Linear.V4:$cdot from linear-1.19.1.3, C

Percentage Accurate: 95.6% → 97.0%

Time: 15.9s

Alternatives: 11

Speedup: 0.5×

• 58.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + t \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
  (if (<= t_1 INFINITY) t_1 (+ (* c i) (* t z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((x * y) + (z * t)) + (a * b)) + (c * i);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (c * i) + (t * z);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((x * y) + (z * t)) + (a * b)) + (c * i);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (c * i) + (t * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (((x * y) + (z * t)) + (a * b)) + (c * i)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (c * i) + (t * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) + Float64(a * b)) + Float64(c * i))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(c * i) + Float64(t * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (((x * y) + (z * t)) + (a * b)) + (c * i);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (c * i) + (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(c * i), $MachinePrecision] + N[(t * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i)) < +inf.0

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   if +inf.0 < (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto c \cdot i + t \cdot \color{blue}{z} \]
   6. Step-by-step derivation

      1. lower-*.f64 51.6%

         \[\leadsto c \cdot i + t \cdot z \]

   7. Applied rewrites 51.6%

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

Alternative 2: 87.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \cdot t \leq -10000000000000000155594161294668430242682013969210614333697705804308337811647557032649853899150474476762062808678400:\\ \;\;\;\;\left(t \cdot z + a \cdot b\right) + c \cdot i\\ \mathbf{elif}\;z \cdot t \leq 10000000000:\\ \;\;\;\;\left(a \cdot b + x \cdot y\right) + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(t \cdot z + x \cdot y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (if (<=
     (* z t)
     -10000000000000000155594161294668430242682013969210614333697705804308337811647557032649853899150474476762062808678400)
  (+ (+ (* t z) (* a b)) (* c i))
  (if (<= (* z t) 10000000000)
    (+ (+ (* a b) (* x y)) (* c i))
    (+ (* c i) (+ (* t z) (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -1e+115) {
		tmp = ((t * z) + (a * b)) + (c * i);
	} else if ((z * t) <= 10000000000.0) {
		tmp = ((a * b) + (x * y)) + (c * i);
	} else {
		tmp = (c * i) + ((t * z) + (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, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z * t) <= (-1d+115)) then
        tmp = ((t * z) + (a * b)) + (c * i)
    else if ((z * t) <= 10000000000.0d0) then
        tmp = ((a * b) + (x * y)) + (c * i)
    else
        tmp = (c * i) + ((t * z) + (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 i) {
	double tmp;
	if ((z * t) <= -1e+115) {
		tmp = ((t * z) + (a * b)) + (c * i);
	} else if ((z * t) <= 10000000000.0) {
		tmp = ((a * b) + (x * y)) + (c * i);
	} else {
		tmp = (c * i) + ((t * z) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z * t) <= -1e+115:
		tmp = ((t * z) + (a * b)) + (c * i)
	elif (z * t) <= 10000000000.0:
		tmp = ((a * b) + (x * y)) + (c * i)
	else:
		tmp = (c * i) + ((t * z) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -1e+115)
		tmp = Float64(Float64(Float64(t * z) + Float64(a * b)) + Float64(c * i));
	elseif (Float64(z * t) <= 10000000000.0)
		tmp = Float64(Float64(Float64(a * b) + Float64(x * y)) + Float64(c * i));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(t * z) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z * t) <= -1e+115)
		tmp = ((t * z) + (a * b)) + (c * i);
	elseif ((z * t) <= 10000000000.0)
		tmp = ((a * b) + (x * y)) + (c * i);
	else
		tmp = (c * i) + ((t * z) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -10000000000000000155594161294668430242682013969210614333697705804308337811647557032649853899150474476762062808678400], N[(N[(N[(t * z), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 10000000000], N[(N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(t * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1e115

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 74.0%

         \[\leadsto \left(t \cdot \color{blue}{z} + a \cdot b\right) + c \cdot i \]

   4. Applied rewrites 74.0%

      \[\leadsto \left(\color{blue}{t \cdot z} + a \cdot b\right) + c \cdot i \]

   if -1e115 < (*.f64 z t) < 1e10

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   if 1e10 < (*.f64 z t)

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

Alternative 3: 86.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := c \cdot i + \left(t \cdot z + x \cdot y\right)\\ \mathbf{if}\;z \cdot t \leq -10000000000000000155594161294668430242682013969210614333697705804308337811647557032649853899150474476762062808678400:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 10000000000:\\ \;\;\;\;\left(a \cdot b + x \cdot y\right) + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (+ (* c i) (+ (* t z) (* x y)))))
  (if (<=
       (* z t)
       -10000000000000000155594161294668430242682013969210614333697705804308337811647557032649853899150474476762062808678400)
    t_1
    (if (<= (* z t) 10000000000)
      (+ (+ (* a b) (* x y)) (* c i))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + ((t * z) + (x * y));
	double tmp;
	if ((z * t) <= -1e+115) {
		tmp = t_1;
	} else if ((z * t) <= 10000000000.0) {
		tmp = ((a * b) + (x * y)) + (c * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * i) + ((t * z) + (x * y))
    if ((z * t) <= (-1d+115)) then
        tmp = t_1
    else if ((z * t) <= 10000000000.0d0) then
        tmp = ((a * b) + (x * y)) + (c * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + ((t * z) + (x * y));
	double tmp;
	if ((z * t) <= -1e+115) {
		tmp = t_1;
	} else if ((z * t) <= 10000000000.0) {
		tmp = ((a * b) + (x * y)) + (c * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + ((t * z) + (x * y))
	tmp = 0
	if (z * t) <= -1e+115:
		tmp = t_1
	elif (z * t) <= 10000000000.0:
		tmp = ((a * b) + (x * y)) + (c * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(Float64(t * z) + Float64(x * y)))
	tmp = 0.0
	if (Float64(z * t) <= -1e+115)
		tmp = t_1;
	elseif (Float64(z * t) <= 10000000000.0)
		tmp = Float64(Float64(Float64(a * b) + Float64(x * y)) + Float64(c * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + ((t * z) + (x * y));
	tmp = 0.0;
	if ((z * t) <= -1e+115)
		tmp = t_1;
	elseif ((z * t) <= 10000000000.0)
		tmp = ((a * b) + (x * y)) + (c * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(N[(t * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -10000000000000000155594161294668430242682013969210614333697705804308337811647557032649853899150474476762062808678400], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 10000000000], N[(N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1e115 or 1e10 < (*.f64 z t)

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   if -1e115 < (*.f64 z t) < 1e10

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

Alternative 4: 81.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := c \cdot i + \left(t \cdot z + x \cdot y\right)\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;t\_2 \leq -999999999999999926539781176481198923508803215199467887262646419780362305536:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2000000000000000000:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (+ (* c i) (+ (* t z) (* x y))))
       (t_2 (+ (* x y) (* z t))))
  (if (<=
       t_2
       -999999999999999926539781176481198923508803215199467887262646419780362305536)
    t_1
    (if (<= t_2 2000000000000000000) (+ (* a b) (* c i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + ((t * z) + (x * y));
	double t_2 = (x * y) + (z * t);
	double tmp;
	if (t_2 <= -1e+75) {
		tmp = t_1;
	} else if (t_2 <= 2e+18) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * i) + ((t * z) + (x * y))
    t_2 = (x * y) + (z * t)
    if (t_2 <= (-1d+75)) then
        tmp = t_1
    else if (t_2 <= 2d+18) then
        tmp = (a * b) + (c * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + ((t * z) + (x * y));
	double t_2 = (x * y) + (z * t);
	double tmp;
	if (t_2 <= -1e+75) {
		tmp = t_1;
	} else if (t_2 <= 2e+18) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + ((t * z) + (x * y))
	t_2 = (x * y) + (z * t)
	tmp = 0
	if t_2 <= -1e+75:
		tmp = t_1
	elif t_2 <= 2e+18:
		tmp = (a * b) + (c * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(Float64(t * z) + Float64(x * y)))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (t_2 <= -1e+75)
		tmp = t_1;
	elseif (t_2 <= 2e+18)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + ((t * z) + (x * y));
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if (t_2 <= -1e+75)
		tmp = t_1;
	elseif (t_2 <= 2e+18)
		tmp = (a * b) + (c * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(N[(t * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -999999999999999926539781176481198923508803215199467887262646419780362305536], t$95$1, If[LessEqual[t$95$2, 2000000000000000000], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (*.f64 z t)) < -9.9999999999999993e74 or 2e18 < (+.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   if -9.9999999999999993e74 < (+.f64 (*.f64 x y) (*.f64 z t)) < 2e18

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto a \cdot \color{blue}{b} + c \cdot i \]
   6. Step-by-step derivation

      1. lower-*.f64 51.6%

         \[\leadsto a \cdot b + c \cdot i \]

   7. Applied rewrites 51.6%

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

Alternative 5: 66.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := c \cdot i + t \cdot z\\ \mathbf{if}\;z \cdot t \leq -999999999999999967336168804116691273849533185806555472917961779471295845921727862608739868455469056:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 4000000000000000000000:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (+ (* c i) (* t z))))
  (if (<=
       (* z t)
       -999999999999999967336168804116691273849533185806555472917961779471295845921727862608739868455469056)
    t_1
    (if (<= (* z t) 4000000000000000000000) (+ (* a b) (* c i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (t * z);
	double tmp;
	if ((z * t) <= -1e+99) {
		tmp = t_1;
	} else if ((z * t) <= 4e+21) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * i) + (t * z)
    if ((z * t) <= (-1d+99)) then
        tmp = t_1
    else if ((z * t) <= 4d+21) then
        tmp = (a * b) + (c * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (t * z);
	double tmp;
	if ((z * t) <= -1e+99) {
		tmp = t_1;
	} else if ((z * t) <= 4e+21) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (t * z)
	tmp = 0
	if (z * t) <= -1e+99:
		tmp = t_1
	elif (z * t) <= 4e+21:
		tmp = (a * b) + (c * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(t * z))
	tmp = 0.0
	if (Float64(z * t) <= -1e+99)
		tmp = t_1;
	elseif (Float64(z * t) <= 4e+21)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (t * z);
	tmp = 0.0;
	if ((z * t) <= -1e+99)
		tmp = t_1;
	elseif ((z * t) <= 4e+21)
		tmp = (a * b) + (c * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -999999999999999967336168804116691273849533185806555472917961779471295845921727862608739868455469056], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 4000000000000000000000], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -9.9999999999999997e98 or 4e21 < (*.f64 z t)

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto c \cdot i + t \cdot \color{blue}{z} \]
   6. Step-by-step derivation

      1. lower-*.f64 51.6%

         \[\leadsto c \cdot i + t \cdot z \]

   7. Applied rewrites 51.6%

      \[\leadsto c \cdot i + t \cdot \color{blue}{z} \]

   if -9.9999999999999997e98 < (*.f64 z t) < 4e21

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto a \cdot \color{blue}{b} + c \cdot i \]
   6. Step-by-step derivation

      1. lower-*.f64 51.6%

         \[\leadsto a \cdot b + c \cdot i \]

   7. Applied rewrites 51.6%

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

Alternative 6: 65.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := c \cdot i + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -20000000000000000746818674942919779438786551508983640762055460820756010161342994202757226742842252830104798058684384018432:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 500000000000000021688648487309593036645146662475969655895886894668058406444840555470661877760:\\ \;\;\;\;c \cdot i + t \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (+ (* c i) (* x y))))
  (if (<=
       (* x y)
       -20000000000000000746818674942919779438786551508983640762055460820756010161342994202757226742842252830104798058684384018432)
    t_1
    (if (<=
         (* x y)
         500000000000000021688648487309593036645146662475969655895886894668058406444840555470661877760)
      (+ (* c i) (* t z))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (x * y);
	double tmp;
	if ((x * y) <= -2e+121) {
		tmp = t_1;
	} else if ((x * y) <= 5e+92) {
		tmp = (c * i) + (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, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * i) + (x * y)
    if ((x * y) <= (-2d+121)) then
        tmp = t_1
    else if ((x * y) <= 5d+92) then
        tmp = (c * i) + (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 i) {
	double t_1 = (c * i) + (x * y);
	double tmp;
	if ((x * y) <= -2e+121) {
		tmp = t_1;
	} else if ((x * y) <= 5e+92) {
		tmp = (c * i) + (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (x * y)
	tmp = 0
	if (x * y) <= -2e+121:
		tmp = t_1
	elif (x * y) <= 5e+92:
		tmp = (c * i) + (t * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -2e+121)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+92)
		tmp = Float64(Float64(c * i) + Float64(t * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (x * y);
	tmp = 0.0;
	if ((x * y) <= -2e+121)
		tmp = t_1;
	elseif ((x * y) <= 5e+92)
		tmp = (c * i) + (t * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -20000000000000000746818674942919779438786551508983640762055460820756010161342994202757226742842252830104798058684384018432], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 500000000000000021688648487309593036645146662475969655895886894668058406444840555470661877760], N[(N[(c * i), $MachinePrecision] + N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.0000000000000001e121 or 5.0000000000000002e92 < (*.f64 x y)

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 51.6%

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

   7. Applied rewrites 51.6%

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

   if -2.0000000000000001e121 < (*.f64 x y) < 5.0000000000000002e92

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto c \cdot i + t \cdot \color{blue}{z} \]
   6. Step-by-step derivation

      1. lower-*.f64 51.6%

         \[\leadsto c \cdot i + t \cdot z \]

   7. Applied rewrites 51.6%

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

Alternative 7: 62.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \cdot t \leq -4000000000000000396608112211993636047680809368650861178353581203006168799918134949639116303462911015707277439406485982346309347056090621591337191498862248353306677366521117116231777349377083535451521648143853612748964240337695861270954300912430284275712:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;z \cdot t \leq 10000000000000000466018071748206975684050858099493768614209804580186827813230862995727677122141957123210339765959854898653172616660068980913606220974926434405874301273673162218994872058950552383264597357715602427843549593600:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (if (<=
     (* z t)
     -4000000000000000396608112211993636047680809368650861178353581203006168799918134949639116303462911015707277439406485982346309347056090621591337191498862248353306677366521117116231777349377083535451521648143853612748964240337695861270954300912430284275712)
  (* t z)
  (if (<=
       (* z t)
       10000000000000000466018071748206975684050858099493768614209804580186827813230862995727677122141957123210339765959854898653172616660068980913606220974926434405874301273673162218994872058950552383264597357715602427843549593600)
    (+ (* c i) (* x y))
    (* t z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -4e+252) {
		tmp = t * z;
	} else if ((z * t) <= 1e+223) {
		tmp = (c * i) + (x * y);
	} else {
		tmp = t * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z * t) <= (-4d+252)) then
        tmp = t * z
    else if ((z * t) <= 1d+223) then
        tmp = (c * i) + (x * y)
    else
        tmp = t * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -4e+252) {
		tmp = t * z;
	} else if ((z * t) <= 1e+223) {
		tmp = (c * i) + (x * y);
	} else {
		tmp = t * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z * t) <= -4e+252:
		tmp = t * z
	elif (z * t) <= 1e+223:
		tmp = (c * i) + (x * y)
	else:
		tmp = t * z
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -4e+252)
		tmp = Float64(t * z);
	elseif (Float64(z * t) <= 1e+223)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	else
		tmp = Float64(t * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z * t) <= -4e+252)
		tmp = t * z;
	elseif ((z * t) <= 1e+223)
		tmp = (c * i) + (x * y);
	else
		tmp = t * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -4000000000000000396608112211993636047680809368650861178353581203006168799918134949639116303462911015707277439406485982346309347056090621591337191498862248353306677366521117116231777349377083535451521648143853612748964240337695861270954300912430284275712], N[(t * z), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 10000000000000000466018071748206975684050858099493768614209804580186827813230862995727677122141957123210339765959854898653172616660068980913606220974926434405874301273673162218994872058950552383264597357715602427843549593600], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(t * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.0000000000000004e252 or 1e223 < (*.f64 z t)

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 51.6%

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

   7. Applied rewrites 51.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto c \cdot i \]
   9. Step-by-step derivation

      1. lower-*.f64 28.0%

         \[\leadsto c \cdot i \]

   10. Applied rewrites 28.0%

       \[\leadsto c \cdot i \]

   11. Taylor expanded in z around inf

       \[\leadsto t \cdot \color{blue}{z} \]
   12. Step-by-step derivation

       1. lower-*.f64 27.2%

          \[\leadsto t \cdot z \]

   13. Applied rewrites 27.2%

       \[\leadsto t \cdot \color{blue}{z} \]

   if -4.0000000000000004e252 < (*.f64 z t) < 1e223

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 51.6%

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

   7. Applied rewrites 51.6%

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

Alternative 8: 43.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;c \cdot i \leq -999999999999999998217443564185241415988928868759412500436543339729940401905904649497115766142268560009777175966751665376232210432:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq \frac{-253}{25300281663413827294061918339864663381194581220517764794612669753428792445999418361495047962679640561898384733039601488923726092173224184608376674992592313740189678034570795170558363467761652042654970959809093133570250935428086587327262919456144944542601257064044846194041676826903812816523290938580750782913463467636686848}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;c \cdot i \leq \frac{5255931591500769}{583992399055640987986069965529637289586333248927815671114136642291107221402710705472756839848623539171666215625420084135768154204336056063776340648924443416096255318318113913610607896607565283328}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq \frac{5981525981032121}{166153499473114484112975882535043072}:\\ \;\;\;\;-\left(-y\right) \cdot x\\ \mathbf{elif}\;c \cdot i \leq 1299999999999999967733223573514609746608608365174467094904635413122985441295687860405609026104539524614751916574900224:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (if (<=
     (* c i)
     -999999999999999998217443564185241415988928868759412500436543339729940401905904649497115766142268560009777175966751665376232210432)
  (* c i)
  (if (<=
       (* c i)
       -253/25300281663413827294061918339864663381194581220517764794612669753428792445999418361495047962679640561898384733039601488923726092173224184608376674992592313740189678034570795170558363467761652042654970959809093133570250935428086587327262919456144944542601257064044846194041676826903812816523290938580750782913463467636686848)
    (* t z)
    (if (<=
         (* c i)
         5255931591500769/583992399055640987986069965529637289586333248927815671114136642291107221402710705472756839848623539171666215625420084135768154204336056063776340648924443416096255318318113913610607896607565283328)
      (* a b)
      (if (<=
           (* c i)
           5981525981032121/166153499473114484112975882535043072)
        (- (* (- y) x))
        (if (<=
             (* c i)
             1299999999999999967733223573514609746608608365174467094904635413122985441295687860405609026104539524614751916574900224)
          (* a b)
          (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1e+129) {
		tmp = c * i;
	} else if ((c * i) <= -1e-320) {
		tmp = t * z;
	} else if ((c * i) <= 9e-180) {
		tmp = a * b;
	} else if ((c * i) <= 3.6e-20) {
		tmp = -(-y * x);
	} else if ((c * i) <= 1.3e+117) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-1d+129)) then
        tmp = c * i
    else if ((c * i) <= (-1d-320)) then
        tmp = t * z
    else if ((c * i) <= 9d-180) then
        tmp = a * b
    else if ((c * i) <= 3.6d-20) then
        tmp = -(-y * x)
    else if ((c * i) <= 1.3d+117) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1e+129) {
		tmp = c * i;
	} else if ((c * i) <= -1e-320) {
		tmp = t * z;
	} else if ((c * i) <= 9e-180) {
		tmp = a * b;
	} else if ((c * i) <= 3.6e-20) {
		tmp = -(-y * x);
	} else if ((c * i) <= 1.3e+117) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1e+129:
		tmp = c * i
	elif (c * i) <= -1e-320:
		tmp = t * z
	elif (c * i) <= 9e-180:
		tmp = a * b
	elif (c * i) <= 3.6e-20:
		tmp = -(-y * x)
	elif (c * i) <= 1.3e+117:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1e+129)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -1e-320)
		tmp = Float64(t * z);
	elseif (Float64(c * i) <= 9e-180)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 3.6e-20)
		tmp = Float64(-Float64(Float64(-y) * x));
	elseif (Float64(c * i) <= 1.3e+117)
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -1e+129)
		tmp = c * i;
	elseif ((c * i) <= -1e-320)
		tmp = t * z;
	elseif ((c * i) <= 9e-180)
		tmp = a * b;
	elseif ((c * i) <= 3.6e-20)
		tmp = -(-y * x);
	elseif ((c * i) <= 1.3e+117)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -999999999999999998217443564185241415988928868759412500436543339729940401905904649497115766142268560009777175966751665376232210432], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -253/25300281663413827294061918339864663381194581220517764794612669753428792445999418361495047962679640561898384733039601488923726092173224184608376674992592313740189678034570795170558363467761652042654970959809093133570250935428086587327262919456144944542601257064044846194041676826903812816523290938580750782913463467636686848], N[(t * z), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5255931591500769/583992399055640987986069965529637289586333248927815671114136642291107221402710705472756839848623539171666215625420084135768154204336056063776340648924443416096255318318113913610607896607565283328], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5981525981032121/166153499473114484112975882535043072], (-N[((-y) * x), $MachinePrecision]), If[LessEqual[N[(c * i), $MachinePrecision], 1299999999999999967733223573514609746608608365174467094904635413122985441295687860405609026104539524614751916574900224], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -1e129 or 1.3e117 < (*.f64 c i)

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 51.6%

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

   7. Applied rewrites 51.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto c \cdot i \]
   9. Step-by-step derivation

      1. lower-*.f64 28.0%

         \[\leadsto c \cdot i \]

   10. Applied rewrites 28.0%

       \[\leadsto c \cdot i \]

   if -1e129 < (*.f64 c i) < -9.9998886718268301e-321

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 51.6%

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

   7. Applied rewrites 51.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto c \cdot i \]
   9. Step-by-step derivation

      1. lower-*.f64 28.0%

         \[\leadsto c \cdot i \]

   10. Applied rewrites 28.0%

       \[\leadsto c \cdot i \]

   11. Taylor expanded in z around inf

       \[\leadsto t \cdot \color{blue}{z} \]
   12. Step-by-step derivation

       1. lower-*.f64 27.2%

          \[\leadsto t \cdot z \]

   13. Applied rewrites 27.2%

       \[\leadsto t \cdot \color{blue}{z} \]

   if -9.9998886718268301e-321 < (*.f64 c i) < 9.0000000000000002e-180 or 3.5999999999999997e-20 < (*.f64 c i) < 1.3e117

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 51.6%

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

   7. Applied rewrites 51.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto c \cdot i \]
   9. Step-by-step derivation

      1. lower-*.f64 28.0%

         \[\leadsto c \cdot i \]

   10. Applied rewrites 28.0%

       \[\leadsto c \cdot i \]

   11. Taylor expanded in a around inf

       \[\leadsto \color{blue}{a \cdot b} \]
   12. Step-by-step derivation

       1. lower-*.f64 27.4%

          \[\leadsto a \cdot \color{blue}{b} \]

   13. Applied rewrites 27.4%

       \[\leadsto \color{blue}{a \cdot b} \]

   if 9.0000000000000002e-180 < (*.f64 c i) < 3.5999999999999997e-20

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 83.7%

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

   4. Applied rewrites 83.7%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 27.4%

         \[\leadsto -1 \cdot \left(-1 \cdot \left(a \cdot b\right)\right) \]

   7. Applied rewrites 27.4%

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

   8. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 27.2%

         \[\leadsto -1 \cdot \left(-1 \cdot \left(x \cdot y\right)\right) \]

   10. Applied rewrites 27.2%

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

       1. lift-*.f64 N/A

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

       2. mul-1-neg N/A

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

       3. lower-neg.f64 27.2%

          \[\leadsto --1 \cdot \left(x \cdot y\right) \]

       4. lift-*.f64 N/A

          \[\leadsto --1 \cdot \left(x \cdot y\right) \]

       5. lift-*.f64 N/A

          \[\leadsto --1 \cdot \left(x \cdot y\right) \]

       6. mul-1-neg N/A

          \[\leadsto -\left(\mathsf{neg}\left(x \cdot y\right)\right) \]

       7. *-commutative N/A

          \[\leadsto -\left(\mathsf{neg}\left(y \cdot x\right)\right) \]

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

          \[\leadsto -\left(\mathsf{neg}\left(y\right)\right) \cdot x \]

       9. lower-*.f64 N/A

          \[\leadsto -\left(\mathsf{neg}\left(y\right)\right) \cdot x \]

       10. lower-neg.f64 27.2%

           \[\leadsto -\left(-y\right) \cdot x \]

   12. Applied rewrites 27.2%

       \[\leadsto -\left(-y\right) \cdot x \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 9: 43.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;c \cdot i \leq -999999999999999998217443564185241415988928868759412500436543339729940401905904649497115766142268560009777175966751665376232210432:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq \frac{4530655075725799}{730750818665451459101842416358141509827966271488}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;c \cdot i \leq 1299999999999999967733223573514609746608608365174467094904635413122985441295687860405609026104539524614751916574900224:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (if (<=
     (* c i)
     -999999999999999998217443564185241415988928868759412500436543339729940401905904649497115766142268560009777175966751665376232210432)
  (* c i)
  (if (<=
       (* c i)
       4530655075725799/730750818665451459101842416358141509827966271488)
    (* t z)
    (if (<=
         (* c i)
         1299999999999999967733223573514609746608608365174467094904635413122985441295687860405609026104539524614751916574900224)
      (* a b)
      (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1e+129) {
		tmp = c * i;
	} else if ((c * i) <= 6.2e-33) {
		tmp = t * z;
	} else if ((c * i) <= 1.3e+117) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-1d+129)) then
        tmp = c * i
    else if ((c * i) <= 6.2d-33) then
        tmp = t * z
    else if ((c * i) <= 1.3d+117) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1e+129) {
		tmp = c * i;
	} else if ((c * i) <= 6.2e-33) {
		tmp = t * z;
	} else if ((c * i) <= 1.3e+117) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1e+129:
		tmp = c * i
	elif (c * i) <= 6.2e-33:
		tmp = t * z
	elif (c * i) <= 1.3e+117:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1e+129)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 6.2e-33)
		tmp = Float64(t * z);
	elseif (Float64(c * i) <= 1.3e+117)
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -1e+129)
		tmp = c * i;
	elseif ((c * i) <= 6.2e-33)
		tmp = t * z;
	elseif ((c * i) <= 1.3e+117)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -999999999999999998217443564185241415988928868759412500436543339729940401905904649497115766142268560009777175966751665376232210432], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4530655075725799/730750818665451459101842416358141509827966271488], N[(t * z), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1299999999999999967733223573514609746608608365174467094904635413122985441295687860405609026104539524614751916574900224], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1e129 or 1.3e117 < (*.f64 c i)

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 51.6%

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

   7. Applied rewrites 51.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto c \cdot i \]
   9. Step-by-step derivation

      1. lower-*.f64 28.0%

         \[\leadsto c \cdot i \]

   10. Applied rewrites 28.0%

       \[\leadsto c \cdot i \]

   if -1e129 < (*.f64 c i) < 6.1999999999999999e-33

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 51.6%

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

   7. Applied rewrites 51.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto c \cdot i \]
   9. Step-by-step derivation

      1. lower-*.f64 28.0%

         \[\leadsto c \cdot i \]

   10. Applied rewrites 28.0%

       \[\leadsto c \cdot i \]

   11. Taylor expanded in z around inf

       \[\leadsto t \cdot \color{blue}{z} \]
   12. Step-by-step derivation

       1. lower-*.f64 27.2%

          \[\leadsto t \cdot z \]

   13. Applied rewrites 27.2%

       \[\leadsto t \cdot \color{blue}{z} \]

   if 6.1999999999999999e-33 < (*.f64 c i) < 1.3e117

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 51.6%

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

   7. Applied rewrites 51.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto c \cdot i \]
   9. Step-by-step derivation

      1. lower-*.f64 28.0%

         \[\leadsto c \cdot i \]

   10. Applied rewrites 28.0%

       \[\leadsto c \cdot i \]

   11. Taylor expanded in a around inf

       \[\leadsto \color{blue}{a \cdot b} \]
   12. Step-by-step derivation

       1. lower-*.f64 27.4%

          \[\leadsto a \cdot \color{blue}{b} \]

   13. Applied rewrites 27.4%

       \[\leadsto \color{blue}{a \cdot b} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 42.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;c \cdot i \leq -999999999999999998217443564185241415988928868759412500436543339729940401905904649497115766142268560009777175966751665376232210432:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 10500000000000000641853867875909401765417069805170575562727212711936:\\ \;\;\;\;t \cdot z\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (if (<=
     (* c i)
     -999999999999999998217443564185241415988928868759412500436543339729940401905904649497115766142268560009777175966751665376232210432)
  (* c i)
  (if (<=
       (* c i)
       10500000000000000641853867875909401765417069805170575562727212711936)
    (* t z)
    (* c i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1e+129) {
		tmp = c * i;
	} else if ((c * i) <= 1.05e+67) {
		tmp = t * z;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-1d+129)) then
        tmp = c * i
    else if ((c * i) <= 1.05d+67) then
        tmp = t * z
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1e+129) {
		tmp = c * i;
	} else if ((c * i) <= 1.05e+67) {
		tmp = t * z;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1e+129:
		tmp = c * i
	elif (c * i) <= 1.05e+67:
		tmp = t * z
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1e+129)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 1.05e+67)
		tmp = Float64(t * z);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -1e+129)
		tmp = c * i;
	elseif ((c * i) <= 1.05e+67)
		tmp = t * z;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -999999999999999998217443564185241415988928868759412500436543339729940401905904649497115766142268560009777175966751665376232210432], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 10500000000000000641853867875909401765417069805170575562727212711936], N[(t * z), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1e129 or 1.0500000000000001e67 < (*.f64 c i)

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 51.6%

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

   7. Applied rewrites 51.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto c \cdot i \]
   9. Step-by-step derivation

      1. lower-*.f64 28.0%

         \[\leadsto c \cdot i \]

   10. Applied rewrites 28.0%

       \[\leadsto c \cdot i \]

   if -1e129 < (*.f64 c i) < 1.0500000000000001e67

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 51.6%

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

   7. Applied rewrites 51.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto c \cdot i \]
   9. Step-by-step derivation

      1. lower-*.f64 28.0%

         \[\leadsto c \cdot i \]

   10. Applied rewrites 28.0%

       \[\leadsto c \cdot i \]

   11. Taylor expanded in z around inf

       \[\leadsto t \cdot \color{blue}{z} \]
   12. Step-by-step derivation

       1. lower-*.f64 27.2%

          \[\leadsto t \cdot z \]

   13. Applied rewrites 27.2%

       \[\leadsto t \cdot \color{blue}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 28.0% accurate, 5.0× speedup

Math

\[c \cdot i \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.6%

   \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

2. Taylor expanded in a around 0

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

   1. lower-+.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower-+.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. lower-*.f64 74.0%

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

4. Applied rewrites 74.0%

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

5. Taylor expanded in z around 0

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

   1. lower-+.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower-*.f64 51.6%

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

7. Applied rewrites 51.6%

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

8. Taylor expanded in x around 0

   \[\leadsto c \cdot i \]
9. Step-by-step derivation

   1. lower-*.f64 28.0%

      \[\leadsto c \cdot i \]

10. Applied rewrites 28.0%

    \[\leadsto c \cdot i \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))