Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, C

Percentage Accurate: 97.5% → 97.6%

Time: 9.1s

Alternatives: 9

Speedup: 1.3×

• 67.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16)) (/ (* a b) 4)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Initial Program: 97.5% accurate, 1.0× speedup

Math

\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16)) (/ (* a b) 4)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Alternative 1: 97.6% accurate, 1.3× speedup

Math

\[\left(\left(x \cdot y + \left(\frac{1}{16} \cdot z\right) \cdot t\right) - \left(b \cdot a\right) \cdot \frac{1}{4}\right) + c \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (+ (- (+ (* x y) (* (* 1/16 z) t)) (* (* b a) 1/4)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((0.0625 * z) * t)) - ((b * a) * 0.25)) + c;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((0.0625d0 * z) * t)) - ((b * a) * 0.25d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((0.0625 * z) * t)) - ((b * a) * 0.25)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((0.0625 * z) * t)) - ((b * a) * 0.25)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(0.0625 * z) * t)) - Float64(Float64(b * a) * 0.25)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((0.0625 * z) * t)) - ((b * a) * 0.25)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(1/16 * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 1/4), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Derivation

1. Initial program 97.5%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \left(\left(x \cdot y + \color{blue}{\frac{z \cdot t}{16}}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. mult-flip N/A

      \[\leadsto \left(\left(x \cdot y + \color{blue}{\left(z \cdot t\right) \cdot \frac{1}{16}}\right) - \frac{a \cdot b}{4}\right) + c \]

   3. lift-*.f64 N/A

      \[\leadsto \left(\left(x \cdot y + \color{blue}{\left(z \cdot t\right)} \cdot \frac{1}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   4. *-commutative N/A

      \[\leadsto \left(\left(x \cdot y + \color{blue}{\left(t \cdot z\right)} \cdot \frac{1}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   5. associate-*l* N/A

      \[\leadsto \left(\left(x \cdot y + \color{blue}{t \cdot \left(z \cdot \frac{1}{16}\right)}\right) - \frac{a \cdot b}{4}\right) + c \]

   6. *-commutative N/A

      \[\leadsto \left(\left(x \cdot y + \color{blue}{\left(z \cdot \frac{1}{16}\right) \cdot t}\right) - \frac{a \cdot b}{4}\right) + c \]

   7. lower-*.f64 N/A

      \[\leadsto \left(\left(x \cdot y + \color{blue}{\left(z \cdot \frac{1}{16}\right) \cdot t}\right) - \frac{a \cdot b}{4}\right) + c \]

   8. *-commutative N/A

      \[\leadsto \left(\left(x \cdot y + \color{blue}{\left(\frac{1}{16} \cdot z\right)} \cdot t\right) - \frac{a \cdot b}{4}\right) + c \]

   9. lower-*.f64 N/A

      \[\leadsto \left(\left(x \cdot y + \color{blue}{\left(\frac{1}{16} \cdot z\right)} \cdot t\right) - \frac{a \cdot b}{4}\right) + c \]

   10. metadata-eval 97.6%

       \[\leadsto \left(\left(x \cdot y + \left(\color{blue}{\frac{1}{16}} \cdot z\right) \cdot t\right) - \frac{a \cdot b}{4}\right) + c \]

3. Applied rewrites 97.6%

   \[\leadsto \left(\left(x \cdot y + \color{blue}{\left(\frac{1}{16} \cdot z\right) \cdot t}\right) - \frac{a \cdot b}{4}\right) + c \]
4. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \left(\left(x \cdot y + \left(\frac{1}{16} \cdot z\right) \cdot t\right) - \color{blue}{\frac{a \cdot b}{4}}\right) + c \]

   2. mult-flip N/A

      \[\leadsto \left(\left(x \cdot y + \left(\frac{1}{16} \cdot z\right) \cdot t\right) - \color{blue}{\left(a \cdot b\right) \cdot \frac{1}{4}}\right) + c \]

   3. metadata-eval N/A

      \[\leadsto \left(\left(x \cdot y + \left(\frac{1}{16} \cdot z\right) \cdot t\right) - \left(a \cdot b\right) \cdot \color{blue}{\frac{1}{4}}\right) + c \]

   4. lower-*.f64 97.6%

      \[\leadsto \left(\left(x \cdot y + \left(\frac{1}{16} \cdot z\right) \cdot t\right) - \color{blue}{\left(a \cdot b\right) \cdot \frac{1}{4}}\right) + c \]

   5. lift-*.f64 N/A

      \[\leadsto \left(\left(x \cdot y + \left(\frac{1}{16} \cdot z\right) \cdot t\right) - \color{blue}{\left(a \cdot b\right)} \cdot \frac{1}{4}\right) + c \]

   6. *-commutative N/A

      \[\leadsto \left(\left(x \cdot y + \left(\frac{1}{16} \cdot z\right) \cdot t\right) - \color{blue}{\left(b \cdot a\right)} \cdot \frac{1}{4}\right) + c \]

   7. lower-*.f64 97.6%

      \[\leadsto \left(\left(x \cdot y + \left(\frac{1}{16} \cdot z\right) \cdot t\right) - \color{blue}{\left(b \cdot a\right)} \cdot \frac{1}{4}\right) + c \]

5. Applied rewrites 97.6%

   \[\leadsto \left(\left(x \cdot y + \left(\frac{1}{16} \cdot z\right) \cdot t\right) - \color{blue}{\left(b \cdot a\right) \cdot \frac{1}{4}}\right) + c \]
6. Add Preprocessing

Alternative 2: 88.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \frac{1}{4} \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \cdot y \leq -500000000000000022442856339037958392774656:\\ \;\;\;\;\left(x \cdot y - t\_1\right) + c\\ \mathbf{elif}\;x \cdot y \leq 40000000000000001313662499568197043159480502654384467820492537050349880275951519821760052625109096507357980191372897423145939625368459673600:\\ \;\;\;\;\left(\frac{1}{16} \cdot \left(t \cdot z\right) - t\_1\right) + c\\ \mathbf{else}:\\ \;\;\;\;c + \left(\left(z \cdot \frac{1}{16}\right) \cdot t + x \cdot y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (* 1/4 (* a b))))
  (if (<= (* x y) -500000000000000022442856339037958392774656)
    (+ (- (* x y) t_1) c)
    (if (<=
         (* x y)
         40000000000000001313662499568197043159480502654384467820492537050349880275951519821760052625109096507357980191372897423145939625368459673600)
      (+ (- (* 1/16 (* t z)) t_1) c)
      (+ c (+ (* (* z 1/16) t) (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.25 * (a * b);
	double tmp;
	if ((x * y) <= -5e+41) {
		tmp = ((x * y) - t_1) + c;
	} else if ((x * y) <= 4e+139) {
		tmp = ((0.0625 * (t * z)) - t_1) + c;
	} else {
		tmp = c + (((z * 0.0625) * t) + (x * y));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.25d0 * (a * b)
    if ((x * y) <= (-5d+41)) then
        tmp = ((x * y) - t_1) + c
    else if ((x * y) <= 4d+139) then
        tmp = ((0.0625d0 * (t * z)) - t_1) + c
    else
        tmp = c + (((z * 0.0625d0) * t) + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.25 * (a * b);
	double tmp;
	if ((x * y) <= -5e+41) {
		tmp = ((x * y) - t_1) + c;
	} else if ((x * y) <= 4e+139) {
		tmp = ((0.0625 * (t * z)) - t_1) + c;
	} else {
		tmp = c + (((z * 0.0625) * t) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.25 * (a * b)
	tmp = 0
	if (x * y) <= -5e+41:
		tmp = ((x * y) - t_1) + c
	elif (x * y) <= 4e+139:
		tmp = ((0.0625 * (t * z)) - t_1) + c
	else:
		tmp = c + (((z * 0.0625) * t) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.25 * Float64(a * b))
	tmp = 0.0
	if (Float64(x * y) <= -5e+41)
		tmp = Float64(Float64(Float64(x * y) - t_1) + c);
	elseif (Float64(x * y) <= 4e+139)
		tmp = Float64(Float64(Float64(0.0625 * Float64(t * z)) - t_1) + c);
	else
		tmp = Float64(c + Float64(Float64(Float64(z * 0.0625) * t) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.25 * (a * b);
	tmp = 0.0;
	if ((x * y) <= -5e+41)
		tmp = ((x * y) - t_1) + c;
	elseif ((x * y) <= 4e+139)
		tmp = ((0.0625 * (t * z)) - t_1) + c;
	else
		tmp = c + (((z * 0.0625) * t) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(1/4 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -500000000000000022442856339037958392774656], N[(N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision] + c), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 40000000000000001313662499568197043159480502654384467820492537050349880275951519821760052625109096507357980191372897423145939625368459673600], N[(N[(N[(1/16 * N[(t * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + c), $MachinePrecision], N[(c + N[(N[(N[(z * 1/16), $MachinePrecision] * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.0000000000000002e41

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x \cdot y - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x \cdot y - \color{blue}{\frac{1}{4} \cdot \left(a \cdot b\right)}\right) + c \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x \cdot y - \color{blue}{\frac{1}{4}} \cdot \left(a \cdot b\right)\right) + c \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x \cdot y - \frac{1}{4} \cdot \color{blue}{\left(a \cdot b\right)}\right) + c \]

      4. lower-*.f64 73.6%

         \[\leadsto \left(x \cdot y - \frac{1}{4} \cdot \left(a \cdot \color{blue}{b}\right)\right) + c \]

   4. Applied rewrites 73.6%

      \[\leadsto \color{blue}{\left(x \cdot y - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]

   if -5.0000000000000002e41 < (*.f64 x y) < 4.0000000000000001e139

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{1}{16} \cdot \left(t \cdot z\right) - \color{blue}{\frac{1}{4} \cdot \left(a \cdot b\right)}\right) + c \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} \cdot \left(t \cdot z\right) - \color{blue}{\frac{1}{4}} \cdot \left(a \cdot b\right)\right) + c \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} \cdot \left(t \cdot z\right) - \frac{1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} \cdot \left(t \cdot z\right) - \frac{1}{4} \cdot \color{blue}{\left(a \cdot b\right)}\right) + c \]

      5. lower-*.f64 73.4%

         \[\leadsto \left(\frac{1}{16} \cdot \left(t \cdot z\right) - \frac{1}{4} \cdot \left(a \cdot \color{blue}{b}\right)\right) + c \]

   4. Applied rewrites 73.4%

      \[\leadsto \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]

   if 4.0000000000000001e139 < (*.f64 x y)

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto c + \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x \cdot y}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x} \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]

      5. lower-*.f64 73.8%

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 73.8%

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x} \cdot y\right) \]

      2. lift-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]

      3. *-commutative N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(z \cdot t\right) + x \cdot y\right) \]

      4. associate-*l* N/A

         \[\leadsto c + \left(\left(\frac{1}{16} \cdot z\right) \cdot t + \color{blue}{x} \cdot y\right) \]

      5. lower-*.f64 N/A

         \[\leadsto c + \left(\left(\frac{1}{16} \cdot z\right) \cdot t + \color{blue}{x} \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto c + \left(\left(z \cdot \frac{1}{16}\right) \cdot t + x \cdot y\right) \]

      7. lower-*.f64 73.8%

         \[\leadsto c + \left(\left(z \cdot \frac{1}{16}\right) \cdot t + x \cdot y\right) \]

   6. Applied rewrites 73.8%

      \[\leadsto c + \left(\left(z \cdot \frac{1}{16}\right) \cdot t + \color{blue}{x} \cdot y\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 87.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq -5000000000000000014339392554976861624351030032307491891786714963455192826951136079841645978666612324808479156564299152005093968192740890223899883592402933027172967020052041660293849107704861024718326980908701245637596009600853559934996040535864898581843704726957456644770889728:\\ \;\;\;\;\left(-\frac{1}{4} \cdot a\right) \cdot b\\ \mathbf{elif}\;t\_1 \leq 100000000000000009190283508143378238084034459715684532224:\\ \;\;\;\;c + \left(\left(z \cdot \frac{1}{16}\right) \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - \frac{1}{4} \cdot \left(a \cdot b\right)\right) + c\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (/ (* a b) 4)))
  (if (<=
       t_1
       -5000000000000000014339392554976861624351030032307491891786714963455192826951136079841645978666612324808479156564299152005093968192740890223899883592402933027172967020052041660293849107704861024718326980908701245637596009600853559934996040535864898581843704726957456644770889728)
    (* (- (* 1/4 a)) b)
    (if (<=
         t_1
         100000000000000009190283508143378238084034459715684532224)
      (+ c (+ (* (* z 1/16) t) (* x y)))
      (+ (- (* x y) (* 1/4 (* a b))) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double tmp;
	if (t_1 <= -5e+276) {
		tmp = -(0.25 * a) * b;
	} else if (t_1 <= 1e+56) {
		tmp = c + (((z * 0.0625) * t) + (x * y));
	} else {
		tmp = ((x * y) - (0.25 * (a * b))) + c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) / 4.0d0
    if (t_1 <= (-5d+276)) then
        tmp = -(0.25d0 * a) * b
    else if (t_1 <= 1d+56) then
        tmp = c + (((z * 0.0625d0) * t) + (x * y))
    else
        tmp = ((x * y) - (0.25d0 * (a * b))) + c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double tmp;
	if (t_1 <= -5e+276) {
		tmp = -(0.25 * a) * b;
	} else if (t_1 <= 1e+56) {
		tmp = c + (((z * 0.0625) * t) + (x * y));
	} else {
		tmp = ((x * y) - (0.25 * (a * b))) + c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) / 4.0
	tmp = 0
	if t_1 <= -5e+276:
		tmp = -(0.25 * a) * b
	elif t_1 <= 1e+56:
		tmp = c + (((z * 0.0625) * t) + (x * y))
	else:
		tmp = ((x * y) - (0.25 * (a * b))) + c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / 4.0)
	tmp = 0.0
	if (t_1 <= -5e+276)
		tmp = Float64(Float64(-Float64(0.25 * a)) * b);
	elseif (t_1 <= 1e+56)
		tmp = Float64(c + Float64(Float64(Float64(z * 0.0625) * t) + Float64(x * y)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(0.25 * Float64(a * b))) + c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) / 4.0;
	tmp = 0.0;
	if (t_1 <= -5e+276)
		tmp = -(0.25 * a) * b;
	elseif (t_1 <= 1e+56)
		tmp = c + (((z * 0.0625) * t) + (x * y));
	else
		tmp = ((x * y) - (0.25 * (a * b))) + c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] / 4), $MachinePrecision]}, If[LessEqual[t$95$1, -5000000000000000014339392554976861624351030032307491891786714963455192826951136079841645978666612324808479156564299152005093968192740890223899883592402933027172967020052041660293849107704861024718326980908701245637596009600853559934996040535864898581843704726957456644770889728], N[((-N[(1/4 * a), $MachinePrecision]) * b), $MachinePrecision], If[LessEqual[t$95$1, 100000000000000009190283508143378238084034459715684532224], N[(c + N[(N[(N[(z * 1/16), $MachinePrecision] * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(1/4 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -5e276

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \color{blue}{\frac{-1}{4} \cdot a}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \color{blue}{\frac{-1}{4}} \cdot a\right)\right) \]

      5. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      6. lower-+.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      7. lower-+.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      11. lower-*.f64 81.3%

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot \color{blue}{a}\right)\right) \]

   4. Applied rewrites 81.3%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right)} \]

   5. Taylor expanded in a around inf

      \[\leadsto -1 \cdot \left(b \cdot \left(\frac{1}{4} \cdot \color{blue}{a}\right)\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 28.5%

         \[\leadsto -1 \cdot \left(b \cdot \left(\frac{1}{4} \cdot a\right)\right) \]

   7. Applied rewrites 28.5%

      \[\leadsto -1 \cdot \left(b \cdot \left(\frac{1}{4} \cdot \color{blue}{a}\right)\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(\frac{1}{4} \cdot a\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(\frac{1}{4} \cdot a\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(\frac{1}{4} \cdot a\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(\frac{1}{4} \cdot a\right) \cdot b\right) \]

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

         \[\leadsto \left(\mathsf{neg}\left(\frac{1}{4} \cdot a\right)\right) \cdot \color{blue}{b} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{1}{4} \cdot a\right)\right) \cdot \color{blue}{b} \]

      7. lower-neg.f64 28.5%

         \[\leadsto \left(-\frac{1}{4} \cdot a\right) \cdot b \]

   9. Applied rewrites 28.5%

      \[\leadsto \left(-\frac{1}{4} \cdot a\right) \cdot \color{blue}{b} \]

   if -5e276 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 1.0000000000000001e56

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto c + \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x \cdot y}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x} \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]

      5. lower-*.f64 73.8%

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 73.8%

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x} \cdot y\right) \]

      2. lift-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]

      3. *-commutative N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(z \cdot t\right) + x \cdot y\right) \]

      4. associate-*l* N/A

         \[\leadsto c + \left(\left(\frac{1}{16} \cdot z\right) \cdot t + \color{blue}{x} \cdot y\right) \]

      5. lower-*.f64 N/A

         \[\leadsto c + \left(\left(\frac{1}{16} \cdot z\right) \cdot t + \color{blue}{x} \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto c + \left(\left(z \cdot \frac{1}{16}\right) \cdot t + x \cdot y\right) \]

      7. lower-*.f64 73.8%

         \[\leadsto c + \left(\left(z \cdot \frac{1}{16}\right) \cdot t + x \cdot y\right) \]

   6. Applied rewrites 73.8%

      \[\leadsto c + \left(\left(z \cdot \frac{1}{16}\right) \cdot t + \color{blue}{x} \cdot y\right) \]

   if 1.0000000000000001e56 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x \cdot y - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x \cdot y - \color{blue}{\frac{1}{4} \cdot \left(a \cdot b\right)}\right) + c \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x \cdot y - \color{blue}{\frac{1}{4}} \cdot \left(a \cdot b\right)\right) + c \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x \cdot y - \frac{1}{4} \cdot \color{blue}{\left(a \cdot b\right)}\right) + c \]

      4. lower-*.f64 73.6%

         \[\leadsto \left(x \cdot y - \frac{1}{4} \cdot \left(a \cdot \color{blue}{b}\right)\right) + c \]

   4. Applied rewrites 73.6%

      \[\leadsto \color{blue}{\left(x \cdot y - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 85.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq -5000000000000000014339392554976861624351030032307491891786714963455192826951136079841645978666612324808479156564299152005093968192740890223899883592402933027172967020052041660293849107704861024718326980908701245637596009600853559934996040535864898581843704726957456644770889728:\\ \;\;\;\;\left(-\frac{1}{4} \cdot a\right) \cdot b\\ \mathbf{elif}\;t\_1 \leq 100000000000000003889357755108838843130737249295202013334302382007691294289384896763079965607877701387326460311941213291353170611409437561654018367221268940354434586262616943544566455807655946219322240663552:\\ \;\;\;\;c + \left(\left(z \cdot \frac{1}{16}\right) \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{4} \cdot \left(a \cdot b\right) + c\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (/ (* a b) 4)))
  (if (<=
       t_1
       -5000000000000000014339392554976861624351030032307491891786714963455192826951136079841645978666612324808479156564299152005093968192740890223899883592402933027172967020052041660293849107704861024718326980908701245637596009600853559934996040535864898581843704726957456644770889728)
    (* (- (* 1/4 a)) b)
    (if (<=
         t_1
         100000000000000003889357755108838843130737249295202013334302382007691294289384896763079965607877701387326460311941213291353170611409437561654018367221268940354434586262616943544566455807655946219322240663552)
      (+ c (+ (* (* z 1/16) t) (* x y)))
      (+ (* -1/4 (* a b)) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double tmp;
	if (t_1 <= -5e+276) {
		tmp = -(0.25 * a) * b;
	} else if (t_1 <= 1e+206) {
		tmp = c + (((z * 0.0625) * t) + (x * y));
	} else {
		tmp = (-0.25 * (a * b)) + c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) / 4.0d0
    if (t_1 <= (-5d+276)) then
        tmp = -(0.25d0 * a) * b
    else if (t_1 <= 1d+206) then
        tmp = c + (((z * 0.0625d0) * t) + (x * y))
    else
        tmp = ((-0.25d0) * (a * b)) + c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double tmp;
	if (t_1 <= -5e+276) {
		tmp = -(0.25 * a) * b;
	} else if (t_1 <= 1e+206) {
		tmp = c + (((z * 0.0625) * t) + (x * y));
	} else {
		tmp = (-0.25 * (a * b)) + c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) / 4.0
	tmp = 0
	if t_1 <= -5e+276:
		tmp = -(0.25 * a) * b
	elif t_1 <= 1e+206:
		tmp = c + (((z * 0.0625) * t) + (x * y))
	else:
		tmp = (-0.25 * (a * b)) + c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / 4.0)
	tmp = 0.0
	if (t_1 <= -5e+276)
		tmp = Float64(Float64(-Float64(0.25 * a)) * b);
	elseif (t_1 <= 1e+206)
		tmp = Float64(c + Float64(Float64(Float64(z * 0.0625) * t) + Float64(x * y)));
	else
		tmp = Float64(Float64(-0.25 * Float64(a * b)) + c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) / 4.0;
	tmp = 0.0;
	if (t_1 <= -5e+276)
		tmp = -(0.25 * a) * b;
	elseif (t_1 <= 1e+206)
		tmp = c + (((z * 0.0625) * t) + (x * y));
	else
		tmp = (-0.25 * (a * b)) + c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] / 4), $MachinePrecision]}, If[LessEqual[t$95$1, -5000000000000000014339392554976861624351030032307491891786714963455192826951136079841645978666612324808479156564299152005093968192740890223899883592402933027172967020052041660293849107704861024718326980908701245637596009600853559934996040535864898581843704726957456644770889728], N[((-N[(1/4 * a), $MachinePrecision]) * b), $MachinePrecision], If[LessEqual[t$95$1, 100000000000000003889357755108838843130737249295202013334302382007691294289384896763079965607877701387326460311941213291353170611409437561654018367221268940354434586262616943544566455807655946219322240663552], N[(c + N[(N[(N[(z * 1/16), $MachinePrecision] * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1/4 * N[(a * b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -5e276

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \color{blue}{\frac{-1}{4} \cdot a}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \color{blue}{\frac{-1}{4}} \cdot a\right)\right) \]

      5. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      6. lower-+.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      7. lower-+.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      11. lower-*.f64 81.3%

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot \color{blue}{a}\right)\right) \]

   4. Applied rewrites 81.3%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right)} \]

   5. Taylor expanded in a around inf

      \[\leadsto -1 \cdot \left(b \cdot \left(\frac{1}{4} \cdot \color{blue}{a}\right)\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 28.5%

         \[\leadsto -1 \cdot \left(b \cdot \left(\frac{1}{4} \cdot a\right)\right) \]

   7. Applied rewrites 28.5%

      \[\leadsto -1 \cdot \left(b \cdot \left(\frac{1}{4} \cdot \color{blue}{a}\right)\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(\frac{1}{4} \cdot a\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(\frac{1}{4} \cdot a\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(\frac{1}{4} \cdot a\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(\frac{1}{4} \cdot a\right) \cdot b\right) \]

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

         \[\leadsto \left(\mathsf{neg}\left(\frac{1}{4} \cdot a\right)\right) \cdot \color{blue}{b} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{1}{4} \cdot a\right)\right) \cdot \color{blue}{b} \]

      7. lower-neg.f64 28.5%

         \[\leadsto \left(-\frac{1}{4} \cdot a\right) \cdot b \]

   9. Applied rewrites 28.5%

      \[\leadsto \left(-\frac{1}{4} \cdot a\right) \cdot \color{blue}{b} \]

   if -5e276 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 1e206

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto c + \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x \cdot y}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x} \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]

      5. lower-*.f64 73.8%

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 73.8%

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x} \cdot y\right) \]

      2. lift-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]

      3. *-commutative N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(z \cdot t\right) + x \cdot y\right) \]

      4. associate-*l* N/A

         \[\leadsto c + \left(\left(\frac{1}{16} \cdot z\right) \cdot t + \color{blue}{x} \cdot y\right) \]

      5. lower-*.f64 N/A

         \[\leadsto c + \left(\left(\frac{1}{16} \cdot z\right) \cdot t + \color{blue}{x} \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto c + \left(\left(z \cdot \frac{1}{16}\right) \cdot t + x \cdot y\right) \]

      7. lower-*.f64 73.8%

         \[\leadsto c + \left(\left(z \cdot \frac{1}{16}\right) \cdot t + x \cdot y\right) \]

   6. Applied rewrites 73.8%

      \[\leadsto c + \left(\left(z \cdot \frac{1}{16}\right) \cdot t + \color{blue}{x} \cdot y\right) \]

   if 1e206 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(a \cdot b\right)} + c \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{-1}{4} \cdot \color{blue}{\left(a \cdot b\right)} + c \]

      2. lower-*.f64 48.3%

         \[\leadsto \frac{-1}{4} \cdot \left(a \cdot \color{blue}{b}\right) + c \]

   4. Applied rewrites 48.3%

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(a \cdot b\right)} + c \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 85.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq -5000000000000000014339392554976861624351030032307491891786714963455192826951136079841645978666612324808479156564299152005093968192740890223899883592402933027172967020052041660293849107704861024718326980908701245637596009600853559934996040535864898581843704726957456644770889728:\\ \;\;\;\;\left(-\frac{1}{4} \cdot a\right) \cdot b\\ \mathbf{elif}\;t\_1 \leq 100000000000000003889357755108838843130737249295202013334302382007691294289384896763079965607877701387326460311941213291353170611409437561654018367221268940354434586262616943544566455807655946219322240663552:\\ \;\;\;\;c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{4} \cdot \left(a \cdot b\right) + c\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (/ (* a b) 4)))
  (if (<=
       t_1
       -5000000000000000014339392554976861624351030032307491891786714963455192826951136079841645978666612324808479156564299152005093968192740890223899883592402933027172967020052041660293849107704861024718326980908701245637596009600853559934996040535864898581843704726957456644770889728)
    (* (- (* 1/4 a)) b)
    (if (<=
         t_1
         100000000000000003889357755108838843130737249295202013334302382007691294289384896763079965607877701387326460311941213291353170611409437561654018367221268940354434586262616943544566455807655946219322240663552)
      (+ c (+ (* 1/16 (* t z)) (* x y)))
      (+ (* -1/4 (* a b)) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double tmp;
	if (t_1 <= -5e+276) {
		tmp = -(0.25 * a) * b;
	} else if (t_1 <= 1e+206) {
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	} else {
		tmp = (-0.25 * (a * b)) + c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) / 4.0d0
    if (t_1 <= (-5d+276)) then
        tmp = -(0.25d0 * a) * b
    else if (t_1 <= 1d+206) then
        tmp = c + ((0.0625d0 * (t * z)) + (x * y))
    else
        tmp = ((-0.25d0) * (a * b)) + c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double tmp;
	if (t_1 <= -5e+276) {
		tmp = -(0.25 * a) * b;
	} else if (t_1 <= 1e+206) {
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	} else {
		tmp = (-0.25 * (a * b)) + c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) / 4.0
	tmp = 0
	if t_1 <= -5e+276:
		tmp = -(0.25 * a) * b
	elif t_1 <= 1e+206:
		tmp = c + ((0.0625 * (t * z)) + (x * y))
	else:
		tmp = (-0.25 * (a * b)) + c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / 4.0)
	tmp = 0.0
	if (t_1 <= -5e+276)
		tmp = Float64(Float64(-Float64(0.25 * a)) * b);
	elseif (t_1 <= 1e+206)
		tmp = Float64(c + Float64(Float64(0.0625 * Float64(t * z)) + Float64(x * y)));
	else
		tmp = Float64(Float64(-0.25 * Float64(a * b)) + c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) / 4.0;
	tmp = 0.0;
	if (t_1 <= -5e+276)
		tmp = -(0.25 * a) * b;
	elseif (t_1 <= 1e+206)
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	else
		tmp = (-0.25 * (a * b)) + c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] / 4), $MachinePrecision]}, If[LessEqual[t$95$1, -5000000000000000014339392554976861624351030032307491891786714963455192826951136079841645978666612324808479156564299152005093968192740890223899883592402933027172967020052041660293849107704861024718326980908701245637596009600853559934996040535864898581843704726957456644770889728], N[((-N[(1/4 * a), $MachinePrecision]) * b), $MachinePrecision], If[LessEqual[t$95$1, 100000000000000003889357755108838843130737249295202013334302382007691294289384896763079965607877701387326460311941213291353170611409437561654018367221268940354434586262616943544566455807655946219322240663552], N[(c + N[(N[(1/16 * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1/4 * N[(a * b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -5e276

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \color{blue}{\frac{-1}{4} \cdot a}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \color{blue}{\frac{-1}{4}} \cdot a\right)\right) \]

      5. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      6. lower-+.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      7. lower-+.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      11. lower-*.f64 81.3%

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot \color{blue}{a}\right)\right) \]

   4. Applied rewrites 81.3%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right)} \]

   5. Taylor expanded in a around inf

      \[\leadsto -1 \cdot \left(b \cdot \left(\frac{1}{4} \cdot \color{blue}{a}\right)\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 28.5%

         \[\leadsto -1 \cdot \left(b \cdot \left(\frac{1}{4} \cdot a\right)\right) \]

   7. Applied rewrites 28.5%

      \[\leadsto -1 \cdot \left(b \cdot \left(\frac{1}{4} \cdot \color{blue}{a}\right)\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(\frac{1}{4} \cdot a\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(\frac{1}{4} \cdot a\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(\frac{1}{4} \cdot a\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(\frac{1}{4} \cdot a\right) \cdot b\right) \]

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

         \[\leadsto \left(\mathsf{neg}\left(\frac{1}{4} \cdot a\right)\right) \cdot \color{blue}{b} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{1}{4} \cdot a\right)\right) \cdot \color{blue}{b} \]

      7. lower-neg.f64 28.5%

         \[\leadsto \left(-\frac{1}{4} \cdot a\right) \cdot b \]

   9. Applied rewrites 28.5%

      \[\leadsto \left(-\frac{1}{4} \cdot a\right) \cdot \color{blue}{b} \]

   if -5e276 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 1e206

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto c + \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x \cdot y}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x} \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]

      5. lower-*.f64 73.8%

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 73.8%

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   if 1e206 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(a \cdot b\right)} + c \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{-1}{4} \cdot \color{blue}{\left(a \cdot b\right)} + c \]

      2. lower-*.f64 48.3%

         \[\leadsto \frac{-1}{4} \cdot \left(a \cdot \color{blue}{b}\right) + c \]

   4. Applied rewrites 48.3%

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(a \cdot b\right)} + c \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 65.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_1 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -500000000000000022442856339037958392774656:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 50000000000000003758724345825910431373571453217620410674145455117888296262120760233227055054887901771413297751942626316333875200:\\ \;\;\;\;c + \frac{1}{16} \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (+ c (* x y))))
  (if (<= (* x y) -500000000000000022442856339037958392774656)
    t_1
    (if (<=
         (* x y)
         50000000000000003758724345825910431373571453217620410674145455117888296262120760233227055054887901771413297751942626316333875200)
      (+ c (* 1/16 (* t z)))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if ((x * y) <= -5e+41) {
		tmp = t_1;
	} else if ((x * y) <= 5e+127) {
		tmp = c + (0.0625 * (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c + (x * y)
    if ((x * y) <= (-5d+41)) then
        tmp = t_1
    else if ((x * y) <= 5d+127) then
        tmp = c + (0.0625d0 * (t * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if ((x * y) <= -5e+41) {
		tmp = t_1;
	} else if ((x * y) <= 5e+127) {
		tmp = c + (0.0625 * (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	tmp = 0
	if (x * y) <= -5e+41:
		tmp = t_1
	elif (x * y) <= 5e+127:
		tmp = c + (0.0625 * (t * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -5e+41)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+127)
		tmp = Float64(c + Float64(0.0625 * Float64(t * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -5e+41)
		tmp = t_1;
	elseif ((x * y) <= 5e+127)
		tmp = c + (0.0625 * (t * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -500000000000000022442856339037958392774656], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 50000000000000003758724345825910431373571453217620410674145455117888296262120760233227055054887901771413297751942626316333875200], N[(c + N[(1/16 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5.0000000000000002e41 or 5.0000000000000004e127 < (*.f64 x y)

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto c + \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x \cdot y}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x} \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]

      5. lower-*.f64 73.8%

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 73.8%

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto c + \color{blue}{x \cdot y} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto c + x \cdot \color{blue}{y} \]

      2. lower-*.f64 48.6%

         \[\leadsto c + x \cdot y \]

   7. Applied rewrites 48.6%

      \[\leadsto c + \color{blue}{x \cdot y} \]

   if -5.0000000000000002e41 < (*.f64 x y) < 5.0000000000000004e127

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto c + \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x \cdot y}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x} \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]

      5. lower-*.f64 73.8%

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 73.8%

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto c + \color{blue}{\frac{1}{16} \cdot \left(t \cdot z\right)} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto c + \frac{1}{16} \cdot \color{blue}{\left(t \cdot z\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto c + \frac{1}{16} \cdot \left(t \cdot \color{blue}{z}\right) \]

      3. lower-*.f64 48.4%

         \[\leadsto c + \frac{1}{16} \cdot \left(t \cdot z\right) \]

   7. Applied rewrites 48.4%

      \[\leadsto c + \color{blue}{\frac{1}{16} \cdot \left(t \cdot z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 63.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ t_2 := -\frac{-1}{16} \cdot \left(t \cdot z\right)\\ \mathbf{if}\;t\_1 \leq -499999999999999976986103364828435105866493856869550354915370776598145356642472906604169238853083206186863000925026831505293584046586944536955141361661791768572429254787072:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 1000000000000000068957567536844582937679826098352437099093782830596656320642208754566186799616905285426599982929417458880300383900478261195703581718577367397759832385751351296:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (/ (* z t) 16)) (t_2 (- (* -1/16 (* t z)))))
  (if (<=
       t_1
       -499999999999999976986103364828435105866493856869550354915370776598145356642472906604169238853083206186863000925026831505293584046586944536955141361661791768572429254787072)
    t_2
    (if (<=
         t_1
         1000000000000000068957567536844582937679826098352437099093782830596656320642208754566186799616905285426599982929417458880300383900478261195703581718577367397759832385751351296)
      (+ c (* x y))
      t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) / 16.0;
	double t_2 = -(-0.0625 * (t * z));
	double tmp;
	if (t_1 <= -5e+170) {
		tmp = t_2;
	} else if (t_1 <= 1e+174) {
		tmp = c + (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * t) / 16.0d0
    t_2 = -((-0.0625d0) * (t * z))
    if (t_1 <= (-5d+170)) then
        tmp = t_2
    else if (t_1 <= 1d+174) then
        tmp = c + (x * y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) / 16.0;
	double t_2 = -(-0.0625 * (t * z));
	double tmp;
	if (t_1 <= -5e+170) {
		tmp = t_2;
	} else if (t_1 <= 1e+174) {
		tmp = c + (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (z * t) / 16.0
	t_2 = -(-0.0625 * (t * z))
	tmp = 0
	if t_1 <= -5e+170:
		tmp = t_2
	elif t_1 <= 1e+174:
		tmp = c + (x * y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(z * t) / 16.0)
	t_2 = Float64(-Float64(-0.0625 * Float64(t * z)))
	tmp = 0.0
	if (t_1 <= -5e+170)
		tmp = t_2;
	elseif (t_1 <= 1e+174)
		tmp = Float64(c + Float64(x * y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (z * t) / 16.0;
	t_2 = -(-0.0625 * (t * z));
	tmp = 0.0;
	if (t_1 <= -5e+170)
		tmp = t_2;
	elseif (t_1 <= 1e+174)
		tmp = c + (x * y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] / 16), $MachinePrecision]}, Block[{t$95$2 = (-N[(-1/16 * N[(t * z), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[t$95$1, -499999999999999976986103364828435105866493856869550354915370776598145356642472906604169238853083206186863000925026831505293584046586944536955141361661791768572429254787072], t$95$2, If[LessEqual[t$95$1, 1000000000000000068957567536844582937679826098352437099093782830596656320642208754566186799616905285426599982929417458880300383900478261195703581718577367397759832385751351296], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -4.9999999999999998e170 or 1.0000000000000001e174 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \color{blue}{\frac{-1}{4} \cdot a}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \color{blue}{\frac{-1}{4}} \cdot a\right)\right) \]

      5. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      6. lower-+.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      7. lower-+.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

      11. lower-*.f64 81.3%

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot \color{blue}{a}\right)\right) \]

   4. Applied rewrites 81.3%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right)} \]

   5. Taylor expanded in c around inf

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{c}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 21.8%

         \[\leadsto -1 \cdot \left(-1 \cdot c\right) \]

   7. Applied rewrites 21.8%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{c}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(-1 \cdot c\right) \]

      3. lower-neg.f64 21.8%

         \[\leadsto --1 \cdot c \]

      4. lift-*.f64 N/A

         \[\leadsto --1 \cdot c \]

      5. mul-1-neg N/A

         \[\leadsto -\left(\mathsf{neg}\left(c\right)\right) \]

      6. lower-neg.f64 21.8%

         \[\leadsto -\left(-c\right) \]

   9. Applied rewrites 21.8%

      \[\leadsto -\left(-c\right) \]

   10. Taylor expanded in z around inf

       \[\leadsto -\frac{-1}{16} \cdot \left(t \cdot z\right) \]
   11. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto -\frac{-1}{16} \cdot \left(t \cdot z\right) \]

       2. lower-*.f64 28.7%

          \[\leadsto -\frac{-1}{16} \cdot \left(t \cdot z\right) \]

   12. Applied rewrites 28.7%

       \[\leadsto -\frac{-1}{16} \cdot \left(t \cdot z\right) \]

   if -4.9999999999999998e170 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 1.0000000000000001e174

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto c + \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x \cdot y}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x} \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]

      5. lower-*.f64 73.8%

         \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 73.8%

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto c + \color{blue}{x \cdot y} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto c + x \cdot \color{blue}{y} \]

      2. lower-*.f64 48.6%

         \[\leadsto c + x \cdot y \]

   7. Applied rewrites 48.6%

      \[\leadsto c + \color{blue}{x \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 48.6% accurate, 5.2× speedup

Math

\[c + x \cdot y \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (+ c (* x y)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + (x * y);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = c + (x * y)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + (x * y);
}

Python

def code(x, y, z, t, a, b, c):
	return c + (x * y)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(c + Float64(x * y))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = c + (x * y);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.5%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

2. Taylor expanded in a around 0

   \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
3. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto c + \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   2. lower-+.f64 N/A

      \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x \cdot y}\right) \]

   3. lower-*.f64 N/A

      \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{x} \cdot y\right) \]

   4. lower-*.f64 N/A

      \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]

   5. lower-*.f64 73.8%

      \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

4. Applied rewrites 73.8%

   \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

5. Taylor expanded in z around 0

   \[\leadsto c + \color{blue}{x \cdot y} \]
6. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto c + x \cdot \color{blue}{y} \]

   2. lower-*.f64 48.6%

      \[\leadsto c + x \cdot y \]

7. Applied rewrites 48.6%

   \[\leadsto c + \color{blue}{x \cdot y} \]
8. Add Preprocessing

Alternative 9: 21.8% accurate, 9.4× speedup

Math

\[-\left(-c\right) \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (- (- c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return -(-c);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = -(-c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return -(-c);
}

Python

def code(x, y, z, t, a, b, c):
	return -(-c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(-Float64(-c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = -(-c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := (-(-c))

Derivation

1. Initial program 97.5%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

2. Taylor expanded in b around -inf

   \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right)} \]

   2. lower-*.f64 N/A

      \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)}\right) \]

   3. lower--.f64 N/A

      \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \color{blue}{\frac{-1}{4} \cdot a}\right)\right) \]

   4. lower-*.f64 N/A

      \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \color{blue}{\frac{-1}{4}} \cdot a\right)\right) \]

   5. lower-/.f64 N/A

      \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

   6. lower-+.f64 N/A

      \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

   7. lower-+.f64 N/A

      \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

   8. lower-*.f64 N/A

      \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

   9. lower-*.f64 N/A

      \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

   10. lower-*.f64 N/A

       \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right) \]

   11. lower-*.f64 81.3%

       \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot \color{blue}{a}\right)\right) \]

4. Applied rewrites 81.3%

   \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right)} \]

5. Taylor expanded in c around inf

   \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{c}\right) \]
6. Step-by-step derivation

   1. lower-*.f64 21.8%

      \[\leadsto -1 \cdot \left(-1 \cdot c\right) \]

7. Applied rewrites 21.8%

   \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{c}\right) \]
8. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot c\right)} \]

   2. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(-1 \cdot c\right) \]

   3. lower-neg.f64 21.8%

      \[\leadsto --1 \cdot c \]

   4. lift-*.f64 N/A

      \[\leadsto --1 \cdot c \]

   5. mul-1-neg N/A

      \[\leadsto -\left(\mathsf{neg}\left(c\right)\right) \]

   6. lower-neg.f64 21.8%

      \[\leadsto -\left(-c\right) \]

9. Applied rewrites 21.8%

   \[\leadsto -\left(-c\right) \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16)) (/ (* a b) 4)) c))