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

Percentage Accurate: 97.4% → 98.7%

Time: 13.9s

Alternatives: 16

Speedup: 1.0×

• 33.7% 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: 98.7% 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 98.1%

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

   3. associate-/l* 98.4%

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

   4. fma-neg 98.8%

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

   5. distribute-neg-frac2 98.8%

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

   6. metadata-eval 98.8%

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

3. Simplified 98.8%

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

Alternative 2: 97.8% 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%

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

   3. associate-+l- 97.7%

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

   4. fma-define 98.1%

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

   5. *-commutative 98.1%

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

   6. associate-/l* 98.4%

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

   7. associate-/l* 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 3: 65.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 10^{-262}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+143}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25)))))
   (if (<= (* a b) -2e+109)
     t_1
     (if (<= (* a b) 1e-262)
       (+ c (* x y))
       (if (<= (* a b) 2e+143) (+ c (* z (* t 0.0625))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double tmp;
	if ((a * b) <= -2e+109) {
		tmp = t_1;
	} else if ((a * b) <= 1e-262) {
		tmp = c + (x * y);
	} else if ((a * b) <= 2e+143) {
		tmp = c + (z * (t * 0.0625));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c + (a * (b * (-0.25d0)))
    if ((a * b) <= (-2d+109)) then
        tmp = t_1
    else if ((a * b) <= 1d-262) then
        tmp = c + (x * y)
    else if ((a * b) <= 2d+143) then
        tmp = c + (z * (t * 0.0625d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double tmp;
	if ((a * b) <= -2e+109) {
		tmp = t_1;
	} else if ((a * b) <= 1e-262) {
		tmp = c + (x * y);
	} else if ((a * b) <= 2e+143) {
		tmp = c + (z * (t * 0.0625));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	tmp = 0
	if (a * b) <= -2e+109:
		tmp = t_1
	elif (a * b) <= 1e-262:
		tmp = c + (x * y)
	elif (a * b) <= 2e+143:
		tmp = c + (z * (t * 0.0625))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	tmp = 0.0
	if (Float64(a * b) <= -2e+109)
		tmp = t_1;
	elseif (Float64(a * b) <= 1e-262)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(a * b) <= 2e+143)
		tmp = Float64(c + Float64(z * Float64(t * 0.0625)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (a * (b * -0.25));
	tmp = 0.0;
	if ((a * b) <= -2e+109)
		tmp = t_1;
	elseif ((a * b) <= 1e-262)
		tmp = c + (x * y);
	elseif ((a * b) <= 2e+143)
		tmp = c + (z * (t * 0.0625));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+109], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1e-262], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+143], N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.99999999999999996e109 or 2e143 < (*.f64 a b)

   1. Initial program 95.9%

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

      1. associate--l+ 95.9%

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

      2. fma-define 95.9%

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

      3. associate-/l* 95.9%

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

      4. fma-neg 97.3%

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

      5. distribute-neg-frac2 97.3%

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

      6. metadata-eval 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in a around inf 81.7%

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

      1. *-commutative 81.7%

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

      2. associate-*r* 81.7%

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

   7. Simplified 81.7%

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

   if -1.99999999999999996e109 < (*.f64 a b) < 1.00000000000000001e-262

   1. Initial program 99.1%

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

   3. Taylor expanded in a around 0 93.5%

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

   4. Taylor expanded in t around 0 66.0%

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

      1. +-commutative 66.0%

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

   6. Simplified 66.0%

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

   if 1.00000000000000001e-262 < (*.f64 a b) < 2e143

   1. Initial program 97.1%

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

   3. Taylor expanded in a around 0 88.2%

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

   4. Taylor expanded in x around inf 82.3%

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

      1. associate-*r/ 82.3%

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

      2. associate-*r* 83.6%

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

      3. *-commutative 83.6%

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

      4. *-commutative 83.6%

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

      5. *-commutative 83.6%

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

   6. Simplified 83.6%

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

   7. Taylor expanded in x around 0 66.5%

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

      1. associate-*r* 67.8%

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

      2. *-commutative 67.8%

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

   9. Simplified 67.8%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+109}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{-262}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+143}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+62}:\\ \;\;\;\;c + x \cdot \left(y + \frac{z \cdot \left(t \cdot 0.0625\right)}{x}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+184}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)))
   (if (<= (* x y) -1e+62)
     (+ c (* x (+ y (/ (* z (* t 0.0625)) x))))
     (if (<= (* x y) 2e+184)
       (- (+ c (* 0.0625 (* z t))) t_1)
       (- (+ c (* x y)) 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 ((x * y) <= -1e+62) {
		tmp = c + (x * (y + ((z * (t * 0.0625)) / x)));
	} else if ((x * y) <= 2e+184) {
		tmp = (c + (0.0625 * (z * t))) - t_1;
	} else {
		tmp = (c + (x * y)) - 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 ((x * y) <= (-1d+62)) then
        tmp = c + (x * (y + ((z * (t * 0.0625d0)) / x)))
    else if ((x * y) <= 2d+184) then
        tmp = (c + (0.0625d0 * (z * t))) - t_1
    else
        tmp = (c + (x * y)) - 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 ((x * y) <= -1e+62) {
		tmp = c + (x * (y + ((z * (t * 0.0625)) / x)));
	} else if ((x * y) <= 2e+184) {
		tmp = (c + (0.0625 * (z * t))) - t_1;
	} else {
		tmp = (c + (x * y)) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	tmp = 0
	if (x * y) <= -1e+62:
		tmp = c + (x * (y + ((z * (t * 0.0625)) / x)))
	elif (x * y) <= 2e+184:
		tmp = (c + (0.0625 * (z * t))) - t_1
	else:
		tmp = (c + (x * y)) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if (Float64(x * y) <= -1e+62)
		tmp = Float64(c + Float64(x * Float64(y + Float64(Float64(z * Float64(t * 0.0625)) / x))));
	elseif (Float64(x * y) <= 2e+184)
		tmp = Float64(Float64(c + Float64(0.0625 * Float64(z * t))) - t_1);
	else
		tmp = Float64(Float64(c + Float64(x * y)) - 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 ((x * y) <= -1e+62)
		tmp = c + (x * (y + ((z * (t * 0.0625)) / x)));
	elseif ((x * y) <= 2e+184)
		tmp = (c + (0.0625 * (z * t))) - t_1;
	else
		tmp = (c + (x * y)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+62], N[(c + N[(x * N[(y + N[(N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+184], N[(N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.00000000000000004e62

   1. Initial program 97.0%

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

   3. Taylor expanded in a around 0 89.3%

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

   4. Taylor expanded in x around inf 89.4%

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

      1. associate-*r/ 89.4%

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

      2. associate-*r* 90.7%

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

      3. *-commutative 90.7%

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

      4. *-commutative 90.7%

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

      5. *-commutative 90.7%

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

   6. Simplified 90.7%

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

   if -1.00000000000000004e62 < (*.f64 x y) < 2.00000000000000003e184

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0 93.9%

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

   if 2.00000000000000003e184 < (*.f64 x y)

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 91.4%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+62}:\\ \;\;\;\;c + x \cdot \left(y + \frac{z \cdot \left(t \cdot 0.0625\right)}{x}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+184}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+71} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+143}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -4e+71) (not (<= (* a b) 2e+143)))
   (- (+ 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) <= -4e+71) || !((a * b) <= 2e+143)) {
		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) <= (-4d+71)) .or. (.not. ((a * b) <= 2d+143))) 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) <= -4e+71) || !((a * b) <= 2e+143)) {
		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) <= -4e+71) or not ((a * b) <= 2e+143):
		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) <= -4e+71) || !(Float64(a * b) <= 2e+143))
		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) <= -4e+71) || ~(((a * b) <= 2e+143)))
		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], -4e+71], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e+143]], $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) < -4.0000000000000002e71 or 2e143 < (*.f64 a b)

   1. Initial program 96.3%

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

   3. Taylor expanded in z around 0 87.5%

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

   if -4.0000000000000002e71 < (*.f64 a b) < 2e143

   1. Initial program 98.4%

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

   3. Taylor expanded in a around 0 92.6%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+71} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+143}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+242}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+143}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -5e+242)
   (- (* x y) (* (* a b) 0.25))
   (if (<= (* a b) 2e+143)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (+ c (* a (* b -0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -5e+242) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((a * b) <= 2e+143) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a * b) <= (-5d+242)) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else if ((a * b) <= 2d+143) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = c + (a * (b * (-0.25d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -5e+242) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((a * b) <= 2e+143) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -5e+242:
		tmp = (x * y) - ((a * b) * 0.25)
	elif (a * b) <= 2e+143:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = c + (a * (b * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -5e+242)
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	elseif (Float64(a * b) <= 2e+143)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -5e+242)
		tmp = (x * y) - ((a * b) * 0.25);
	elseif ((a * b) <= 2e+143)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = c + (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+242], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+143], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.0000000000000004e242

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0 93.2%

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

   4. Taylor expanded in c around 0 93.2%

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

   if -5.0000000000000004e242 < (*.f64 a b) < 2e143

   1. Initial program 98.5%

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

   3. Taylor expanded in a around 0 90.2%

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

   if 2e143 < (*.f64 a b)

   1. Initial program 94.0%

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

      1. associate--l+ 94.0%

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

      2. fma-define 94.0%

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

      3. associate-/l* 94.0%

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

      4. fma-neg 97.0%

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

      5. distribute-neg-frac2 97.0%

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

      6. metadata-eval 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in a around inf 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-*r* 84.4%

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

   7. Simplified 84.4%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+242}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+143}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+62} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+184}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1e+62) (not (<= (* x y) 2e+184)))
   (- (* x y) (* (* a b) 0.25))
   (+ 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+62) || !((x * y) <= 2e+184)) {
		tmp = (x * y) - ((a * b) * 0.25);
	} 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+62)) .or. (.not. ((x * y) <= 2d+184))) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    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+62) || !((x * y) <= 2e+184)) {
		tmp = (x * y) - ((a * b) * 0.25);
	} 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+62) or not ((x * y) <= 2e+184):
		tmp = (x * y) - ((a * b) * 0.25)
	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+62) || !(Float64(x * y) <= 2e+184))
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	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+62) || ~(((x * y) <= 2e+184)))
		tmp = (x * y) - ((a * b) * 0.25);
	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+62], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+184]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $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) < -1.00000000000000004e62 or 2.00000000000000003e184 < (*.f64 x y)

   1. Initial program 95.9%

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

   3. Taylor expanded in z around 0 85.8%

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

   4. Taylor expanded in c around 0 80.2%

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

   if -1.00000000000000004e62 < (*.f64 x y) < 2.00000000000000003e184

   1. Initial program 98.7%

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

   3. Taylor expanded in a around 0 68.8%

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

   4. Taylor expanded in x around inf 59.0%

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

      1. associate-*r/ 59.0%

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

      2. associate-*r* 59.0%

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

      3. *-commutative 59.0%

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

      4. *-commutative 59.0%

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

      5. *-commutative 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in x around 0 64.3%

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

      1. associate-*r* 64.3%

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

      2. *-commutative 64.3%

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

   9. Simplified 64.3%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+62} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+184}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+62} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+184}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1e+62) (not (<= (* x y) 2e+184)))
   (+ 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+62) || !((x * y) <= 2e+184)) {
		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+62)) .or. (.not. ((x * y) <= 2d+184))) 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+62) || !((x * y) <= 2e+184)) {
		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+62) or not ((x * y) <= 2e+184):
		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+62) || !(Float64(x * y) <= 2e+184))
		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+62) || ~(((x * y) <= 2e+184)))
		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+62], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+184]], $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) < -1.00000000000000004e62 or 2.00000000000000003e184 < (*.f64 x y)

   1. Initial program 95.9%

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

   3. Taylor expanded in a around 0 86.9%

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

   4. Taylor expanded in t around 0 75.7%

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

      1. +-commutative 75.7%

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

   6. Simplified 75.7%

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

   if -1.00000000000000004e62 < (*.f64 x y) < 2.00000000000000003e184

   1. Initial program 98.7%

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

   3. Taylor expanded in a around 0 68.8%

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

   4. Taylor expanded in x around inf 59.0%

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

      1. associate-*r/ 59.0%

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

      2. associate-*r* 59.0%

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

      3. *-commutative 59.0%

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

      4. *-commutative 59.0%

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

      5. *-commutative 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in x around 0 64.3%

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

      1. associate-*r* 64.3%

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

      2. *-commutative 64.3%

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

   9. Simplified 64.3%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+62} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+184}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+62} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+184}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1e+62) (not (<= (* x y) 2e+184)))
   (+ 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+62) || !((x * y) <= 2e+184)) {
		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+62)) .or. (.not. ((x * y) <= 2d+184))) 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+62) || !((x * y) <= 2e+184)) {
		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+62) or not ((x * y) <= 2e+184):
		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+62) || !(Float64(x * y) <= 2e+184))
		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+62) || ~(((x * y) <= 2e+184)))
		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+62], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+184]], $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) < -1.00000000000000004e62 or 2.00000000000000003e184 < (*.f64 x y)

   1. Initial program 95.9%

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

   3. Taylor expanded in a around 0 86.9%

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

   4. Taylor expanded in t around 0 75.7%

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

      1. +-commutative 75.7%

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

   6. Simplified 75.7%

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

   if -1.00000000000000004e62 < (*.f64 x y) < 2.00000000000000003e184

   1. Initial program 98.7%

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

   3. Taylor expanded in a around 0 68.8%

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

   4. Taylor expanded in x around 0 64.3%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+62} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+184}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.62 \cdot 10^{+59} \lor \neg \left(x \cdot y \leq 2.45 \cdot 10^{+184}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.62e+59) (not (<= (* x y) 2.45e+184)))
   (* 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) <= -1.62e+59) || !((x * y) <= 2.45e+184)) {
		tmp = x * y;
	} else {
		tmp = 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) <= (-1.62d+59)) .or. (.not. ((x * y) <= 2.45d+184))) then
        tmp = x * y
    else
        tmp = 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) <= -1.62e+59) || !((x * y) <= 2.45e+184)) {
		tmp = x * y;
	} else {
		tmp = z * (t * 0.0625);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.62e+59) or not ((x * y) <= 2.45e+184):
		tmp = x * y
	else:
		tmp = z * (t * 0.0625)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.62e+59) || !(Float64(x * y) <= 2.45e+184))
		tmp = Float64(x * y);
	else
		tmp = 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) <= -1.62e+59) || ~(((x * y) <= 2.45e+184)))
		tmp = x * y;
	else
		tmp = 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], -1.62e+59], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.45e+184]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.6200000000000001e59 or 2.45000000000000015e184 < (*.f64 x y)

   1. Initial program 96.0%

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

   3. Taylor expanded in a around 0 87.0%

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

   4. Taylor expanded in t around 0 76.0%

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

      1. +-commutative 76.0%

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

   6. Simplified 76.0%

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

   7. Taylor expanded in x around inf 69.3%

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

   if -1.6200000000000001e59 < (*.f64 x y) < 2.45000000000000015e184

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0 93.8%

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

   4. Taylor expanded in z around inf 83.9%

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

      1. associate--l+ 83.9%

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

      2. associate-*r/ 83.9%

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

      3. div-sub 84.0%

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

      4. *-commutative 84.0%

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

      5. cancel-sign-sub-inv 84.0%

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

      6. distribute-lft-neg-in 84.0%

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

      7. distribute-rgt-neg-in 84.0%

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

      8. metadata-eval 84.0%

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

      9. associate-*r* 84.0%

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

   6. Simplified 84.0%

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

   7. Taylor expanded in t around inf 37.2%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.62 \cdot 10^{+59} \lor \neg \left(x \cdot y \leq 2.45 \cdot 10^{+184}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.08 \cdot 10^{+60} \lor \neg \left(x \cdot y \leq 1.9 \cdot 10^{+146}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.08e+60) (not (<= (* x y) 1.9e+146)))
   (* x y)
   (* 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) <= -1.08e+60) || !((x * y) <= 1.9e+146)) {
		tmp = x * y;
	} else {
		tmp = 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) <= (-1.08d+60)) .or. (.not. ((x * y) <= 1.9d+146))) then
        tmp = x * y
    else
        tmp = 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) <= -1.08e+60) || !((x * y) <= 1.9e+146)) {
		tmp = x * y;
	} else {
		tmp = b * (a * -0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.08e+60) or not ((x * y) <= 1.9e+146):
		tmp = x * y
	else:
		tmp = b * (a * -0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.08e+60) || !(Float64(x * y) <= 1.9e+146))
		tmp = Float64(x * y);
	else
		tmp = 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) <= -1.08e+60) || ~(((x * y) <= 1.9e+146)))
		tmp = x * y;
	else
		tmp = 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], -1.08e+60], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.9e+146]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.08e60 or 1.8999999999999999e146 < (*.f64 x y)

   1. Initial program 96.1%

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

   3. Taylor expanded in a around 0 87.6%

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

   4. Taylor expanded in t around 0 73.0%

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

      1. +-commutative 73.0%

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

   6. Simplified 73.0%

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

   7. Taylor expanded in x around inf 67.6%

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

   if -1.08e60 < (*.f64 x y) < 1.8999999999999999e146

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0 94.3%

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

   4. Taylor expanded in t around 0 61.7%

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

   5. Taylor expanded in c around 0 33.4%

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

      1. *-commutative 33.4%

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

      2. *-commutative 33.4%

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

      3. associate-*r* 33.4%

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

   7. Simplified 33.4%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.08 \cdot 10^{+60} \lor \neg \left(x \cdot y \leq 1.9 \cdot 10^{+146}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 41.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+61} \lor \neg \left(x \cdot y \leq 4.4 \cdot 10^{+138}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2.7e+61) (not (<= (* x y) 4.4e+138))) (* 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) <= -2.7e+61) || !((x * y) <= 4.4e+138)) {
		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) <= (-2.7d+61)) .or. (.not. ((x * y) <= 4.4d+138))) 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) <= -2.7e+61) || !((x * y) <= 4.4e+138)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -2.7e+61) or not ((x * y) <= 4.4e+138):
		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) <= -2.7e+61) || !(Float64(x * y) <= 4.4e+138))
		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) <= -2.7e+61) || ~(((x * y) <= 4.4e+138)))
		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], -2.7e+61], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.4e+138]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.7000000000000002e61 or 4.4000000000000001e138 < (*.f64 x y)

   1. Initial program 96.1%

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

   3. Taylor expanded in a around 0 87.6%

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

   4. Taylor expanded in t around 0 73.0%

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

      1. +-commutative 73.0%

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

   6. Simplified 73.0%

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

   7. Taylor expanded in x around inf 67.6%

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

   if -2.7000000000000002e61 < (*.f64 x y) < 4.4000000000000001e138

   1. Initial program 98.7%

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

   3. Taylor expanded in c around inf 29.9%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+61} \lor \neg \left(x \cdot y \leq 4.4 \cdot 10^{+138}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ c + \left(\left(x \cdot y + z \cdot \left(t \cdot 0.0625\right)\right) - a \cdot \frac{b}{4}\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ c (- (+ (* x y) (* z (* t 0.0625))) (* 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 * 0.0625))) - (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 * 0.0625d0))) - (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 * 0.0625))) - (a * (b / 4.0)));
}

Python

def code(x, y, z, t, a, b, c):
	return c + (((x * y) + (z * (t * 0.0625))) - (a * (b / 4.0)))

Julia

function code(x, y, z, t, a, b, c)
	return Float64(c + Float64(Float64(Float64(x * y) + Float64(z * Float64(t * 0.0625))) - Float64(a * Float64(b / 4.0))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = c + (((x * y) + (z * (t * 0.0625))) - (a * (b / 4.0)));
end

Wolfram

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

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%

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

   3. associate-+l- 97.7%

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

   4. fma-define 98.1%

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

   5. *-commutative 98.1%

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

   6. associate-/l* 98.4%

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

   7. associate-/l* 98.4%

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

3. Simplified 98.4%

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

   1. fma-undefine 98.0%

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

   2. associate-*r/ 97.7%

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

   3. +-commutative 97.7%

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

   4. associate-*r/ 98.0%

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

   5. div-inv 98.0%

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

   6. metadata-eval 98.0%

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

6. Applied egg-rr 98.0%

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

7. Final simplification 98.0%

   \[\leadsto c + \left(\left(x \cdot y + z \cdot \left(t \cdot 0.0625\right)\right) - a \cdot \frac{b}{4}\right) \]
8. Add Preprocessing

Alternative 14: 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 97.7%

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

3. Final simplification 97.7%

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

Alternative 15: 52.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+181} \lor \neg \left(z \leq 2 \cdot 10^{-55}\right):\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -5.7e+181) (not (<= z 2e-55)))
   (* z (* t 0.0625))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5.7e+181) || !(z <= 2e-55)) {
		tmp = z * (t * 0.0625);
	} 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 ((z <= (-5.7d+181)) .or. (.not. (z <= 2d-55))) then
        tmp = z * (t * 0.0625d0)
    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 ((z <= -5.7e+181) || !(z <= 2e-55)) {
		tmp = z * (t * 0.0625);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -5.7e+181) or not (z <= 2e-55):
		tmp = z * (t * 0.0625)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -5.7e+181) || !(z <= 2e-55))
		tmp = Float64(z * Float64(t * 0.0625));
	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 ((z <= -5.7e+181) || ~((z <= 2e-55)))
		tmp = z * (t * 0.0625);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -5.7e+181], N[Not[LessEqual[z, 2e-55]], $MachinePrecision]], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7000000000000002e181 or 1.99999999999999999e-55 < z

   1. Initial program 95.5%

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

   3. Taylor expanded in x around 0 78.0%

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

   4. Taylor expanded in z around inf 78.9%

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

      1. associate--l+ 78.9%

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

      2. associate-*r/ 78.9%

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

      3. div-sub 78.9%

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

      4. *-commutative 78.9%

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

      5. cancel-sign-sub-inv 78.9%

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

      6. distribute-lft-neg-in 78.9%

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

      7. distribute-rgt-neg-in 78.9%

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

      8. metadata-eval 78.9%

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

      9. associate-*r* 78.9%

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

   6. Simplified 78.9%

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

   7. Taylor expanded in t around inf 48.0%

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

   if -5.7000000000000002e181 < z < 1.99999999999999999e-55

   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 72.1%

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

   4. Taylor expanded in t around 0 58.7%

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

      1. +-commutative 58.7%

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

   6. Simplified 58.7%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+181} \lor \neg \left(z \leq 2 \cdot 10^{-55}\right):\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 22.8% 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 21.0%

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

Reproduce

herbie shell --seed 2024129 
(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))