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

Percentage Accurate: 97.3% → 97.3%

Time: 11.5s

Alternatives: 10

Speedup: 1.0×

• 66.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Initial Program: 97.3% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Alternative 1: 85.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ t_2 := 0.25 \cdot \left(a \cdot b\right)\\ t_3 := \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+202}:\\ \;\;\;\;\left(t\_1 - t\_2\right) + c\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{-109}:\\ \;\;\;\;c + \left(t\_1 + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - t\_2\right) + c\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (* 0.0625 (* t z)))
       (t_2 (* 0.25 (* a b)))
       (t_3 (/ (* a b) 4.0)))
  (if (<= t_3 -1e+202)
    (+ (- t_1 t_2) c)
    (if (<= t_3 2e-109) (+ c (+ t_1 (* x y))) (+ (- (* x y) t_2) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (t * z);
	double t_2 = 0.25 * (a * b);
	double t_3 = (a * b) / 4.0;
	double tmp;
	if (t_3 <= -1e+202) {
		tmp = (t_1 - t_2) + c;
	} else if (t_3 <= 2e-109) {
		tmp = c + (t_1 + (x * y));
	} else {
		tmp = ((x * y) - t_2) + c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 0.0625d0 * (t * z)
    t_2 = 0.25d0 * (a * b)
    t_3 = (a * b) / 4.0d0
    if (t_3 <= (-1d+202)) then
        tmp = (t_1 - t_2) + c
    else if (t_3 <= 2d-109) then
        tmp = c + (t_1 + (x * y))
    else
        tmp = ((x * y) - t_2) + c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (t * z);
	double t_2 = 0.25 * (a * b);
	double t_3 = (a * b) / 4.0;
	double tmp;
	if (t_3 <= -1e+202) {
		tmp = (t_1 - t_2) + c;
	} else if (t_3 <= 2e-109) {
		tmp = c + (t_1 + (x * y));
	} else {
		tmp = ((x * y) - t_2) + c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (t * z)
	t_2 = 0.25 * (a * b)
	t_3 = (a * b) / 4.0
	tmp = 0
	if t_3 <= -1e+202:
		tmp = (t_1 - t_2) + c
	elif t_3 <= 2e-109:
		tmp = c + (t_1 + (x * y))
	else:
		tmp = ((x * y) - t_2) + c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(t * z))
	t_2 = Float64(0.25 * Float64(a * b))
	t_3 = Float64(Float64(a * b) / 4.0)
	tmp = 0.0
	if (t_3 <= -1e+202)
		tmp = Float64(Float64(t_1 - t_2) + c);
	elseif (t_3 <= 2e-109)
		tmp = Float64(c + Float64(t_1 + Float64(x * y)));
	else
		tmp = Float64(Float64(Float64(x * y) - t_2) + c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (t * z);
	t_2 = 0.25 * (a * b);
	t_3 = (a * b) / 4.0;
	tmp = 0.0;
	if (t_3 <= -1e+202)
		tmp = (t_1 - t_2) + c;
	elseif (t_3 <= 2e-109)
		tmp = c + (t_1 + (x * y));
	else
		tmp = ((x * y) - t_2) + c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+202], N[(N[(t$95$1 - t$95$2), $MachinePrecision] + c), $MachinePrecision], If[LessEqual[t$95$3, 2e-109], N[(c + N[(t$95$1 + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - t$95$2), $MachinePrecision] + c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -9.999999999999999e201

   1. Initial program 97.3%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.1%

         \[\leadsto \left(0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot \color{blue}{b}\right)\right) + c \]

   4. Applied rewrites 74.1%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)\right)} + c \]

   if -9.999999999999999e201 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 2e-109

   1. Initial program 97.3%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 73.1%

         \[\leadsto c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 73.1%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   if 2e-109 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 97.3%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 73.9%

         \[\leadsto \left(x \cdot y - 0.25 \cdot \left(a \cdot \color{blue}{b}\right)\right) + c \]

   4. Applied rewrites 73.9%

      \[\leadsto \color{blue}{\left(x \cdot y - 0.25 \cdot \left(a \cdot b\right)\right)} + c \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 85.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+202}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-109}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - 0.25 \cdot \left(a \cdot b\right)\right) + c\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (/ (* a b) 4.0)))
  (if (<= t_1 -1e+202)
    (* -0.25 (* a b))
    (if (<= t_1 2e-109)
      (+ c (+ (* 0.0625 (* t z)) (* x y)))
      (+ (- (* x y) (* 0.25 (* a b))) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double tmp;
	if (t_1 <= -1e+202) {
		tmp = -0.25 * (a * b);
	} else if (t_1 <= 2e-109) {
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	} else {
		tmp = ((x * y) - (0.25 * (a * b))) + c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) / 4.0d0
    if (t_1 <= (-1d+202)) then
        tmp = (-0.25d0) * (a * b)
    else if (t_1 <= 2d-109) then
        tmp = c + ((0.0625d0 * (t * z)) + (x * y))
    else
        tmp = ((x * y) - (0.25d0 * (a * b))) + c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double tmp;
	if (t_1 <= -1e+202) {
		tmp = -0.25 * (a * b);
	} else if (t_1 <= 2e-109) {
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	} else {
		tmp = ((x * y) - (0.25 * (a * b))) + c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) / 4.0
	tmp = 0
	if t_1 <= -1e+202:
		tmp = -0.25 * (a * b)
	elif t_1 <= 2e-109:
		tmp = c + ((0.0625 * (t * z)) + (x * y))
	else:
		tmp = ((x * y) - (0.25 * (a * b))) + c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / 4.0)
	tmp = 0.0
	if (t_1 <= -1e+202)
		tmp = Float64(-0.25 * Float64(a * b));
	elseif (t_1 <= 2e-109)
		tmp = Float64(c + Float64(Float64(0.0625 * Float64(t * z)) + Float64(x * y)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(0.25 * Float64(a * b))) + c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) / 4.0;
	tmp = 0.0;
	if (t_1 <= -1e+202)
		tmp = -0.25 * (a * b);
	elseif (t_1 <= 2e-109)
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	else
		tmp = ((x * y) - (0.25 * (a * b))) + c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+202], N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-109], N[(c + N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -9.999999999999999e201

   1. Initial program 97.3%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 81.3%

          \[\leadsto -1 \cdot \left(z \cdot \left(-1 \cdot \frac{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)}{z} + -0.0625 \cdot \color{blue}{t}\right)\right) \]

   4. Applied rewrites 81.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(-1 \cdot \frac{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)}{z} + -0.0625 \cdot t\right)\right)} \]

   5. Taylor expanded in c around inf

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

      1. lower-*.f64 22.4%

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

   7. Applied rewrites 22.4%

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

   8. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 28.9%

         \[\leadsto -0.25 \cdot \left(a \cdot b\right) \]

   10. Applied rewrites 28.9%

       \[\leadsto -0.25 \cdot \color{blue}{\left(a \cdot b\right)} \]

   if -9.999999999999999e201 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 2e-109

   1. Initial program 97.3%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 73.1%

         \[\leadsto c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 73.1%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   if 2e-109 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 97.3%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 73.9%

         \[\leadsto \left(x \cdot y - 0.25 \cdot \left(a \cdot \color{blue}{b}\right)\right) + c \]

   4. Applied rewrites 73.9%

      \[\leadsto \color{blue}{\left(x \cdot y - 0.25 \cdot \left(a \cdot b\right)\right)} + c \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 85.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ t_2 := -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+202}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+196}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + c\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (/ (* a b) 4.0)) (t_2 (* -0.25 (* a b))))
  (if (<= t_1 -1e+202)
    t_2
    (if (<= t_1 5e+196)
      (+ c (+ (* 0.0625 (* t z)) (* x y)))
      (+ t_2 c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double t_2 = -0.25 * (a * b);
	double tmp;
	if (t_1 <= -1e+202) {
		tmp = t_2;
	} else if (t_1 <= 5e+196) {
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	} else {
		tmp = t_2 + c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) / 4.0d0
    t_2 = (-0.25d0) * (a * b)
    if (t_1 <= (-1d+202)) then
        tmp = t_2
    else if (t_1 <= 5d+196) then
        tmp = c + ((0.0625d0 * (t * z)) + (x * y))
    else
        tmp = t_2 + c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double t_2 = -0.25 * (a * b);
	double tmp;
	if (t_1 <= -1e+202) {
		tmp = t_2;
	} else if (t_1 <= 5e+196) {
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	} else {
		tmp = t_2 + c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) / 4.0
	t_2 = -0.25 * (a * b)
	tmp = 0
	if t_1 <= -1e+202:
		tmp = t_2
	elif t_1 <= 5e+196:
		tmp = c + ((0.0625 * (t * z)) + (x * y))
	else:
		tmp = t_2 + c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / 4.0)
	t_2 = Float64(-0.25 * Float64(a * b))
	tmp = 0.0
	if (t_1 <= -1e+202)
		tmp = t_2;
	elseif (t_1 <= 5e+196)
		tmp = Float64(c + Float64(Float64(0.0625 * Float64(t * z)) + Float64(x * y)));
	else
		tmp = Float64(t_2 + c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) / 4.0;
	t_2 = -0.25 * (a * b);
	tmp = 0.0;
	if (t_1 <= -1e+202)
		tmp = t_2;
	elseif (t_1 <= 5e+196)
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	else
		tmp = t_2 + c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+202], t$95$2, If[LessEqual[t$95$1, 5e+196], N[(c + N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + c), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -9.999999999999999e201

   1. Initial program 97.3%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 81.3%

          \[\leadsto -1 \cdot \left(z \cdot \left(-1 \cdot \frac{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)}{z} + -0.0625 \cdot \color{blue}{t}\right)\right) \]

   4. Applied rewrites 81.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(-1 \cdot \frac{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)}{z} + -0.0625 \cdot t\right)\right)} \]

   5. Taylor expanded in c around inf

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

      1. lower-*.f64 22.4%

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

   7. Applied rewrites 22.4%

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

   8. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 28.9%

         \[\leadsto -0.25 \cdot \left(a \cdot b\right) \]

   10. Applied rewrites 28.9%

       \[\leadsto -0.25 \cdot \color{blue}{\left(a \cdot b\right)} \]

   if -9.999999999999999e201 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 4.9999999999999998e196

   1. Initial program 97.3%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 73.1%

         \[\leadsto c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 73.1%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   if 4.9999999999999998e196 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 97.3%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.3%

         \[\leadsto -0.25 \cdot \left(a \cdot \color{blue}{b}\right) + c \]

   4. Applied rewrites 49.3%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 72.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right) + x \cdot y\\ t_2 := x \cdot y + \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-68}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t\_2 \leq 10^{+180}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right) + c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (+ (* 0.0625 (* t z)) (* x y)))
       (t_2 (+ (* x y) (/ (* z t) 16.0))))
  (if (<= t_2 -1e+215)
    t_1
    (if (<= t_2 -5e-68)
      (+ c (* x y))
      (if (<= t_2 1e+180) (+ (* -0.25 (* a b)) c) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (0.0625 * (t * z)) + (x * y);
	double t_2 = (x * y) + ((z * t) / 16.0);
	double tmp;
	if (t_2 <= -1e+215) {
		tmp = t_1;
	} else if (t_2 <= -5e-68) {
		tmp = c + (x * y);
	} else if (t_2 <= 1e+180) {
		tmp = (-0.25 * (a * b)) + c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (0.0625d0 * (t * z)) + (x * y)
    t_2 = (x * y) + ((z * t) / 16.0d0)
    if (t_2 <= (-1d+215)) then
        tmp = t_1
    else if (t_2 <= (-5d-68)) then
        tmp = c + (x * y)
    else if (t_2 <= 1d+180) then
        tmp = ((-0.25d0) * (a * b)) + c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (0.0625 * (t * z)) + (x * y);
	double t_2 = (x * y) + ((z * t) / 16.0);
	double tmp;
	if (t_2 <= -1e+215) {
		tmp = t_1;
	} else if (t_2 <= -5e-68) {
		tmp = c + (x * y);
	} else if (t_2 <= 1e+180) {
		tmp = (-0.25 * (a * b)) + c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (0.0625 * (t * z)) + (x * y)
	t_2 = (x * y) + ((z * t) / 16.0)
	tmp = 0
	if t_2 <= -1e+215:
		tmp = t_1
	elif t_2 <= -5e-68:
		tmp = c + (x * y)
	elif t_2 <= 1e+180:
		tmp = (-0.25 * (a * b)) + c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(0.0625 * Float64(t * z)) + Float64(x * y))
	t_2 = Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0))
	tmp = 0.0
	if (t_2 <= -1e+215)
		tmp = t_1;
	elseif (t_2 <= -5e-68)
		tmp = Float64(c + Float64(x * y));
	elseif (t_2 <= 1e+180)
		tmp = Float64(Float64(-0.25 * Float64(a * b)) + c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (0.0625 * (t * z)) + (x * y);
	t_2 = (x * y) + ((z * t) / 16.0);
	tmp = 0.0;
	if (t_2 <= -1e+215)
		tmp = t_1;
	elseif (t_2 <= -5e-68)
		tmp = c + (x * y);
	elseif (t_2 <= 1e+180)
		tmp = (-0.25 * (a * b)) + c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+215], t$95$1, If[LessEqual[t$95$2, -5e-68], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+180], N[(N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) < -9.9999999999999991e214 or 1e180 < (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64)))

   1. Initial program 97.3%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 73.1%

         \[\leadsto c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 73.1%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 48.7%

         \[\leadsto c + 0.0625 \cdot \left(t \cdot z\right) \]

   7. Applied rewrites 48.7%

      \[\leadsto c + 0.0625 \cdot \color{blue}{\left(t \cdot z\right)} \]

   8. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 48.5%

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

   10. Applied rewrites 48.5%

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

   11. Taylor expanded in c around 0

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

       1. lower-+.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-*.f64 52.6%

          \[\leadsto 0.0625 \cdot \left(t \cdot z\right) + x \cdot y \]

   13. Applied rewrites 52.6%

       \[\leadsto 0.0625 \cdot \left(t \cdot z\right) + \color{blue}{x \cdot y} \]

   if -9.9999999999999991e214 < (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) < -4.9999999999999997e-68

   1. Initial program 97.3%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 73.1%

         \[\leadsto c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 73.1%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 48.7%

         \[\leadsto c + 0.0625 \cdot \left(t \cdot z\right) \]

   7. Applied rewrites 48.7%

      \[\leadsto c + 0.0625 \cdot \color{blue}{\left(t \cdot z\right)} \]

   8. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 48.5%

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

   10. Applied rewrites 48.5%

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

   if -4.9999999999999997e-68 < (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) < 1e180

   1. Initial program 97.3%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.3%

         \[\leadsto -0.25 \cdot \left(a \cdot \color{blue}{b}\right) + c \]

   4. Applied rewrites 49.3%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 64.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-33}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+175}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right) + c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (+ c (* x y))))
  (if (<= (* x y) -2e+96)
    t_1
    (if (<= (* x y) 2e-33)
      (+ c (* 0.0625 (* t z)))
      (if (<= (* x y) 1e+175) (+ (* -0.25 (* a b)) c) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if ((x * y) <= -2e+96) {
		tmp = t_1;
	} else if ((x * y) <= 2e-33) {
		tmp = c + (0.0625 * (t * z));
	} else if ((x * y) <= 1e+175) {
		tmp = (-0.25 * (a * b)) + c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c + (x * y)
    if ((x * y) <= (-2d+96)) then
        tmp = t_1
    else if ((x * y) <= 2d-33) then
        tmp = c + (0.0625d0 * (t * z))
    else if ((x * y) <= 1d+175) then
        tmp = ((-0.25d0) * (a * b)) + c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if ((x * y) <= -2e+96) {
		tmp = t_1;
	} else if ((x * y) <= 2e-33) {
		tmp = c + (0.0625 * (t * z));
	} else if ((x * y) <= 1e+175) {
		tmp = (-0.25 * (a * b)) + c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	tmp = 0
	if (x * y) <= -2e+96:
		tmp = t_1
	elif (x * y) <= 2e-33:
		tmp = c + (0.0625 * (t * z))
	elif (x * y) <= 1e+175:
		tmp = (-0.25 * (a * b)) + c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -2e+96)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-33)
		tmp = Float64(c + Float64(0.0625 * Float64(t * z)));
	elseif (Float64(x * y) <= 1e+175)
		tmp = Float64(Float64(-0.25 * Float64(a * b)) + c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -2e+96)
		tmp = t_1;
	elseif ((x * y) <= 2e-33)
		tmp = c + (0.0625 * (t * z));
	elseif ((x * y) <= 1e+175)
		tmp = (-0.25 * (a * b)) + c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+96], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-33], N[(c + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+175], N[(N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.0000000000000001e96 or 9.9999999999999994e174 < (*.f64 x y)

   1. Initial program 97.3%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 73.1%

         \[\leadsto c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 73.1%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 48.7%

         \[\leadsto c + 0.0625 \cdot \left(t \cdot z\right) \]

   7. Applied rewrites 48.7%

      \[\leadsto c + 0.0625 \cdot \color{blue}{\left(t \cdot z\right)} \]

   8. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 48.5%

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

   10. Applied rewrites 48.5%

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

   if -2.0000000000000001e96 < (*.f64 x y) < 2.0000000000000001e-33

   1. Initial program 97.3%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 73.1%

         \[\leadsto c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 73.1%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 48.7%

         \[\leadsto c + 0.0625 \cdot \left(t \cdot z\right) \]

   7. Applied rewrites 48.7%

      \[\leadsto c + 0.0625 \cdot \color{blue}{\left(t \cdot z\right)} \]

   if 2.0000000000000001e-33 < (*.f64 x y) < 9.9999999999999994e174

   1. Initial program 97.3%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.3%

         \[\leadsto -0.25 \cdot \left(a \cdot \color{blue}{b}\right) + c \]

   4. Applied rewrites 49.3%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 62.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := c + x \cdot y\\ t_2 := \frac{a \cdot b}{4}\\ t_3 := -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+202}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-318}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-207}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (+ c (* x y)))
       (t_2 (/ (* a b) 4.0))
       (t_3 (* -0.25 (* a b))))
  (if (<= t_2 -1e+202)
    t_3
    (if (<= t_2 -1e-318)
      t_1
      (if (<= t_2 5e-207)
        (+ c (* 0.0625 (* t z)))
        (if (<= t_2 5e+196) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = (a * b) / 4.0;
	double t_3 = -0.25 * (a * b);
	double tmp;
	if (t_2 <= -1e+202) {
		tmp = t_3;
	} else if (t_2 <= -1e-318) {
		tmp = t_1;
	} else if (t_2 <= 5e-207) {
		tmp = c + (0.0625 * (t * z));
	} else if (t_2 <= 5e+196) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = (a * b) / 4.0d0
    t_3 = (-0.25d0) * (a * b)
    if (t_2 <= (-1d+202)) then
        tmp = t_3
    else if (t_2 <= (-1d-318)) then
        tmp = t_1
    else if (t_2 <= 5d-207) then
        tmp = c + (0.0625d0 * (t * z))
    else if (t_2 <= 5d+196) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = (a * b) / 4.0;
	double t_3 = -0.25 * (a * b);
	double tmp;
	if (t_2 <= -1e+202) {
		tmp = t_3;
	} else if (t_2 <= -1e-318) {
		tmp = t_1;
	} else if (t_2 <= 5e-207) {
		tmp = c + (0.0625 * (t * z));
	} else if (t_2 <= 5e+196) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = (a * b) / 4.0
	t_3 = -0.25 * (a * b)
	tmp = 0
	if t_2 <= -1e+202:
		tmp = t_3
	elif t_2 <= -1e-318:
		tmp = t_1
	elif t_2 <= 5e-207:
		tmp = c + (0.0625 * (t * z))
	elif t_2 <= 5e+196:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(Float64(a * b) / 4.0)
	t_3 = Float64(-0.25 * Float64(a * b))
	tmp = 0.0
	if (t_2 <= -1e+202)
		tmp = t_3;
	elseif (t_2 <= -1e-318)
		tmp = t_1;
	elseif (t_2 <= 5e-207)
		tmp = Float64(c + Float64(0.0625 * Float64(t * z)));
	elseif (t_2 <= 5e+196)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = (a * b) / 4.0;
	t_3 = -0.25 * (a * b);
	tmp = 0.0;
	if (t_2 <= -1e+202)
		tmp = t_3;
	elseif (t_2 <= -1e-318)
		tmp = t_1;
	elseif (t_2 <= 5e-207)
		tmp = c + (0.0625 * (t * z));
	elseif (t_2 <= 5e+196)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]}, Block[{t$95$3 = N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+202], t$95$3, If[LessEqual[t$95$2, -1e-318], t$95$1, If[LessEqual[t$95$2, 5e-207], N[(c + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+196], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -9.999999999999999e201 or 4.9999999999999998e196 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 97.3%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 81.3%

          \[\leadsto -1 \cdot \left(z \cdot \left(-1 \cdot \frac{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)}{z} + -0.0625 \cdot \color{blue}{t}\right)\right) \]

   4. Applied rewrites 81.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(-1 \cdot \frac{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)}{z} + -0.0625 \cdot t\right)\right)} \]

   5. Taylor expanded in c around inf

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

      1. lower-*.f64 22.4%

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

   7. Applied rewrites 22.4%

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

   8. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 28.9%

         \[\leadsto -0.25 \cdot \left(a \cdot b\right) \]

   10. Applied rewrites 28.9%

       \[\leadsto -0.25 \cdot \color{blue}{\left(a \cdot b\right)} \]

   if -9.999999999999999e201 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -9.9999874849559983e-319 or 5.0000000000000001e-207 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 4.9999999999999998e196

   1. Initial program 97.3%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 73.1%

         \[\leadsto c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 73.1%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 48.7%

         \[\leadsto c + 0.0625 \cdot \left(t \cdot z\right) \]

   7. Applied rewrites 48.7%

      \[\leadsto c + 0.0625 \cdot \color{blue}{\left(t \cdot z\right)} \]

   8. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 48.5%

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

   10. Applied rewrites 48.5%

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

   if -9.9999874849559983e-319 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 5.0000000000000001e-207

   1. Initial program 97.3%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 73.1%

         \[\leadsto c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 73.1%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 48.7%

         \[\leadsto c + 0.0625 \cdot \left(t \cdot z\right) \]

   7. Applied rewrites 48.7%

      \[\leadsto c + 0.0625 \cdot \color{blue}{\left(t \cdot z\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 62.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ t_2 := -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+202}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+196}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (/ (* a b) 4.0)) (t_2 (* -0.25 (* a b))))
  (if (<= t_1 -1e+202) t_2 (if (<= t_1 5e+196) (+ c (* x y)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double t_2 = -0.25 * (a * b);
	double tmp;
	if (t_1 <= -1e+202) {
		tmp = t_2;
	} else if (t_1 <= 5e+196) {
		tmp = c + (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) / 4.0d0
    t_2 = (-0.25d0) * (a * b)
    if (t_1 <= (-1d+202)) then
        tmp = t_2
    else if (t_1 <= 5d+196) then
        tmp = c + (x * y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double t_2 = -0.25 * (a * b);
	double tmp;
	if (t_1 <= -1e+202) {
		tmp = t_2;
	} else if (t_1 <= 5e+196) {
		tmp = c + (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) / 4.0
	t_2 = -0.25 * (a * b)
	tmp = 0
	if t_1 <= -1e+202:
		tmp = t_2
	elif t_1 <= 5e+196:
		tmp = c + (x * y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / 4.0)
	t_2 = Float64(-0.25 * Float64(a * b))
	tmp = 0.0
	if (t_1 <= -1e+202)
		tmp = t_2;
	elseif (t_1 <= 5e+196)
		tmp = Float64(c + Float64(x * y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) / 4.0;
	t_2 = -0.25 * (a * b);
	tmp = 0.0;
	if (t_1 <= -1e+202)
		tmp = t_2;
	elseif (t_1 <= 5e+196)
		tmp = c + (x * y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+202], t$95$2, If[LessEqual[t$95$1, 5e+196], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -9.999999999999999e201 or 4.9999999999999998e196 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 97.3%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 81.3%

          \[\leadsto -1 \cdot \left(z \cdot \left(-1 \cdot \frac{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)}{z} + -0.0625 \cdot \color{blue}{t}\right)\right) \]

   4. Applied rewrites 81.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(-1 \cdot \frac{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)}{z} + -0.0625 \cdot t\right)\right)} \]

   5. Taylor expanded in c around inf

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

      1. lower-*.f64 22.4%

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

   7. Applied rewrites 22.4%

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

   8. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 28.9%

         \[\leadsto -0.25 \cdot \left(a \cdot b\right) \]

   10. Applied rewrites 28.9%

       \[\leadsto -0.25 \cdot \color{blue}{\left(a \cdot b\right)} \]

   if -9.999999999999999e201 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 4.9999999999999998e196

   1. Initial program 97.3%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 73.1%

         \[\leadsto c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 73.1%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 48.7%

         \[\leadsto c + 0.0625 \cdot \left(t \cdot z\right) \]

   7. Applied rewrites 48.7%

      \[\leadsto c + 0.0625 \cdot \color{blue}{\left(t \cdot z\right)} \]

   8. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 48.5%

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

   10. Applied rewrites 48.5%

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

Alternative 8: 48.5% accurate, 5.2× speedup

Math

\[c + x \cdot y \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

2. Taylor expanded in a around 0

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

   1. lower-+.f64 N/A

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

   2. lower-+.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. lower-*.f64 73.1%

      \[\leadsto c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

4. Applied rewrites 73.1%

   \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

5. Taylor expanded in x around 0

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 48.7%

      \[\leadsto c + 0.0625 \cdot \left(t \cdot z\right) \]

7. Applied rewrites 48.7%

   \[\leadsto c + 0.0625 \cdot \color{blue}{\left(t \cdot z\right)} \]

8. Taylor expanded in z around 0

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

   1. lower-+.f64 N/A

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

   2. lower-*.f64 48.5%

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

10. Applied rewrites 48.5%

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

Alternative 9: 22.4% accurate, 47.0× speedup

Math

\[c \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

2. Taylor expanded in a around 0

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

   1. lower-+.f64 N/A

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

   2. lower-+.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. lower-*.f64 73.1%

      \[\leadsto c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot \color{blue}{y}\right) \]

4. Applied rewrites 73.1%

   \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

5. Taylor expanded in x around 0

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 48.7%

      \[\leadsto c + 0.0625 \cdot \left(t \cdot z\right) \]

7. Applied rewrites 48.7%

   \[\leadsto c + 0.0625 \cdot \color{blue}{\left(t \cdot z\right)} \]

8. Taylor expanded in z around 0

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

   1. lower-+.f64 N/A

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

   2. lower-*.f64 48.5%

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

10. Applied rewrites 48.5%

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

11. Taylor expanded in x around 0

    \[\leadsto c \]
12. Step-by-step derivation

13. Applied rewrites 22.4%

    \[\leadsto c \]
14. Add Preprocessing

Reproduce

herbie shell --seed 2025258 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))