin_fmax_functions
    real(8), intent (in) :: a_m
    real(8), intent (in) :: b_m
    real(8) :: tmp
    if (a_m <= 3.35d-155) then
        tmp = -a_m * ((b_m * a_m) * b_m)
    else
        tmp = -(((a_m * a_m) * b_m) * b_m)
    end if
    code = tmp
end function

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
assert a_m < b_m;
public static double code(double a_m, double b_m) {
	double tmp;
	if (a_m <= 3.35e-155) {
		tmp = -a_m * ((b_m * a_m) * b_m);
	} else {
		tmp = -(((a_m * a_m) * b_m) * b_m);
	}
	return tmp;
}

Python

a_m = math.fabs(a)
b_m = math.fabs(b)
[a_m, b_m] = sort([a_m, b_m])
def code(a_m, b_m):
	tmp = 0
	if a_m <= 3.35e-155:
		tmp = -a_m * ((b_m * a_m) * b_m)
	else:
		tmp = -(((a_m * a_m) * b_m) * b_m)
	return tmp

Julia

a_m = abs(a)
b_m = abs(b)
a_m, b_m = sort([a_m, b_m])
function code(a_m, b_m)
	tmp = 0.0
	if (a_m <= 3.35e-155)
		tmp = Float64(Float64(-a_m) * Float64(Float64(b_m * a_m) * b_m));
	else
		tmp = Float64(-Float64(Float64(Float64(a_m * a_m) * b_m) * b_m));
	end
	return tmp
end

MATLAB

a_m = abs(a);
b_m = abs(b);
a_m, b_m = num2cell(sort([a_m, b_m])){:}
function tmp_2 = code(a_m, b_m)
	tmp = 0.0;
	if (a_m <= 3.35e-155)
		tmp = -a_m * ((b_m * a_m) * b_m);
	else
		tmp = -(((a_m * a_m) * b_m) * b_m);
	end
	tmp_2 = tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
NOTE: a_m and b_m should be sorted in increasing order before calling this function.
code[a$95$m_, b$95$m_] := If[LessEqual[a$95$m, 3.35e-155], N[((-a$95$m) * N[(N[(b$95$m * a$95$m), $MachinePrecision] * b$95$m), $MachinePrecision]), $MachinePrecision], (-N[(N[(N[(a$95$m * a$95$m), $MachinePrecision] * b$95$m), $MachinePrecision] * b$95$m), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if a < 3.35000000000000014e-155

   1. Initial program 81.9%

      \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-neg.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. associate-*l* N/A

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

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

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

      8. lower-*.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 94.1

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

   3. Applied rewrites 94.1%

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

   if 3.35000000000000014e-155 < a

   1. Initial program 81.9%

      \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ [a_m, b_m] = \mathsf{sort}([a_m, b_m])\\ \\ \left(\left(-b\_m\right) \cdot a\_m\right) \cdot \left(b\_m \cdot a\_m\right) \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
NOTE: a_m and b_m should be sorted in increasing order before calling this function.
(FPCore (a_m b_m) :precision binary64 (* (* (- b_m) a_m) (* b_m a_m)))

C

a_m = fabs(a);
b_m = fabs(b);
assert(a_m < b_m);
double code(double a_m, double b_m) {
	return (-b_m * a_m) * (b_m * a_m);
}

Fortran

a_m =     private
b_m =     private
NOTE: a_m and b_m should be sorted in increasing order before calling this function.
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(a_m, b_m)
use fmin_fmax_functions
    real(8), intent (in) :: a_m
    real(8), intent (in) :: b_m
    code = (-b_m * a_m) * (b_m * a_m)
end function

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
assert a_m < b_m;
public static double code(double a_m, double b_m) {
	return (-b_m * a_m) * (b_m * a_m);
}

Python

a_m = math.fabs(a)
b_m = math.fabs(b)
[a_m, b_m] = sort([a_m, b_m])
def code(a_m, b_m):
	return (-b_m * a_m) * (b_m * a_m)

Julia

a_m = abs(a)
b_m = abs(b)
a_m, b_m = sort([a_m, b_m])
function code(a_m, b_m)
	return Float64(Float64(Float64(-b_m) * a_m) * Float64(b_m * a_m))
end

MATLAB

a_m = abs(a);
b_m = abs(b);
a_m, b_m = num2cell(sort([a_m, b_m])){:}
function tmp = code(a_m, b_m)
	tmp = (-b_m * a_m) * (b_m * a_m);
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
NOTE: a_m and b_m should be sorted in increasing order before calling this function.
code[a$95$m_, b$95$m_] := N[(N[((-b$95$m) * a$95$m), $MachinePrecision] * N[(b$95$m * a$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 81.9%

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
2. Step-by-step derivation

   1. lift-neg.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. associate-*l* N/A

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

   5. lift-*.f64 N/A

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

   6. unswap-sqr N/A

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

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

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

   8. *-commutative N/A

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

   9. distribute-rgt-neg-out N/A

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

   10. lower-*.f64 N/A

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

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

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

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

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

   13. lower-*.f64 N/A

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

   14. lower-neg.f64 N/A

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

   15. *-commutative N/A

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

   16. lower-*.f64 99.7

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

3. Applied rewrites 99.7%

   \[\leadsto \color{blue}{\left(\left(-b\right) \cdot a\right) \cdot \left(b \cdot a\right)} \]
4. Add Preprocessing

Alternative 3: 81.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ [a_m, b_m] = \mathsf{sort}([a_m, b_m])\\ \\ -\left(\left(a\_m \cdot a\_m\right) \cdot b\_m\right) \cdot b\_m \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
NOTE: a_m and b_m should be sorted in increasing order before calling this function.
(FPCore (a_m b_m) :precision binary64 (- (* (* (* a_m a_m) b_m) b_m)))

C

a_m = fabs(a);
b_m = fabs(b);
assert(a_m < b_m);
double code(double a_m, double b_m) {
	return -(((a_m * a_m) * b_m) * b_m);
}

Fortran

a_m =     private
b_m =     private
NOTE: a_m and b_m should be sorted in increasing order before calling this function.
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(a_m, b_m)
use fmin_fmax_functions
    real(8), intent (in) :: a_m
    real(8), intent (in) :: b_m
    code = -(((a_m * a_m) * b_m) * b_m)
end function

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
assert a_m < b_m;
public static double code(double a_m, double b_m) {
	return -(((a_m * a_m) * b_m) * b_m);
}

Python

a_m = math.fabs(a)
b_m = math.fabs(b)
[a_m, b_m] = sort([a_m, b_m])
def code(a_m, b_m):
	return -(((a_m * a_m) * b_m) * b_m)

Julia

a_m = abs(a)
b_m = abs(b)
a_m, b_m = sort([a_m, b_m])
function code(a_m, b_m)
	return Float64(-Float64(Float64(Float64(a_m * a_m) * b_m) * b_m))
end

MATLAB

a_m = abs(a);
b_m = abs(b);
a_m, b_m = num2cell(sort([a_m, b_m])){:}
function tmp = code(a_m, b_m)
	tmp = -(((a_m * a_m) * b_m) * b_m);
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
NOTE: a_m and b_m should be sorted in increasing order before calling this function.
code[a$95$m_, b$95$m_] := (-N[(N[(N[(a$95$m * a$95$m), $MachinePrecision] * b$95$m), $MachinePrecision] * b$95$m), $MachinePrecision])

Derivation

1. Initial program 81.9%

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
2. Add Preprocessing

Reproduce

herbie shell --seed 2025149 
(FPCore (a b)
  :name "ab-angle->ABCF D"
  :precision binary64
  (- (* (* (* a a) b) b)))