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

Percentage Accurate: 97.6% → 98.9%

Time: 12.4s

Alternatives: 15

Speedup: 1.0×

• 32.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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

real(8) function code(x, y, z, t, a, b, c)
    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: 97.6% accurate, 1.0× speedup

Math

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

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

real(8) function code(x, y, z, t, a, b, c)
    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: 98.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

   1. associate-+l- 97.3%

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

   2. associate--l+ 97.3%

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

   3. fma-def 98.1%

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

   4. associate-*l/ 98.4%

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

   5. fma-neg 98.8%

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

   6. sub-neg 98.8%

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

   7. distribute-neg-in 98.8%

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

   8. remove-double-neg 98.8%

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

   9. associate-/l* 98.8%

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

   10. distribute-frac-neg 98.8%

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

   11. associate-/r/ 98.8%

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

   12. fma-def 98.8%

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

   13. neg-mul-1 98.8%

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

   14. *-commutative 98.8%

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

   15. associate-/l* 98.8%

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

   16. metadata-eval 98.8%

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

3. Simplified 98.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]
4. Add Preprocessing

5. Final simplification 98.8%

   \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right) \]
6. Add Preprocessing

Alternative 2: 98.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ c + \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, b \cdot \left(a \cdot -0.25\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ c (+ (* x y) (fma t (* z 0.0625) (* b (* a -0.25))))))

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(c + N[(N[(x * y), $MachinePrecision] + N[(t * N[(z * 0.0625), $MachinePrecision] + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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. Add Preprocessing
3. Step-by-step derivation

   1. associate--l+ 97.3%

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

   2. associate-*l/ 97.6%

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

   3. *-commutative 97.6%

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

   4. fma-neg 98.0%

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

   5. div-inv 98.0%

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

   6. metadata-eval 98.0%

      \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot \color{blue}{0.0625}, -\frac{a \cdot b}{4}\right)\right) + c \]

   7. associate-/l* 98.0%

      \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, -\color{blue}{\frac{a}{\frac{4}{b}}}\right)\right) + c \]

   8. distribute-frac-neg 98.0%

      \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, \color{blue}{\frac{-a}{\frac{4}{b}}}\right)\right) + c \]

   9. metadata-eval 98.0%

      \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, \frac{-a}{\frac{\color{blue}{--4}}{b}}\right)\right) + c \]

   10. distribute-neg-frac 98.0%

       \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, \frac{-a}{\color{blue}{-\frac{-4}{b}}}\right)\right) + c \]

   11. frac-2neg 98.0%

       \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, \color{blue}{\frac{a}{\frac{-4}{b}}}\right)\right) + c \]

   12. associate-/r/ 98.0%

       \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, \color{blue}{\frac{a}{-4} \cdot b}\right)\right) + c \]

   13. div-inv 98.0%

       \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, \color{blue}{\left(a \cdot \frac{1}{-4}\right)} \cdot b\right)\right) + c \]

   14. metadata-eval 98.0%

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

4. Applied egg-rr 98.0%

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

5. Final simplification 98.0%

   \[\leadsto c + \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, b \cdot \left(a \cdot -0.25\right)\right)\right) \]
6. Add Preprocessing

Alternative 3: 66.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + z \cdot \left(t \cdot 0.0625\right)\\ t_2 := c + a \cdot \left(b \cdot -0.25\right)\\ t_3 := x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -1.3 \cdot 10^{+62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -1.16 \cdot 10^{-157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -8.4 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1.3 \cdot 10^{-278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 9.5 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 3.3 \cdot 10^{+162}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* z (* t 0.0625))))
        (t_2 (+ c (* a (* b -0.25))))
        (t_3 (+ (* x y) (* 0.0625 (* z t)))))
   (if (<= (* x y) -1.3e+62)
     t_3
     (if (<= (* x y) -1.16e-157)
       t_2
       (if (<= (* x y) -8.4e-221)
         t_1
         (if (<= (* x y) -1.3e-278)
           t_2
           (if (<= (* x y) 9.5e-166)
             t_1
             (if (<= (* x y) 4.1e+74)
               t_2
               (if (<= (* x y) 3.3e+162)
                 t_3
                 (- (* x y) (* (* a b) 0.25)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (z * (t * 0.0625));
	double t_2 = c + (a * (b * -0.25));
	double t_3 = (x * y) + (0.0625 * (z * t));
	double tmp;
	if ((x * y) <= -1.3e+62) {
		tmp = t_3;
	} else if ((x * y) <= -1.16e-157) {
		tmp = t_2;
	} else if ((x * y) <= -8.4e-221) {
		tmp = t_1;
	} else if ((x * y) <= -1.3e-278) {
		tmp = t_2;
	} else if ((x * y) <= 9.5e-166) {
		tmp = t_1;
	} else if ((x * y) <= 4.1e+74) {
		tmp = t_2;
	} else if ((x * y) <= 3.3e+162) {
		tmp = t_3;
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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 + (z * (t * 0.0625d0))
    t_2 = c + (a * (b * (-0.25d0)))
    t_3 = (x * y) + (0.0625d0 * (z * t))
    if ((x * y) <= (-1.3d+62)) then
        tmp = t_3
    else if ((x * y) <= (-1.16d-157)) then
        tmp = t_2
    else if ((x * y) <= (-8.4d-221)) then
        tmp = t_1
    else if ((x * y) <= (-1.3d-278)) then
        tmp = t_2
    else if ((x * y) <= 9.5d-166) then
        tmp = t_1
    else if ((x * y) <= 4.1d+74) then
        tmp = t_2
    else if ((x * y) <= 3.3d+162) then
        tmp = t_3
    else
        tmp = (x * y) - ((a * b) * 0.25d0)
    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 + (z * (t * 0.0625));
	double t_2 = c + (a * (b * -0.25));
	double t_3 = (x * y) + (0.0625 * (z * t));
	double tmp;
	if ((x * y) <= -1.3e+62) {
		tmp = t_3;
	} else if ((x * y) <= -1.16e-157) {
		tmp = t_2;
	} else if ((x * y) <= -8.4e-221) {
		tmp = t_1;
	} else if ((x * y) <= -1.3e-278) {
		tmp = t_2;
	} else if ((x * y) <= 9.5e-166) {
		tmp = t_1;
	} else if ((x * y) <= 4.1e+74) {
		tmp = t_2;
	} else if ((x * y) <= 3.3e+162) {
		tmp = t_3;
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (z * (t * 0.0625))
	t_2 = c + (a * (b * -0.25))
	t_3 = (x * y) + (0.0625 * (z * t))
	tmp = 0
	if (x * y) <= -1.3e+62:
		tmp = t_3
	elif (x * y) <= -1.16e-157:
		tmp = t_2
	elif (x * y) <= -8.4e-221:
		tmp = t_1
	elif (x * y) <= -1.3e-278:
		tmp = t_2
	elif (x * y) <= 9.5e-166:
		tmp = t_1
	elif (x * y) <= 4.1e+74:
		tmp = t_2
	elif (x * y) <= 3.3e+162:
		tmp = t_3
	else:
		tmp = (x * y) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(z * Float64(t * 0.0625)))
	t_2 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_3 = Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t)))
	tmp = 0.0
	if (Float64(x * y) <= -1.3e+62)
		tmp = t_3;
	elseif (Float64(x * y) <= -1.16e-157)
		tmp = t_2;
	elseif (Float64(x * y) <= -8.4e-221)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.3e-278)
		tmp = t_2;
	elseif (Float64(x * y) <= 9.5e-166)
		tmp = t_1;
	elseif (Float64(x * y) <= 4.1e+74)
		tmp = t_2;
	elseif (Float64(x * y) <= 3.3e+162)
		tmp = t_3;
	else
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (z * (t * 0.0625));
	t_2 = c + (a * (b * -0.25));
	t_3 = (x * y) + (0.0625 * (z * t));
	tmp = 0.0;
	if ((x * y) <= -1.3e+62)
		tmp = t_3;
	elseif ((x * y) <= -1.16e-157)
		tmp = t_2;
	elseif ((x * y) <= -8.4e-221)
		tmp = t_1;
	elseif ((x * y) <= -1.3e-278)
		tmp = t_2;
	elseif ((x * y) <= 9.5e-166)
		tmp = t_1;
	elseif ((x * y) <= 4.1e+74)
		tmp = t_2;
	elseif ((x * y) <= 3.3e+162)
		tmp = t_3;
	else
		tmp = (x * y) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.3e+62], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -1.16e-157], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -8.4e-221], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.3e-278], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 9.5e-166], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4.1e+74], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 3.3e+162], t$95$3, N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.29999999999999992e62 or 4.1e74 < (*.f64 x y) < 3.29999999999999987e162

   1. Initial program 95.9%

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

   3. Taylor expanded in a around 0 84.2%

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

   4. Taylor expanded in c around 0 79.9%

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

   if -1.29999999999999992e62 < (*.f64 x y) < -1.15999999999999992e-157 or -8.4000000000000001e-221 < (*.f64 x y) < -1.2999999999999999e-278 or 9.50000000000000046e-166 < (*.f64 x y) < 4.1e74

   1. Initial program 98.6%

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

   3. Taylor expanded in a around inf 76.6%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 76.6%

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

      2. associate-*r* 76.6%

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

   5. Simplified 76.6%

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

   if -1.15999999999999992e-157 < (*.f64 x y) < -8.4000000000000001e-221 or -1.2999999999999999e-278 < (*.f64 x y) < 9.50000000000000046e-166

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 79.0%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 79.0%

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

      2. *-commutative 79.0%

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

      3. associate-*l* 80.1%

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

   5. Simplified 80.1%

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

   if 3.29999999999999987e162 < (*.f64 x y)

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 94.4%

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

   4. Taylor expanded in c around 0 91.6%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.3 \cdot 10^{+62}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -1.16 \cdot 10^{-157}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -8.4 \cdot 10^{-221}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -1.3 \cdot 10^{-278}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 9.5 \cdot 10^{-166}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{+74}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 3.3 \cdot 10^{+162}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + z \cdot \left(t \cdot 0.0625\right)\\ t_2 := c + a \cdot \left(b \cdot -0.25\right)\\ t_3 := x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -8.2 \cdot 10^{+56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -6.8 \cdot 10^{-161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -1.7 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -5.4 \cdot 10^{-280}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 8.2 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* z (* t 0.0625))))
        (t_2 (+ c (* a (* b -0.25))))
        (t_3 (+ (* x y) (* 0.0625 (* z t)))))
   (if (<= (* x y) -8.2e+56)
     t_3
     (if (<= (* x y) -6.8e-161)
       t_2
       (if (<= (* x y) -1.7e-221)
         t_1
         (if (<= (* x y) -5.4e-280)
           t_2
           (if (<= (* x y) 2.1e-163)
             t_1
             (if (<= (* x y) 8.2e+73) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (z * (t * 0.0625));
	double t_2 = c + (a * (b * -0.25));
	double t_3 = (x * y) + (0.0625 * (z * t));
	double tmp;
	if ((x * y) <= -8.2e+56) {
		tmp = t_3;
	} else if ((x * y) <= -6.8e-161) {
		tmp = t_2;
	} else if ((x * y) <= -1.7e-221) {
		tmp = t_1;
	} else if ((x * y) <= -5.4e-280) {
		tmp = t_2;
	} else if ((x * y) <= 2.1e-163) {
		tmp = t_1;
	} else if ((x * y) <= 8.2e+73) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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 + (z * (t * 0.0625d0))
    t_2 = c + (a * (b * (-0.25d0)))
    t_3 = (x * y) + (0.0625d0 * (z * t))
    if ((x * y) <= (-8.2d+56)) then
        tmp = t_3
    else if ((x * y) <= (-6.8d-161)) then
        tmp = t_2
    else if ((x * y) <= (-1.7d-221)) then
        tmp = t_1
    else if ((x * y) <= (-5.4d-280)) then
        tmp = t_2
    else if ((x * y) <= 2.1d-163) then
        tmp = t_1
    else if ((x * y) <= 8.2d+73) then
        tmp = t_2
    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 + (z * (t * 0.0625));
	double t_2 = c + (a * (b * -0.25));
	double t_3 = (x * y) + (0.0625 * (z * t));
	double tmp;
	if ((x * y) <= -8.2e+56) {
		tmp = t_3;
	} else if ((x * y) <= -6.8e-161) {
		tmp = t_2;
	} else if ((x * y) <= -1.7e-221) {
		tmp = t_1;
	} else if ((x * y) <= -5.4e-280) {
		tmp = t_2;
	} else if ((x * y) <= 2.1e-163) {
		tmp = t_1;
	} else if ((x * y) <= 8.2e+73) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (z * (t * 0.0625))
	t_2 = c + (a * (b * -0.25))
	t_3 = (x * y) + (0.0625 * (z * t))
	tmp = 0
	if (x * y) <= -8.2e+56:
		tmp = t_3
	elif (x * y) <= -6.8e-161:
		tmp = t_2
	elif (x * y) <= -1.7e-221:
		tmp = t_1
	elif (x * y) <= -5.4e-280:
		tmp = t_2
	elif (x * y) <= 2.1e-163:
		tmp = t_1
	elif (x * y) <= 8.2e+73:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(z * Float64(t * 0.0625)))
	t_2 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_3 = Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t)))
	tmp = 0.0
	if (Float64(x * y) <= -8.2e+56)
		tmp = t_3;
	elseif (Float64(x * y) <= -6.8e-161)
		tmp = t_2;
	elseif (Float64(x * y) <= -1.7e-221)
		tmp = t_1;
	elseif (Float64(x * y) <= -5.4e-280)
		tmp = t_2;
	elseif (Float64(x * y) <= 2.1e-163)
		tmp = t_1;
	elseif (Float64(x * y) <= 8.2e+73)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (z * (t * 0.0625));
	t_2 = c + (a * (b * -0.25));
	t_3 = (x * y) + (0.0625 * (z * t));
	tmp = 0.0;
	if ((x * y) <= -8.2e+56)
		tmp = t_3;
	elseif ((x * y) <= -6.8e-161)
		tmp = t_2;
	elseif ((x * y) <= -1.7e-221)
		tmp = t_1;
	elseif ((x * y) <= -5.4e-280)
		tmp = t_2;
	elseif ((x * y) <= 2.1e-163)
		tmp = t_1;
	elseif ((x * y) <= 8.2e+73)
		tmp = t_2;
	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[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -8.2e+56], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -6.8e-161], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -1.7e-221], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5.4e-280], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2.1e-163], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 8.2e+73], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.2000000000000007e56 or 8.1999999999999996e73 < (*.f64 x y)

   1. Initial program 95.3%

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

   3. Taylor expanded in a around 0 86.1%

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

   4. Taylor expanded in c around 0 82.3%

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

   if -8.2000000000000007e56 < (*.f64 x y) < -6.79999999999999964e-161 or -1.7000000000000001e-221 < (*.f64 x y) < -5.39999999999999967e-280 or 2.09999999999999998e-163 < (*.f64 x y) < 8.1999999999999996e73

   1. Initial program 98.6%

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

   3. Taylor expanded in a around inf 76.6%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 76.6%

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

      2. associate-*r* 76.6%

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

   5. Simplified 76.6%

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

   if -6.79999999999999964e-161 < (*.f64 x y) < -1.7000000000000001e-221 or -5.39999999999999967e-280 < (*.f64 x y) < 2.09999999999999998e-163

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 79.0%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 79.0%

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

      2. *-commutative 79.0%

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

      3. associate-*l* 80.1%

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

   5. Simplified 80.1%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.2 \cdot 10^{+56}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -6.8 \cdot 10^{-161}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -1.7 \cdot 10^{-221}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -5.4 \cdot 10^{-280}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{-163}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 8.2 \cdot 10^{+73}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 42.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9 \cdot 10^{+51}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 5.2 \cdot 10^{-218}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{-88}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq 1.24 \cdot 10^{+70}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -9e+51)
   (* x y)
   (if (<= (* x y) 5.2e-218)
     c
     (if (<= (* x y) 7.5e-88)
       (* -0.25 (* a b))
       (if (<= (* x y) 1.24e+70) c (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -9e+51) {
		tmp = x * y;
	} else if ((x * y) <= 5.2e-218) {
		tmp = c;
	} else if ((x * y) <= 7.5e-88) {
		tmp = -0.25 * (a * b);
	} else if ((x * y) <= 1.24e+70) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if ((x * y) <= (-9d+51)) then
        tmp = x * y
    else if ((x * y) <= 5.2d-218) then
        tmp = c
    else if ((x * y) <= 7.5d-88) then
        tmp = (-0.25d0) * (a * b)
    else if ((x * y) <= 1.24d+70) then
        tmp = c
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -9e+51) {
		tmp = x * y;
	} else if ((x * y) <= 5.2e-218) {
		tmp = c;
	} else if ((x * y) <= 7.5e-88) {
		tmp = -0.25 * (a * b);
	} else if ((x * y) <= 1.24e+70) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -9e+51:
		tmp = x * y
	elif (x * y) <= 5.2e-218:
		tmp = c
	elif (x * y) <= 7.5e-88:
		tmp = -0.25 * (a * b)
	elif (x * y) <= 1.24e+70:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -9e+51)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 5.2e-218)
		tmp = c;
	elseif (Float64(x * y) <= 7.5e-88)
		tmp = Float64(-0.25 * Float64(a * b));
	elseif (Float64(x * y) <= 1.24e+70)
		tmp = c;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -9e+51)
		tmp = x * y;
	elseif ((x * y) <= 5.2e-218)
		tmp = c;
	elseif ((x * y) <= 7.5e-88)
		tmp = -0.25 * (a * b);
	elseif ((x * y) <= 1.24e+70)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -9e+51], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5.2e-218], c, If[LessEqual[N[(x * y), $MachinePrecision], 7.5e-88], N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.24e+70], c, N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.9999999999999999e51 or 1.2399999999999999e70 < (*.f64 x y)

   1. Initial program 95.4%

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

   3. Taylor expanded in a around 0 85.3%

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

   4. Taylor expanded in c around 0 81.6%

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

   5. Taylor expanded in t around 0 68.1%

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

   if -8.9999999999999999e51 < (*.f64 x y) < 5.19999999999999966e-218 or 7.50000000000000041e-88 < (*.f64 x y) < 1.2399999999999999e70

   1. Initial program 98.6%

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

   3. Taylor expanded in c around inf 41.4%

      \[\leadsto \color{blue}{c} \]

   if 5.19999999999999966e-218 < (*.f64 x y) < 7.50000000000000041e-88

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 65.9%

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

   4. Taylor expanded in x around 0 65.9%

      \[\leadsto \color{blue}{c - 0.25 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 65.9%

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

      2. *-commutative 65.9%

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

      3. *-commutative 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in c around 0 48.1%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9 \cdot 10^{+51}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 5.2 \cdot 10^{-218}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{-88}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq 1.24 \cdot 10^{+70}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -1.55 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -3.6 \cdot 10^{-279}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.25 \cdot 10^{-46}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))))
   (if (<= (* x y) -1.55e+81)
     t_1
     (if (<= (* x y) -3.6e-279)
       (+ c (* a (* b -0.25)))
       (if (<= (* x y) 1.25e-46) (+ c (* z (* t 0.0625))) 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) <= -1.55e+81) {
		tmp = t_1;
	} else if ((x * y) <= -3.6e-279) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 1.25e-46) {
		tmp = c + (z * (t * 0.0625));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) <= (-1.55d+81)) then
        tmp = t_1
    else if ((x * y) <= (-3.6d-279)) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((x * y) <= 1.25d-46) then
        tmp = c + (z * (t * 0.0625d0))
    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) <= -1.55e+81) {
		tmp = t_1;
	} else if ((x * y) <= -3.6e-279) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 1.25e-46) {
		tmp = c + (z * (t * 0.0625));
	} 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) <= -1.55e+81:
		tmp = t_1
	elif (x * y) <= -3.6e-279:
		tmp = c + (a * (b * -0.25))
	elif (x * y) <= 1.25e-46:
		tmp = c + (z * (t * 0.0625))
	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) <= -1.55e+81)
		tmp = t_1;
	elseif (Float64(x * y) <= -3.6e-279)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 1.25e-46)
		tmp = Float64(c + Float64(z * Float64(t * 0.0625)));
	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) <= -1.55e+81)
		tmp = t_1;
	elseif ((x * y) <= -3.6e-279)
		tmp = c + (a * (b * -0.25));
	elseif ((x * y) <= 1.25e-46)
		tmp = c + (z * (t * 0.0625));
	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], -1.55e+81], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -3.6e-279], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.25e-46], N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.55e81 or 1.24999999999999998e-46 < (*.f64 x y)

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf 71.8%

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

   if -1.55e81 < (*.f64 x y) < -3.5999999999999997e-279

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 73.7%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 73.7%

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

      2. associate-*r* 73.7%

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

   5. Simplified 73.7%

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

   if -3.5999999999999997e-279 < (*.f64 x y) < 1.24999999999999998e-46

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 72.5%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-*l* 73.5%

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

   5. Simplified 73.5%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.55 \cdot 10^{+81}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.6 \cdot 10^{-279}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.25 \cdot 10^{-46}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+230}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+221}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -5e+230)
   (+ c (* a (* b -0.25)))
   (if (<= (* a b) 5e+221)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (- (* x y) (* (* a b) 0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -5e+230) {
		tmp = c + (a * (b * -0.25));
	} else if ((a * b) <= 5e+221) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if ((a * b) <= (-5d+230)) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((a * b) <= 5d+221) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = (x * y) - ((a * b) * 0.25d0)
    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 tmp;
	if ((a * b) <= -5e+230) {
		tmp = c + (a * (b * -0.25));
	} else if ((a * b) <= 5e+221) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -5e+230:
		tmp = c + (a * (b * -0.25))
	elif (a * b) <= 5e+221:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = (x * y) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -5e+230)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(a * b) <= 5e+221)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -5e+230)
		tmp = c + (a * (b * -0.25));
	elseif ((a * b) <= 5e+221)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = (x * y) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -5e+230], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+221], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.0000000000000003e230

   1. Initial program 90.9%

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

   3. Taylor expanded in a around inf 95.8%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 95.8%

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

      2. associate-*r* 95.8%

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

   5. Simplified 95.8%

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

   if -5.0000000000000003e230 < (*.f64 a b) < 5.0000000000000002e221

   1. Initial program 98.6%

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

   3. Taylor expanded in a around 0 89.9%

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

   if 5.0000000000000002e221 < (*.f64 a b)

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0 88.9%

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

   4. Taylor expanded in c around 0 85.1%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+230}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+221}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+230}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+46}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -5e+230)
   (+ c (* a (* b -0.25)))
   (if (<= (* a b) 2e+46)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (- (+ c (* x y)) (* (* a b) 0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -5e+230) {
		tmp = c + (a * (b * -0.25));
	} else if ((a * b) <= 2e+46) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if ((a * b) <= (-5d+230)) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((a * b) <= 2d+46) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = (c + (x * y)) - ((a * b) * 0.25d0)
    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 tmp;
	if ((a * b) <= -5e+230) {
		tmp = c + (a * (b * -0.25));
	} else if ((a * b) <= 2e+46) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -5e+230:
		tmp = c + (a * (b * -0.25))
	elif (a * b) <= 2e+46:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -5e+230)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(a * b) <= 2e+46)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -5e+230)
		tmp = c + (a * (b * -0.25));
	elseif ((a * b) <= 2e+46)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -5e+230], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+46], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.0000000000000003e230

   1. Initial program 90.9%

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

   3. Taylor expanded in a around inf 95.8%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 95.8%

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

      2. associate-*r* 95.8%

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

   5. Simplified 95.8%

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

   if -5.0000000000000003e230 < (*.f64 a b) < 2e46

   1. Initial program 98.4%

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

   3. Taylor expanded in a around 0 92.4%

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

   if 2e46 < (*.f64 a b)

   1. Initial program 96.1%

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

   3. Taylor expanded in z around 0 88.6%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+230}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+46}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+107}:\\ \;\;\;\;\left(c + t_1\right) - t_2\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+46}:\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (* (* a b) 0.25)))
   (if (<= (* a b) -5e+107)
     (- (+ c t_1) t_2)
     (if (<= (* a b) 2e+46) (+ c (+ (* x y) t_1)) (- (+ 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 = 0.0625 * (z * t);
	double t_2 = (a * b) * 0.25;
	double tmp;
	if ((a * b) <= -5e+107) {
		tmp = (c + t_1) - t_2;
	} else if ((a * b) <= 2e+46) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + (x * y)) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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 * (z * t)
    t_2 = (a * b) * 0.25d0
    if ((a * b) <= (-5d+107)) then
        tmp = (c + t_1) - t_2
    else if ((a * b) <= 2d+46) then
        tmp = c + ((x * y) + t_1)
    else
        tmp = (c + (x * y)) - 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 = 0.0625 * (z * t);
	double t_2 = (a * b) * 0.25;
	double tmp;
	if ((a * b) <= -5e+107) {
		tmp = (c + t_1) - t_2;
	} else if ((a * b) <= 2e+46) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + (x * y)) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = (a * b) * 0.25
	tmp = 0
	if (a * b) <= -5e+107:
		tmp = (c + t_1) - t_2
	elif (a * b) <= 2e+46:
		tmp = c + ((x * y) + t_1)
	else:
		tmp = (c + (x * y)) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if (Float64(a * b) <= -5e+107)
		tmp = Float64(Float64(c + t_1) - t_2);
	elseif (Float64(a * b) <= 2e+46)
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	else
		tmp = Float64(Float64(c + Float64(x * y)) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	t_2 = (a * b) * 0.25;
	tmp = 0.0;
	if ((a * b) <= -5e+107)
		tmp = (c + t_1) - t_2;
	elseif ((a * b) <= 2e+46)
		tmp = c + ((x * y) + t_1);
	else
		tmp = (c + (x * y)) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+107], N[(N[(c + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+46], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.0000000000000002e107

   1. Initial program 95.0%

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

   3. Taylor expanded in x around 0 87.0%

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

   if -5.0000000000000002e107 < (*.f64 a b) < 2e46

   1. Initial program 98.3%

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

   3. Taylor expanded in a around 0 94.7%

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

   if 2e46 < (*.f64 a b)

   1. Initial program 96.1%

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

   3. Taylor expanded in z around 0 88.6%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+107}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+46}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.45 \cdot 10^{+79} \lor \neg \left(x \cdot y \leq 7.2 \cdot 10^{+66}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.45e+79) (not (<= (* x y) 7.2e+66)))
   (+ c (* x y))
   (+ c (* a (* b -0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.45e+79) || !((x * y) <= 7.2e+66)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if (((x * y) <= (-1.45d+79)) .or. (.not. ((x * y) <= 7.2d+66))) then
        tmp = c + (x * y)
    else
        tmp = c + (a * (b * (-0.25d0)))
    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 tmp;
	if (((x * y) <= -1.45e+79) || !((x * y) <= 7.2e+66)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.45e+79) or not ((x * y) <= 7.2e+66):
		tmp = c + (x * y)
	else:
		tmp = c + (a * (b * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.45e+79) || !(Float64(x * y) <= 7.2e+66))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1.45e+79) || ~(((x * y) <= 7.2e+66)))
		tmp = c + (x * y);
	else
		tmp = c + (a * (b * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.45e+79], N[Not[LessEqual[N[(x * y), $MachinePrecision], 7.2e+66]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.44999999999999996e79 or 7.2e66 < (*.f64 x y)

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf 74.0%

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

   if -1.44999999999999996e79 < (*.f64 x y) < 7.2e66

   1. Initial program 98.8%

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

   3. Taylor expanded in a around inf 67.0%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 67.0%

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

      2. associate-*r* 67.0%

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

   5. Simplified 67.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.45 \cdot 10^{+79} \lor \neg \left(x \cdot y \leq 7.2 \cdot 10^{+66}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.3 \cdot 10^{+221} \lor \neg \left(a \cdot b \leq 2.1 \cdot 10^{+183}\right):\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -1.3e+221) (not (<= (* a b) 2.1e+183)))
   (* -0.25 (* a b))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -1.3e+221) || !((a * b) <= 2.1e+183)) {
		tmp = -0.25 * (a * b);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if (((a * b) <= (-1.3d+221)) .or. (.not. ((a * b) <= 2.1d+183))) then
        tmp = (-0.25d0) * (a * b)
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -1.3e+221) || !((a * b) <= 2.1e+183)) {
		tmp = -0.25 * (a * b);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -1.3e+221) or not ((a * b) <= 2.1e+183):
		tmp = -0.25 * (a * b)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -1.3e+221) || !(Float64(a * b) <= 2.1e+183))
		tmp = Float64(-0.25 * Float64(a * b));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -1.3e+221) || ~(((a * b) <= 2.1e+183)))
		tmp = -0.25 * (a * b);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.3e+221], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2.1e+183]], $MachinePrecision]], N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.30000000000000002e221 or 2.1e183 < (*.f64 a b)

   1. Initial program 92.5%

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

   3. Taylor expanded in z around 0 90.8%

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

   4. Taylor expanded in x around 0 87.2%

      \[\leadsto \color{blue}{c - 0.25 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 87.2%

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

      2. *-commutative 87.2%

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

      3. *-commutative 87.2%

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

   6. Simplified 87.2%

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

   7. Taylor expanded in c around 0 78.7%

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

   if -1.30000000000000002e221 < (*.f64 a b) < 2.1e183

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf 65.1%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.3 \cdot 10^{+221} \lor \neg \left(a \cdot b \leq 2.1 \cdot 10^{+183}\right):\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-27}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-272}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-27}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -9.5e-27)
   (* x y)
   (if (<= y -8e-272) (* t (* z 0.0625)) (if (<= y 5.4e-27) c (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -9.5e-27) {
		tmp = x * y;
	} else if (y <= -8e-272) {
		tmp = t * (z * 0.0625);
	} else if (y <= 5.4e-27) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if (y <= (-9.5d-27)) then
        tmp = x * y
    else if (y <= (-8d-272)) then
        tmp = t * (z * 0.0625d0)
    else if (y <= 5.4d-27) then
        tmp = c
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -9.5e-27) {
		tmp = x * y;
	} else if (y <= -8e-272) {
		tmp = t * (z * 0.0625);
	} else if (y <= 5.4e-27) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -9.5e-27:
		tmp = x * y
	elif y <= -8e-272:
		tmp = t * (z * 0.0625)
	elif y <= 5.4e-27:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -9.5e-27)
		tmp = Float64(x * y);
	elseif (y <= -8e-272)
		tmp = Float64(t * Float64(z * 0.0625));
	elseif (y <= 5.4e-27)
		tmp = c;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -9.5e-27)
		tmp = x * y;
	elseif (y <= -8e-272)
		tmp = t * (z * 0.0625);
	elseif (y <= 5.4e-27)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -9.5e-27], N[(x * y), $MachinePrecision], If[LessEqual[y, -8e-272], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e-27], c, N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.50000000000000037e-27 or 5.39999999999999978e-27 < y

   1. Initial program 96.1%

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

   3. Taylor expanded in a around 0 81.4%

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

   4. Taylor expanded in c around 0 67.7%

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

   5. Taylor expanded in t around 0 55.4%

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

   if -9.50000000000000037e-27 < y < -7.99999999999999944e-272

   1. Initial program 98.5%

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

   3. Taylor expanded in x around 0 89.6%

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

   4. Taylor expanded in c around 0 57.9%

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

   5. Taylor expanded in t around inf 31.0%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 31.0%

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

      2. associate-*l* 32.5%

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

      3. *-commutative 32.5%

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

   7. Simplified 32.5%

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

   if -7.99999999999999944e-272 < y < 5.39999999999999978e-27

   1. Initial program 98.6%

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

   3. Taylor expanded in c around inf 35.6%

      \[\leadsto \color{blue}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-27}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-272}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-27}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.2 \cdot 10^{+51} \lor \neg \left(x \cdot y \leq 1.1 \cdot 10^{+70}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -7.2e+51) (not (<= (* x y) 1.1e+70))) (* x y) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -7.2e+51) || !((x * y) <= 1.1e+70)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if (((x * y) <= (-7.2d+51)) .or. (.not. ((x * y) <= 1.1d+70))) then
        tmp = x * y
    else
        tmp = 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 tmp;
	if (((x * y) <= -7.2e+51) || !((x * y) <= 1.1e+70)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -7.2e+51) or not ((x * y) <= 1.1e+70):
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -7.2e+51) || !(Float64(x * y) <= 1.1e+70))
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -7.2e+51) || ~(((x * y) <= 1.1e+70)))
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -7.2e+51], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.1e+70]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -7.20000000000000022e51 or 1.1e70 < (*.f64 x y)

   1. Initial program 95.4%

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

   3. Taylor expanded in a around 0 85.3%

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

   4. Taylor expanded in c around 0 81.6%

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

   5. Taylor expanded in t around 0 68.1%

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

   if -7.20000000000000022e51 < (*.f64 x y) < 1.1e70

   1. Initial program 98.7%

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

   3. Taylor expanded in c around inf 39.0%

      \[\leadsto \color{blue}{c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.2 \cdot 10^{+51} \lor \neg \left(x \cdot y \leq 1.1 \cdot 10^{+70}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0))
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) + ((z * t) / 16.0)) - ((a * b) / 4.0));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

3. Final simplification 97.3%

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

Alternative 15: 22.3% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ c \end{array} \]

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

real(8) function code(x, y, z, t, a, b, c)
    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. Add Preprocessing

3. Taylor expanded in c around inf 25.3%

   \[\leadsto \color{blue}{c} \]

4. Final simplification 25.3%

   \[\leadsto c \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024020 
(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))