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

Percentage Accurate: 97.4% → 98.9%

Time: 8.1s

Alternatives: 12

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: 97.4% 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 99.2%

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

   1. associate-+l- 99.2%

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

   2. associate--l+ 99.2%

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

   3. fma-def 99.2%

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

   4. associate-*l/ 99.2%

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

   5. fma-neg 99.6%

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

   6. sub-neg 99.6%

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

   7. distribute-neg-in 99.6%

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

   8. remove-double-neg 99.6%

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

   9. associate-/l* 99.5%

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

   10. distribute-frac-neg 99.5%

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

   11. associate-/r/ 99.6%

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

   12. fma-def 99.6%

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

   13. neg-mul-1 99.6%

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

   14. *-commutative 99.6%

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

   15. associate-/l* 99.6%

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

   16. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 61.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.6 \cdot 10^{+236}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -9 \cdot 10^{+138} \lor \neg \left(x \cdot y \leq -3.2 \cdot 10^{-80}\right) \land \left(x \cdot y \leq 7.2 \cdot 10^{-53} \lor \neg \left(x \cdot y \leq 3.4 \cdot 10^{+127}\right) \land x \cdot y \leq 1.95 \cdot 10^{+164}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -4.6e+236)
   (* x y)
   (if (or (<= (* x y) -9e+138)
           (and (not (<= (* x y) -3.2e-80))
                (or (<= (* x y) 7.2e-53)
                    (and (not (<= (* x y) 3.4e+127)) (<= (* x y) 1.95e+164)))))
     (+ c (* a (* b -0.25)))
     (+ (* x y) (* (* z t) 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -4.6e+236) {
		tmp = x * y;
	} else if (((x * y) <= -9e+138) || (!((x * y) <= -3.2e-80) && (((x * y) <= 7.2e-53) || (!((x * y) <= 3.4e+127) && ((x * y) <= 1.95e+164))))) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = (x * y) + ((z * t) * 0.0625);
	}
	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) <= (-4.6d+236)) then
        tmp = x * y
    else if (((x * y) <= (-9d+138)) .or. (.not. ((x * y) <= (-3.2d-80))) .and. ((x * y) <= 7.2d-53) .or. (.not. ((x * y) <= 3.4d+127)) .and. ((x * y) <= 1.95d+164)) then
        tmp = c + (a * (b * (-0.25d0)))
    else
        tmp = (x * y) + ((z * t) * 0.0625d0)
    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) <= -4.6e+236) {
		tmp = x * y;
	} else if (((x * y) <= -9e+138) || (!((x * y) <= -3.2e-80) && (((x * y) <= 7.2e-53) || (!((x * y) <= 3.4e+127) && ((x * y) <= 1.95e+164))))) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = (x * y) + ((z * t) * 0.0625);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -4.6e+236:
		tmp = x * y
	elif ((x * y) <= -9e+138) or (not ((x * y) <= -3.2e-80) and (((x * y) <= 7.2e-53) or (not ((x * y) <= 3.4e+127) and ((x * y) <= 1.95e+164)))):
		tmp = c + (a * (b * -0.25))
	else:
		tmp = (x * y) + ((z * t) * 0.0625)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -4.6e+236)
		tmp = Float64(x * y);
	elseif ((Float64(x * y) <= -9e+138) || (!(Float64(x * y) <= -3.2e-80) && ((Float64(x * y) <= 7.2e-53) || (!(Float64(x * y) <= 3.4e+127) && (Float64(x * y) <= 1.95e+164)))))
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	else
		tmp = Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -4.6e+236)
		tmp = x * y;
	elseif (((x * y) <= -9e+138) || (~(((x * y) <= -3.2e-80)) && (((x * y) <= 7.2e-53) || (~(((x * y) <= 3.4e+127)) && ((x * y) <= 1.95e+164)))))
		tmp = c + (a * (b * -0.25));
	else
		tmp = (x * y) + ((z * t) * 0.0625);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -4.6e+236], N[(x * y), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], -9e+138], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -3.2e-80]], $MachinePrecision], Or[LessEqual[N[(x * y), $MachinePrecision], 7.2e-53], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.4e+127]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 1.95e+164]]]]], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.5999999999999999e236

   1. Initial program 94.1%

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

   2. Taylor expanded in a around 0 94.1%

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

   3. Taylor expanded in c around 0 94.1%

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

   4. Taylor expanded in t around 0 100.0%

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

   if -4.5999999999999999e236 < (*.f64 x y) < -8.99999999999999963e138 or -3.1999999999999999e-80 < (*.f64 x y) < 7.1999999999999998e-53 or 3.39999999999999977e127 < (*.f64 x y) < 1.94999999999999993e164

   1. Initial program 99.3%

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

   2. Taylor expanded in a around inf 77.4%

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

      1. *-commutative 77.4%

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

      2. associate-*r* 77.4%

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

   4. Simplified 77.4%

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

   if -8.99999999999999963e138 < (*.f64 x y) < -3.1999999999999999e-80 or 7.1999999999999998e-53 < (*.f64 x y) < 3.39999999999999977e127 or 1.94999999999999993e164 < (*.f64 x y)

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 83.2%

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

   3. Taylor expanded in c around 0 70.0%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.6 \cdot 10^{+236}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -9 \cdot 10^{+138} \lor \neg \left(x \cdot y \leq -3.2 \cdot 10^{-80}\right) \land \left(x \cdot y \leq 7.2 \cdot 10^{-53} \lor \neg \left(x \cdot y \leq 3.4 \cdot 10^{+127}\right) \land x \cdot y \leq 1.95 \cdot 10^{+164}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \end{array} \]

Alternative 3: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ t_2 := c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{if}\;x \cdot y \leq -4.6 \cdot 10^{+236}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.6 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -3.4 \cdot 10^{-212}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -8.5 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 9.5 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))) (t_2 (+ c (* t (* z 0.0625)))))
   (if (<= (* x y) -4.6e+236)
     (* x y)
     (if (<= (* x y) -1.6e+147)
       t_1
       (if (<= (* x y) -3.4e-212)
         t_2
         (if (<= (* x y) -8.5e-301)
           t_1
           (if (<= (* x y) 9.5e+33) t_2 (+ c (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double t_2 = c + (t * (z * 0.0625));
	double tmp;
	if ((x * y) <= -4.6e+236) {
		tmp = x * y;
	} else if ((x * y) <= -1.6e+147) {
		tmp = t_1;
	} else if ((x * y) <= -3.4e-212) {
		tmp = t_2;
	} else if ((x * y) <= -8.5e-301) {
		tmp = t_1;
	} else if ((x * y) <= 9.5e+33) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (b * (-0.25d0))
    t_2 = c + (t * (z * 0.0625d0))
    if ((x * y) <= (-4.6d+236)) then
        tmp = x * y
    else if ((x * y) <= (-1.6d+147)) then
        tmp = t_1
    else if ((x * y) <= (-3.4d-212)) then
        tmp = t_2
    else if ((x * y) <= (-8.5d-301)) then
        tmp = t_1
    else if ((x * y) <= 9.5d+33) then
        tmp = t_2
    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 t_1 = a * (b * -0.25);
	double t_2 = c + (t * (z * 0.0625));
	double tmp;
	if ((x * y) <= -4.6e+236) {
		tmp = x * y;
	} else if ((x * y) <= -1.6e+147) {
		tmp = t_1;
	} else if ((x * y) <= -3.4e-212) {
		tmp = t_2;
	} else if ((x * y) <= -8.5e-301) {
		tmp = t_1;
	} else if ((x * y) <= 9.5e+33) {
		tmp = t_2;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	t_2 = c + (t * (z * 0.0625))
	tmp = 0
	if (x * y) <= -4.6e+236:
		tmp = x * y
	elif (x * y) <= -1.6e+147:
		tmp = t_1
	elif (x * y) <= -3.4e-212:
		tmp = t_2
	elif (x * y) <= -8.5e-301:
		tmp = t_1
	elif (x * y) <= 9.5e+33:
		tmp = t_2
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	t_2 = Float64(c + Float64(t * Float64(z * 0.0625)))
	tmp = 0.0
	if (Float64(x * y) <= -4.6e+236)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.6e+147)
		tmp = t_1;
	elseif (Float64(x * y) <= -3.4e-212)
		tmp = t_2;
	elseif (Float64(x * y) <= -8.5e-301)
		tmp = t_1;
	elseif (Float64(x * y) <= 9.5e+33)
		tmp = t_2;
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b * -0.25);
	t_2 = c + (t * (z * 0.0625));
	tmp = 0.0;
	if ((x * y) <= -4.6e+236)
		tmp = x * y;
	elseif ((x * y) <= -1.6e+147)
		tmp = t_1;
	elseif ((x * y) <= -3.4e-212)
		tmp = t_2;
	elseif ((x * y) <= -8.5e-301)
		tmp = t_1;
	elseif ((x * y) <= 9.5e+33)
		tmp = t_2;
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.6e+236], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.6e+147], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -3.4e-212], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -8.5e-301], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 9.5e+33], t$95$2, N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4.5999999999999999e236

   1. Initial program 94.1%

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

   2. Taylor expanded in a around 0 94.1%

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

   3. Taylor expanded in c around 0 94.1%

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

   4. Taylor expanded in t around 0 100.0%

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

   if -4.5999999999999999e236 < (*.f64 x y) < -1.59999999999999989e147 or -3.39999999999999998e-212 < (*.f64 x y) < -8.50000000000000046e-301

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 80.0%

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

      1. *-commutative 80.0%

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

      2. associate-*r* 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in a around inf 66.2%

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

      1. *-commutative 66.2%

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

      2. associate-*r* 66.2%

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

      3. *-commutative 66.2%

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

   7. Simplified 66.2%

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

   if -1.59999999999999989e147 < (*.f64 x y) < -3.39999999999999998e-212 or -8.50000000000000046e-301 < (*.f64 x y) < 9.5000000000000003e33

   1. Initial program 99.4%

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

   2. Taylor expanded in a around 0 69.8%

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

   3. Taylor expanded in t around inf 63.9%

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

      1. associate-*r* 63.9%

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

      2. *-commutative 63.9%

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

      3. associate-*l* 63.9%

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

   5. Simplified 63.9%

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

   if 9.5000000000000003e33 < (*.f64 x y)

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 84.9%

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

   3. Taylor expanded in t around 0 64.3%

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

      1. +-commutative 64.3%

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

   5. Simplified 64.3%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.6 \cdot 10^{+236}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.6 \cdot 10^{+147}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -3.4 \cdot 10^{-212}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -8.5 \cdot 10^{-301}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 9.5 \cdot 10^{+33}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 4: 62.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+243}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.5 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1.7 \cdot 10^{-168}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25)))))
   (if (<= (* x y) -2.7e+243)
     (* x y)
     (if (<= (* x y) -3.5e+142)
       t_1
       (if (<= (* x y) -1.7e-168)
         (+ c (* t (* z 0.0625)))
         (if (<= (* x y) 5e+29) t_1 (+ c (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double tmp;
	if ((x * y) <= -2.7e+243) {
		tmp = x * y;
	} else if ((x * y) <= -3.5e+142) {
		tmp = t_1;
	} else if ((x * y) <= -1.7e-168) {
		tmp = c + (t * (z * 0.0625));
	} else if ((x * y) <= 5e+29) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = c + (a * (b * (-0.25d0)))
    if ((x * y) <= (-2.7d+243)) then
        tmp = x * y
    else if ((x * y) <= (-3.5d+142)) then
        tmp = t_1
    else if ((x * y) <= (-1.7d-168)) then
        tmp = c + (t * (z * 0.0625d0))
    else if ((x * y) <= 5d+29) then
        tmp = t_1
    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 t_1 = c + (a * (b * -0.25));
	double tmp;
	if ((x * y) <= -2.7e+243) {
		tmp = x * y;
	} else if ((x * y) <= -3.5e+142) {
		tmp = t_1;
	} else if ((x * y) <= -1.7e-168) {
		tmp = c + (t * (z * 0.0625));
	} else if ((x * y) <= 5e+29) {
		tmp = t_1;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	tmp = 0
	if (x * y) <= -2.7e+243:
		tmp = x * y
	elif (x * y) <= -3.5e+142:
		tmp = t_1
	elif (x * y) <= -1.7e-168:
		tmp = c + (t * (z * 0.0625))
	elif (x * y) <= 5e+29:
		tmp = t_1
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	tmp = 0.0
	if (Float64(x * y) <= -2.7e+243)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -3.5e+142)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.7e-168)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (Float64(x * y) <= 5e+29)
		tmp = t_1;
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (a * (b * -0.25));
	tmp = 0.0;
	if ((x * y) <= -2.7e+243)
		tmp = x * y;
	elseif ((x * y) <= -3.5e+142)
		tmp = t_1;
	elseif ((x * y) <= -1.7e-168)
		tmp = c + (t * (z * 0.0625));
	elseif ((x * y) <= 5e+29)
		tmp = t_1;
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.7e+243], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.5e+142], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.7e-168], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+29], t$95$1, N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2.7000000000000001e243

   1. Initial program 94.1%

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

   2. Taylor expanded in a around 0 94.1%

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

   3. Taylor expanded in c around 0 94.1%

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

   4. Taylor expanded in t around 0 100.0%

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

   if -2.7000000000000001e243 < (*.f64 x y) < -3.49999999999999997e142 or -1.70000000000000011e-168 < (*.f64 x y) < 5.0000000000000001e29

   1. Initial program 99.3%

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

   2. Taylor expanded in a around inf 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-*r* 74.4%

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

   4. Simplified 74.4%

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

   if -3.49999999999999997e142 < (*.f64 x y) < -1.70000000000000011e-168

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 76.9%

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

   3. Taylor expanded in t around inf 62.8%

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

      1. associate-*r* 62.8%

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

      2. *-commutative 62.8%

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

      3. associate-*l* 62.8%

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

   5. Simplified 62.8%

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

   if 5.0000000000000001e29 < (*.f64 x y)

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 84.9%

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

   3. Taylor expanded in t around 0 64.3%

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

      1. +-commutative 64.3%

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

   5. Simplified 64.3%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+243}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.5 \cdot 10^{+142}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -1.7 \cdot 10^{-168}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+29}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 5: 86.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+188} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{-81}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e+188) (not (<= (* a b) 5e-81)))
   (- (+ c (* x y)) (* (* a b) 0.25))
   (+ c (+ (* x y) (* (* z t) 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+188) || !((a * b) <= 5e-81)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	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+188)) .or. (.not. ((a * b) <= 5d-81))) then
        tmp = (c + (x * y)) - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + ((z * t) * 0.0625d0))
    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+188) || !((a * b) <= 5e-81)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -5e+188) or not ((a * b) <= 5e-81):
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + ((z * t) * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -5e+188) || !(Float64(a * b) <= 5e-81))
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -5e+188) || ~(((a * b) <= 5e-81)))
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e+188], N[Not[LessEqual[N[(a * b), $MachinePrecision], 5e-81]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.0000000000000001e188 or 4.99999999999999981e-81 < (*.f64 a b)

   1. Initial program 98.2%

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

   2. Taylor expanded in z around 0 89.5%

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

   if -5.0000000000000001e188 < (*.f64 a b) < 4.99999999999999981e-81

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 95.7%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+188} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{-81}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 6: 97.4% 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 99.2%

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

2. Final simplification 99.2%

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

Alternative 7: 36.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-297}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-52}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+21}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+101}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))))
   (if (<= b -5e-65)
     t_1
     (if (<= b -2.3e-297)
       (* x y)
       (if (<= b 1.1e-52)
         c
         (if (<= b 2.05e+21) (* x y) (if (<= b 3.6e+101) c t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double tmp;
	if (b <= -5e-65) {
		tmp = t_1;
	} else if (b <= -2.3e-297) {
		tmp = x * y;
	} else if (b <= 1.1e-52) {
		tmp = c;
	} else if (b <= 2.05e+21) {
		tmp = x * y;
	} else if (b <= 3.6e+101) {
		tmp = c;
	} 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 = a * (b * (-0.25d0))
    if (b <= (-5d-65)) then
        tmp = t_1
    else if (b <= (-2.3d-297)) then
        tmp = x * y
    else if (b <= 1.1d-52) then
        tmp = c
    else if (b <= 2.05d+21) then
        tmp = x * y
    else if (b <= 3.6d+101) then
        tmp = 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 = a * (b * -0.25);
	double tmp;
	if (b <= -5e-65) {
		tmp = t_1;
	} else if (b <= -2.3e-297) {
		tmp = x * y;
	} else if (b <= 1.1e-52) {
		tmp = c;
	} else if (b <= 2.05e+21) {
		tmp = x * y;
	} else if (b <= 3.6e+101) {
		tmp = c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	tmp = 0
	if b <= -5e-65:
		tmp = t_1
	elif b <= -2.3e-297:
		tmp = x * y
	elif b <= 1.1e-52:
		tmp = c
	elif b <= 2.05e+21:
		tmp = x * y
	elif b <= 3.6e+101:
		tmp = c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (b <= -5e-65)
		tmp = t_1;
	elseif (b <= -2.3e-297)
		tmp = Float64(x * y);
	elseif (b <= 1.1e-52)
		tmp = c;
	elseif (b <= 2.05e+21)
		tmp = Float64(x * y);
	elseif (b <= 3.6e+101)
		tmp = c;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b * -0.25);
	tmp = 0.0;
	if (b <= -5e-65)
		tmp = t_1;
	elseif (b <= -2.3e-297)
		tmp = x * y;
	elseif (b <= 1.1e-52)
		tmp = c;
	elseif (b <= 2.05e+21)
		tmp = x * y;
	elseif (b <= 3.6e+101)
		tmp = c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e-65], t$95$1, If[LessEqual[b, -2.3e-297], N[(x * y), $MachinePrecision], If[LessEqual[b, 1.1e-52], c, If[LessEqual[b, 2.05e+21], N[(x * y), $MachinePrecision], If[LessEqual[b, 3.6e+101], c, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.99999999999999983e-65 or 3.60000000000000029e101 < b

   1. Initial program 98.3%

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

   2. Taylor expanded in a around inf 68.9%

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

      1. *-commutative 68.9%

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

      2. associate-*r* 68.9%

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

   4. Simplified 68.9%

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

   5. Taylor expanded in a around inf 52.4%

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

      1. *-commutative 52.4%

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

      2. associate-*r* 52.4%

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

      3. *-commutative 52.4%

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

   7. Simplified 52.4%

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

   if -4.99999999999999983e-65 < b < -2.2999999999999999e-297 or 1.10000000000000005e-52 < b < 2.05e21

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 86.0%

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

   3. Taylor expanded in c around 0 62.6%

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

   4. Taylor expanded in t around 0 34.2%

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

   if -2.2999999999999999e-297 < b < 1.10000000000000005e-52 or 2.05e21 < b < 3.60000000000000029e101

   1. Initial program 100.0%

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

   2. Taylor expanded in c around inf 39.3%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-65}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-297}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-52}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+21}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+101}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]

Alternative 8: 75.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.4 \cdot 10^{-50} \lor \neg \left(b \leq 8.5 \cdot 10^{+165}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -8.4e-50) (not (<= b 8.5e+165)))
   (+ c (* a (* b -0.25)))
   (+ c (+ (* x y) (* (* z t) 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -8.4e-50) || !(b <= 8.5e+165)) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	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 ((b <= (-8.4d-50)) .or. (.not. (b <= 8.5d+165))) then
        tmp = c + (a * (b * (-0.25d0)))
    else
        tmp = c + ((x * y) + ((z * t) * 0.0625d0))
    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 ((b <= -8.4e-50) || !(b <= 8.5e+165)) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -8.4e-50) or not (b <= 8.5e+165):
		tmp = c + (a * (b * -0.25))
	else:
		tmp = c + ((x * y) + ((z * t) * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -8.4e-50) || !(b <= 8.5e+165))
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -8.4e-50) || ~((b <= 8.5e+165)))
		tmp = c + (a * (b * -0.25));
	else
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -8.4e-50], N[Not[LessEqual[b, 8.5e+165]], $MachinePrecision]], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.4000000000000003e-50 or 8.5000000000000001e165 < b

   1. Initial program 98.1%

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

   2. Taylor expanded in a around inf 70.2%

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

      1. *-commutative 70.2%

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

      2. associate-*r* 70.2%

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

   4. Simplified 70.2%

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

   if -8.4000000000000003e-50 < b < 8.5000000000000001e165

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 86.0%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.4 \cdot 10^{-50} \lor \neg \left(b \leq 8.5 \cdot 10^{+165}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 9: 37.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-296}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-15}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))))
   (if (<= b -5.5e-65)
     t_1
     (if (<= b -1.3e-296)
       (* x y)
       (if (<= b 5.5e-15) c (if (<= b 3.1e+41) (* t (* z 0.0625)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double tmp;
	if (b <= -5.5e-65) {
		tmp = t_1;
	} else if (b <= -1.3e-296) {
		tmp = x * y;
	} else if (b <= 5.5e-15) {
		tmp = c;
	} else if (b <= 3.1e+41) {
		tmp = t * (z * 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 = a * (b * (-0.25d0))
    if (b <= (-5.5d-65)) then
        tmp = t_1
    else if (b <= (-1.3d-296)) then
        tmp = x * y
    else if (b <= 5.5d-15) then
        tmp = c
    else if (b <= 3.1d+41) then
        tmp = t * (z * 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 = a * (b * -0.25);
	double tmp;
	if (b <= -5.5e-65) {
		tmp = t_1;
	} else if (b <= -1.3e-296) {
		tmp = x * y;
	} else if (b <= 5.5e-15) {
		tmp = c;
	} else if (b <= 3.1e+41) {
		tmp = t * (z * 0.0625);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	tmp = 0
	if b <= -5.5e-65:
		tmp = t_1
	elif b <= -1.3e-296:
		tmp = x * y
	elif b <= 5.5e-15:
		tmp = c
	elif b <= 3.1e+41:
		tmp = t * (z * 0.0625)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (b <= -5.5e-65)
		tmp = t_1;
	elseif (b <= -1.3e-296)
		tmp = Float64(x * y);
	elseif (b <= 5.5e-15)
		tmp = c;
	elseif (b <= 3.1e+41)
		tmp = Float64(t * Float64(z * 0.0625));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b * -0.25);
	tmp = 0.0;
	if (b <= -5.5e-65)
		tmp = t_1;
	elseif (b <= -1.3e-296)
		tmp = x * y;
	elseif (b <= 5.5e-15)
		tmp = c;
	elseif (b <= 3.1e+41)
		tmp = t * (z * 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[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e-65], t$95$1, If[LessEqual[b, -1.3e-296], N[(x * y), $MachinePrecision], If[LessEqual[b, 5.5e-15], c, If[LessEqual[b, 3.1e+41], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.4999999999999999e-65 or 3.1e41 < b

   1. Initial program 98.5%

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

   2. Taylor expanded in a around inf 69.0%

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

      1. *-commutative 69.0%

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

      2. associate-*r* 69.0%

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

   4. Simplified 69.0%

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

   5. Taylor expanded in a around inf 49.0%

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

      1. *-commutative 49.0%

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

      2. associate-*r* 49.0%

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

      3. *-commutative 49.0%

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

   7. Simplified 49.0%

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

   if -5.4999999999999999e-65 < b < -1.3e-296

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 91.6%

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

   3. Taylor expanded in c around 0 59.3%

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

   4. Taylor expanded in t around 0 35.6%

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

   if -1.3e-296 < b < 5.5000000000000002e-15

   1. Initial program 100.0%

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

   2. Taylor expanded in c around inf 35.0%

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

   if 5.5000000000000002e-15 < b < 3.1e41

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 73.8%

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

   3. Taylor expanded in t around inf 54.7%

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

      1. associate-*r* 54.7%

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

      2. *-commutative 54.7%

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

      3. associate-*l* 54.7%

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

   5. Simplified 54.7%

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

   6. Taylor expanded in c around 0 52.2%

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

      1. associate-*r* 52.2%

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

      2. *-commutative 52.2%

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

      3. associate-*r* 52.2%

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

   8. Simplified 52.2%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-65}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-296}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-15}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]

Alternative 10: 40.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.5 \cdot 10^{-79} \lor \neg \left(x \cdot y \leq 1.15 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.5e-79) (not (<= (* x y) 1.15e+42))) (* 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) <= -1.5e-79) || !((x * y) <= 1.15e+42)) {
		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) <= (-1.5d-79)) .or. (.not. ((x * y) <= 1.15d+42))) 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) <= -1.5e-79) || !((x * y) <= 1.15e+42)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.5e-79) or not ((x * y) <= 1.15e+42):
		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) <= -1.5e-79) || !(Float64(x * y) <= 1.15e+42))
		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) <= -1.5e-79) || ~(((x * y) <= 1.15e+42)))
		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], -1.5e-79], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.15e+42]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.5e-79 or 1.15e42 < (*.f64 x y)

   1. Initial program 99.1%

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

   2. Taylor expanded in a around 0 77.9%

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

   3. Taylor expanded in c around 0 68.0%

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

   4. Taylor expanded in t around 0 47.9%

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

   if -1.5e-79 < (*.f64 x y) < 1.15e42

   1. Initial program 99.3%

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

   2. Taylor expanded in c around inf 39.2%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.5 \cdot 10^{-79} \lor \neg \left(x \cdot y \leq 1.15 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 11: 51.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+82} \lor \neg \left(a \leq 4 \cdot 10^{-52}\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -2e+82) (not (<= a 4e-52))) (* a (* b -0.25)) (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -2e+82) || !(a <= 4e-52)) {
		tmp = a * (b * -0.25);
	} 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 <= (-2d+82)) .or. (.not. (a <= 4d-52))) then
        tmp = a * (b * (-0.25d0))
    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 <= -2e+82) || !(a <= 4e-52)) {
		tmp = a * (b * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -2e+82) or not (a <= 4e-52):
		tmp = a * (b * -0.25)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -2e+82) || !(a <= 4e-52))
		tmp = Float64(a * Float64(b * -0.25));
	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 <= -2e+82) || ~((a <= 4e-52)))
		tmp = a * (b * -0.25);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -2e+82], N[Not[LessEqual[a, 4e-52]], $MachinePrecision]], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9999999999999999e82 or 4e-52 < a

   1. Initial program 99.1%

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

   2. Taylor expanded in a around inf 70.7%

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

      1. *-commutative 70.7%

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

      2. associate-*r* 70.7%

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

   4. Simplified 70.7%

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

   5. Taylor expanded in a around inf 55.9%

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

      1. *-commutative 55.9%

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

      2. associate-*r* 55.9%

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

      3. *-commutative 55.9%

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

   7. Simplified 55.9%

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

   if -1.9999999999999999e82 < a < 4e-52

   1. Initial program 99.3%

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

   2. Taylor expanded in a around 0 90.4%

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

   3. Taylor expanded in t around 0 62.6%

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

      1. +-commutative 62.6%

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

   5. Simplified 62.6%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+82} \lor \neg \left(a \leq 4 \cdot 10^{-52}\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 12: 22.5% 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 99.2%

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

2. Taylor expanded in c around inf 26.3%

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

3. Final simplification 26.3%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023318 
(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))