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

Percentage Accurate: 97.7% → 98.6%

Time: 13.5s

Alternatives: 14

Speedup: 0.5×

• 33.2% 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: 97.7% 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: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(x \cdot y + z \cdot \left(t \cdot 0.0625\right)\right) - a \cdot \frac{b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) INFINITY)
   (+ c (- (+ (* x y) (* z (* t 0.0625))) (* a (/ b 4.0))))
   (- (+ 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 ((((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) <= ((double) INFINITY)) {
		tmp = c + (((x * y) + (z * (t * 0.0625))) - (a * (b / 4.0)));
	} else {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) <= Double.POSITIVE_INFINITY) {
		tmp = c + (((x * y) + (z * (t * 0.0625))) - (a * (b / 4.0)));
	} else {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) <= math.inf:
		tmp = c + (((x * y) + (z * (t * 0.0625))) - (a * (b / 4.0)))
	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(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) <= Inf)
		tmp = Float64(c + Float64(Float64(Float64(x * y) + Float64(z * Float64(t * 0.0625))) - Float64(a * Float64(b / 4.0))));
	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 ((((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) <= Inf)
		tmp = c + (((x * y) + (z * (t * 0.0625))) - (a * (b / 4.0)));
	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[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision], Infinity], N[(c + N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(b / 4.0), $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 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64))) < +inf.0

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+l- 99.7%

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

      6. fma-define 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-/l* 100.0%

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

      9. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-*r/ 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-*r/ 100.0%

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

      5. div-inv 100.0%

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

      6. metadata-eval 100.0%

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

   6. Applied egg-rr 100.0%

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

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64)))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0 80.0%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(x \cdot y + z \cdot \left(t \cdot 0.0625\right)\right) - a \cdot \frac{b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. associate--l+ 97.7%

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

   2. fma-define 97.7%

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

   3. associate-/l* 98.0%

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

   4. fmm-def 99.2%

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

   5. distribute-neg-frac2 99.2%

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

   6. metadata-eval 99.2%

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

3. Simplified 99.2%

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

Alternative 3: 98.3% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. associate-+l- 97.7%

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

   2. +-commutative 97.7%

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

   3. *-commutative 97.7%

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

   4. +-commutative 97.7%

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

   5. associate-+l- 97.7%

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

   6. fma-define 97.7%

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

   7. *-commutative 97.7%

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

   8. associate-/l* 98.0%

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

   9. associate-/l* 98.0%

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

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 4: 63.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+192}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-145}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{+61}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+201}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25)))) (t_2 (+ c (* x y))))
   (if (<= (* x y) -1e+192)
     t_2
     (if (<= (* x y) -2e-145)
       (+ c (* 0.0625 (* z t)))
       (if (<= (* x y) 2e-182)
         t_1
         (if (<= (* x y) 1e+61)
           (+ c (* z (* t 0.0625)))
           (if (<= (* x y) 4e+201) t_1 t_2)))))))

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 t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -1e+192) {
		tmp = t_2;
	} else if ((x * y) <= -2e-145) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 2e-182) {
		tmp = t_1;
	} else if ((x * y) <= 1e+61) {
		tmp = c + (z * (t * 0.0625));
	} else if ((x * y) <= 4e+201) {
		tmp = t_1;
	} else {
		tmp = 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 = c + (a * (b * (-0.25d0)))
    t_2 = c + (x * y)
    if ((x * y) <= (-1d+192)) then
        tmp = t_2
    else if ((x * y) <= (-2d-145)) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((x * y) <= 2d-182) then
        tmp = t_1
    else if ((x * y) <= 1d+61) then
        tmp = c + (z * (t * 0.0625d0))
    else if ((x * y) <= 4d+201) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -1e+192) {
		tmp = t_2;
	} else if ((x * y) <= -2e-145) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 2e-182) {
		tmp = t_1;
	} else if ((x * y) <= 1e+61) {
		tmp = c + (z * (t * 0.0625));
	} else if ((x * y) <= 4e+201) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	t_2 = c + (x * y)
	tmp = 0
	if (x * y) <= -1e+192:
		tmp = t_2
	elif (x * y) <= -2e-145:
		tmp = c + (0.0625 * (z * t))
	elif (x * y) <= 2e-182:
		tmp = t_1
	elif (x * y) <= 1e+61:
		tmp = c + (z * (t * 0.0625))
	elif (x * y) <= 4e+201:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_2 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1e+192)
		tmp = t_2;
	elseif (Float64(x * y) <= -2e-145)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(x * y) <= 2e-182)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e+61)
		tmp = Float64(c + Float64(z * Float64(t * 0.0625)));
	elseif (Float64(x * y) <= 4e+201)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (a * (b * -0.25));
	t_2 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -1e+192)
		tmp = t_2;
	elseif ((x * y) <= -2e-145)
		tmp = c + (0.0625 * (z * t));
	elseif ((x * y) <= 2e-182)
		tmp = t_1;
	elseif ((x * y) <= 1e+61)
		tmp = c + (z * (t * 0.0625));
	elseif ((x * y) <= 4e+201)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+192], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -2e-145], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-182], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e+61], N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+201], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.00000000000000004e192 or 4.00000000000000015e201 < (*.f64 x y)

   1. Initial program 93.9%

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

   3. Taylor expanded in a around 0 91.1%

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

   4. Taylor expanded in t around 0 91.2%

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

   if -1.00000000000000004e192 < (*.f64 x y) < -1.99999999999999983e-145

   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 x around 0 96.6%

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

   4. Taylor expanded in a around 0 69.1%

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

   if -1.99999999999999983e-145 < (*.f64 x y) < 2.0000000000000001e-182 or 9.99999999999999949e60 < (*.f64 x y) < 4.00000000000000015e201

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. fma-define 100.0%

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

      3. associate-/l* 100.0%

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

      4. fmm-def 100.0%

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

      5. distribute-neg-frac2 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 72.2%

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

      1. *-commutative 72.2%

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

      2. associate-*r* 72.2%

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

   7. Simplified 72.2%

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

   if 2.0000000000000001e-182 < (*.f64 x y) < 9.99999999999999949e60

   1. Initial program 94.6%

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

   3. Taylor expanded in x around 0 87.8%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 87.8%

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

      2. associate-*r* 90.3%

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

      3. *-commutative 90.3%

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

      4. *-commutative 90.3%

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

      5. associate-*r* 90.3%

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

   5. Applied egg-rr 90.3%

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

   6. Taylor expanded in z around inf 74.2%

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

      1. associate-*r* 76.7%

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

      2. *-commutative 76.7%

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

   8. Simplified 76.7%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+192}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-145}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-182}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+61}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+201}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-145}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-182}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+61}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* a b) 0.25))))
   (if (<= (* x y) -1e+191)
     t_1
     (if (<= (* x y) -2e-145)
       (+ c (* 0.0625 (* z t)))
       (if (<= (* x y) 2e-182)
         (+ c (* a (* b -0.25)))
         (if (<= (* x y) 1e+61) (+ 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 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((x * y) <= -1e+191) {
		tmp = t_1;
	} else if ((x * y) <= -2e-145) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 2e-182) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 1e+61) {
		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 = (x * y) - ((a * b) * 0.25d0)
    if ((x * y) <= (-1d+191)) then
        tmp = t_1
    else if ((x * y) <= (-2d-145)) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((x * y) <= 2d-182) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((x * y) <= 1d+61) 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 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((x * y) <= -1e+191) {
		tmp = t_1;
	} else if ((x * y) <= -2e-145) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 2e-182) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 1e+61) {
		tmp = c + (z * (t * 0.0625));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) - ((a * b) * 0.25)
	tmp = 0
	if (x * y) <= -1e+191:
		tmp = t_1
	elif (x * y) <= -2e-145:
		tmp = c + (0.0625 * (z * t))
	elif (x * y) <= 2e-182:
		tmp = c + (a * (b * -0.25))
	elif (x * y) <= 1e+61:
		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(Float64(x * y) - Float64(Float64(a * b) * 0.25))
	tmp = 0.0
	if (Float64(x * y) <= -1e+191)
		tmp = t_1;
	elseif (Float64(x * y) <= -2e-145)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(x * y) <= 2e-182)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 1e+61)
		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 = (x * y) - ((a * b) * 0.25);
	tmp = 0.0;
	if ((x * y) <= -1e+191)
		tmp = t_1;
	elseif ((x * y) <= -2e-145)
		tmp = c + (0.0625 * (z * t));
	elseif ((x * y) <= 2e-182)
		tmp = c + (a * (b * -0.25));
	elseif ((x * y) <= 1e+61)
		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[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+191], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2e-145], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-182], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+61], N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.00000000000000007e191 or 9.99999999999999949e60 < (*.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 z around 0 94.5%

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

   4. Taylor expanded in c around 0 88.4%

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

   if -1.00000000000000007e191 < (*.f64 x y) < -1.99999999999999983e-145

   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 x around 0 96.5%

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

   4. Taylor expanded in a around 0 70.4%

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

   if -1.99999999999999983e-145 < (*.f64 x y) < 2.0000000000000001e-182

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. fma-define 100.0%

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

      3. associate-/l* 100.0%

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

      4. fmm-def 100.0%

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

      5. distribute-neg-frac2 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 74.2%

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

      1. *-commutative 74.2%

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

      2. associate-*r* 74.2%

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

   7. Simplified 74.2%

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

   if 2.0000000000000001e-182 < (*.f64 x y) < 9.99999999999999949e60

   1. Initial program 94.6%

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

   3. Taylor expanded in x around 0 87.8%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 87.8%

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

      2. associate-*r* 90.3%

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

      3. *-commutative 90.3%

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

      4. *-commutative 90.3%

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

      5. associate-*r* 90.3%

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

   5. Applied egg-rr 90.3%

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

   6. Taylor expanded in z around inf 74.2%

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

      1. associate-*r* 76.7%

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

      2. *-commutative 76.7%

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

   8. Simplified 76.7%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+191}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-145}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-182}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+61}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;c + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
   (if (<= t_1 INFINITY) (+ c t_1) (- (+ 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 t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = c + t_1;
	} else {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = c + t_1;
	} else {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)
	tmp = 0
	if t_1 <= math.inf:
		tmp = c + t_1
	else:
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(c + t_1);
	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)
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = c + t_1;
	else
		tmp = (c + (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[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(c + t$95$1), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64))) < +inf.0

   1. Initial program 99.7%

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

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64)))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0 80.0%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+192} \lor \neg \left(x \cdot y \leq 10^{+61}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(z \cdot \left(t \cdot 0.0625\right) - b \cdot \left(a \cdot 0.25\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1e+192) (not (<= (* x y) 1e+61)))
   (- (+ c (* x y)) (* (* a b) 0.25))
   (+ c (- (* z (* t 0.0625)) (* b (* a 0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1e+192) || !((x * y) <= 1e+61)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((z * (t * 0.0625)) - (b * (a * 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) <= (-1d+192)) .or. (.not. ((x * y) <= 1d+61))) then
        tmp = (c + (x * y)) - ((a * b) * 0.25d0)
    else
        tmp = c + ((z * (t * 0.0625d0)) - (b * (a * 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) <= -1e+192) || !((x * y) <= 1e+61)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((z * (t * 0.0625)) - (b * (a * 0.25)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1e+192) or not ((x * y) <= 1e+61):
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	else:
		tmp = c + ((z * (t * 0.0625)) - (b * (a * 0.25)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1e+192) || !(Float64(x * y) <= 1e+61))
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(z * Float64(t * 0.0625)) - Float64(b * Float64(a * 0.25))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1e+192) || ~(((x * y) <= 1e+61)))
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	else
		tmp = c + ((z * (t * 0.0625)) - (b * (a * 0.25)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1e+192], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+61]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision] - N[(b * N[(a * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.00000000000000004e192 or 9.99999999999999949e60 < (*.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 z around 0 94.5%

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

   if -1.00000000000000004e192 < (*.f64 x y) < 9.99999999999999949e60

   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 x around 0 96.4%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 96.4%

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

      2. associate-*r* 96.9%

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

      3. *-commutative 96.9%

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

      4. *-commutative 96.9%

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

      5. associate-*r* 96.9%

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

   5. Applied egg-rr 96.9%

      \[\leadsto \color{blue}{c + \left(z \cdot \left(t \cdot 0.0625\right) - \left(0.25 \cdot a\right) \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+192} \lor \neg \left(x \cdot y \leq 10^{+61}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(z \cdot \left(t \cdot 0.0625\right) - b \cdot \left(a \cdot 0.25\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+147} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+28}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e+147) (not (<= (* a b) 2e+28)))
   (- (+ c (* x y)) (* (* a b) 0.25))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+147) || !((a * b) <= 2e+28)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	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+147)) .or. (.not. ((a * b) <= 2d+28))) then
        tmp = (c + (x * y)) - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    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+147) || !((a * b) <= 2e+28)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -5e+147) or not ((a * b) <= 2e+28):
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -5e+147) || !(Float64(a * b) <= 2e+28))
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -5e+147) || ~(((a * b) <= 2e+28)))
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e+147], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e+28]], $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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.0000000000000002e147 or 1.99999999999999992e28 < (*.f64 a b)

   1. Initial program 94.8%

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

   3. Taylor expanded in z around 0 85.5%

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

   if -5.0000000000000002e147 < (*.f64 a b) < 1.99999999999999992e28

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 93.6%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+147} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+28}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+147}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+75}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -5e+147)
   (+ c (* a (* b -0.25)))
   (if (<= (* a b) 5e+75)
     (+ 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+147) {
		tmp = c + (a * (b * -0.25));
	} else if ((a * b) <= 5e+75) {
		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+147)) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((a * b) <= 5d+75) 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+147) {
		tmp = c + (a * (b * -0.25));
	} else if ((a * b) <= 5e+75) {
		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+147:
		tmp = c + (a * (b * -0.25))
	elif (a * b) <= 5e+75:
		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+147)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(a * b) <= 5e+75)
		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+147)
		tmp = c + (a * (b * -0.25));
	elseif ((a * b) <= 5e+75)
		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+147], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+75], 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) < -5.0000000000000002e147

   1. Initial program 95.1%

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

      1. associate--l+ 95.1%

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

      2. fma-define 95.1%

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

      3. associate-/l* 95.1%

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

      4. fmm-def 100.0%

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

      5. distribute-neg-frac2 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 80.9%

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

      1. *-commutative 80.9%

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

      2. associate-*r* 80.9%

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

   7. Simplified 80.9%

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

   if -5.0000000000000002e147 < (*.f64 a b) < 5.0000000000000002e75

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 93.2%

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

   if 5.0000000000000002e75 < (*.f64 a b)

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 86.4%

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

   4. Taylor expanded in c around 0 77.2%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+147}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+75}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+192} \lor \neg \left(x \cdot y \leq 10^{+61}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1e+192) (not (<= (* x y) 1e+61)))
   (+ c (* x y))
   (+ c (* 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) <= -1e+192) || !((x * y) <= 1e+61)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (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) <= (-1d+192)) .or. (.not. ((x * y) <= 1d+61))) then
        tmp = c + (x * y)
    else
        tmp = c + (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) <= -1e+192) || !((x * y) <= 1e+61)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (z * (t * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1e+192) or not ((x * y) <= 1e+61):
		tmp = c + (x * y)
	else:
		tmp = c + (z * (t * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1e+192) || !(Float64(x * y) <= 1e+61))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(z * Float64(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) <= -1e+192) || ~(((x * y) <= 1e+61)))
		tmp = c + (x * y);
	else
		tmp = c + (z * (t * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1e+192], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+61]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.00000000000000004e192 or 9.99999999999999949e60 < (*.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 82.1%

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

   4. Taylor expanded in t around 0 80.2%

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

   if -1.00000000000000004e192 < (*.f64 x y) < 9.99999999999999949e60

   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 x around 0 96.4%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 96.4%

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

      2. associate-*r* 96.9%

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

      3. *-commutative 96.9%

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

      4. *-commutative 96.9%

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

      5. associate-*r* 96.9%

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

   5. Applied egg-rr 96.9%

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

   6. Taylor expanded in z around inf 66.5%

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

      1. associate-*r* 67.0%

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

      2. *-commutative 67.0%

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

   8. Simplified 67.0%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+192} \lor \neg \left(x \cdot y \leq 10^{+61}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+192} \lor \neg \left(x \cdot y \leq 10^{+61}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1e+192) (not (<= (* x y) 1e+61)))
   (+ c (* x y))
   (+ c (* 0.0625 (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1e+192) || !((x * y) <= 1e+61)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	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) <= (-1d+192)) .or. (.not. ((x * y) <= 1d+61))) then
        tmp = c + (x * y)
    else
        tmp = c + (0.0625d0 * (z * t))
    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) <= -1e+192) || !((x * y) <= 1e+61)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1e+192) or not ((x * y) <= 1e+61):
		tmp = c + (x * y)
	else:
		tmp = c + (0.0625 * (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1e+192) || !(Float64(x * y) <= 1e+61))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1e+192) || ~(((x * y) <= 1e+61)))
		tmp = c + (x * y);
	else
		tmp = c + (0.0625 * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1e+192], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+61]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.00000000000000004e192 or 9.99999999999999949e60 < (*.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 82.1%

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

   4. Taylor expanded in t around 0 80.2%

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

   if -1.00000000000000004e192 < (*.f64 x y) < 9.99999999999999949e60

   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 x around 0 96.4%

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

   4. Taylor expanded in a around 0 66.5%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+192} \lor \neg \left(x \cdot y \leq 10^{+61}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+194} \lor \neg \left(a \leq 3 \cdot 10^{-32}\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -1.25e+194) (not (<= a 3e-32)))
   (* 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 <= -1.25e+194) || !(a <= 3e-32)) {
		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 <= (-1.25d+194)) .or. (.not. (a <= 3d-32))) 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 <= -1.25e+194) || !(a <= 3e-32)) {
		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 <= -1.25e+194) or not (a <= 3e-32):
		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 <= -1.25e+194) || !(a <= 3e-32))
		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 <= -1.25e+194) || ~((a <= 3e-32)))
		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, -1.25e+194], N[Not[LessEqual[a, 3e-32]], $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 < -1.24999999999999997e194 or 3e-32 < a

   1. Initial program 94.2%

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

   3. Taylor expanded in z around inf 73.6%

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

   4. Taylor expanded in a around inf 47.1%

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

      1. associate-*r/ 44.8%

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

      2. associate-*r* 44.8%

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

      3. *-commutative 44.8%

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

   6. Simplified 44.8%

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

   7. Taylor expanded in z around 0 53.9%

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

      1. *-commutative 53.9%

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

      2. associate-*l* 53.9%

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

      3. *-commutative 53.9%

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

   9. Simplified 53.9%

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

   if -1.24999999999999997e194 < a < 3e-32

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 87.2%

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

   4. Taylor expanded in t around 0 59.7%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+194} \lor \neg \left(a \leq 3 \cdot 10^{-32}\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.25 \cdot 10^{+73}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+24}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -2.25e+73) c (if (<= c 5.5e+24) (* a (* b -0.25)) c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -2.25e+73) {
		tmp = c;
	} else if (c <= 5.5e+24) {
		tmp = a * (b * -0.25);
	} 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 (c <= (-2.25d+73)) then
        tmp = c
    else if (c <= 5.5d+24) then
        tmp = a * (b * (-0.25d0))
    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 (c <= -2.25e+73) {
		tmp = c;
	} else if (c <= 5.5e+24) {
		tmp = a * (b * -0.25);
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -2.25e+73:
		tmp = c
	elif c <= 5.5e+24:
		tmp = a * (b * -0.25)
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -2.25e+73)
		tmp = c;
	elseif (c <= 5.5e+24)
		tmp = Float64(a * Float64(b * -0.25));
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -2.25e+73)
		tmp = c;
	elseif (c <= 5.5e+24)
		tmp = a * (b * -0.25);
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -2.25e+73], c, If[LessEqual[c, 5.5e+24], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], c]]

Derivation

1. Split input into 2 regimes

2. if c < -2.24999999999999992e73 or 5.5000000000000002e24 < c

   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 50.7%

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

   if -2.24999999999999992e73 < c < 5.5000000000000002e24

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 80.4%

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

   4. Taylor expanded in a around inf 29.3%

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

      1. associate-*r/ 27.3%

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

      2. associate-*r* 27.3%

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

      3. *-commutative 27.3%

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

   6. Simplified 27.3%

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

   7. Taylor expanded in z around 0 37.8%

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

      1. *-commutative 37.8%

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

      2. associate-*l* 37.8%

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

      3. *-commutative 37.8%

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

   9. Simplified 37.8%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.25 \cdot 10^{+73}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+24}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 21.9% 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 97.7%

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

3. Taylor expanded in c around inf 25.2%

   \[\leadsto \color{blue}{c} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024163 
(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))