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

Percentage Accurate: 97.7% → 98.9%

Time: 10.1s

Alternatives: 12

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: 98.9% 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 96.9%

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

   1. associate--l+ 96.9%

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

   2. fma-define 99.2%

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

   3. associate-/l* 99.2%

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

   4. fma-neg 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. Final simplification 99.2%

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

Alternative 2: 98.6% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) INFINITY)
   (+ c (- (fma x y (* z (/ t 16.0))) (* a (/ b 4.0))))
   (+ c (- (* 0.0625 (* z t)) (* (* 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 + (fma(x, y, (z * (t / 16.0))) - (a * (b / 4.0)));
	} else {
		tmp = c + ((0.0625 * (z * t)) - ((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(fma(x, y, Float64(z * Float64(t / 16.0))) - Float64(a * Float64(b / 4.0))));
	else
		tmp = Float64(c + Float64(Float64(0.0625 * Float64(z * t)) - Float64(Float64(a * b) * 0.25)));
	end
	return 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[(x * y + N[(z * N[(t / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(b / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   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%

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

      2. *-commutative 100.0%

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

      3. associate-+l- 100.0%

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

      4. fma-define 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-/l* 100.0%

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

      7. associate-/l* 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

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

   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 x around 0 75.0%

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

4. Final simplification 99.2%

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

Alternative 3: 87.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ t_2 := c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+105}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+211}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+247}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (+ (* x y) (* 0.0625 (* z t)))))
        (t_2 (+ c (- (* x y) (* (* a b) 0.25)))))
   (if (<= (* a b) -2e+105)
     t_2
     (if (<= (* a b) 1e+21)
       t_1
       (if (<= (* a b) 5e+211)
         t_2
         (if (<= (* a b) 2e+247) t_1 (* a (* b -0.25))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + ((x * y) + (0.0625 * (z * t)));
	double t_2 = c + ((x * y) - ((a * b) * 0.25));
	double tmp;
	if ((a * b) <= -2e+105) {
		tmp = t_2;
	} else if ((a * b) <= 1e+21) {
		tmp = t_1;
	} else if ((a * b) <= 5e+211) {
		tmp = t_2;
	} else if ((a * b) <= 2e+247) {
		tmp = t_1;
	} else {
		tmp = a * (b * -0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + ((x * y) + (0.0625d0 * (z * t)))
    t_2 = c + ((x * y) - ((a * b) * 0.25d0))
    if ((a * b) <= (-2d+105)) then
        tmp = t_2
    else if ((a * b) <= 1d+21) then
        tmp = t_1
    else if ((a * b) <= 5d+211) then
        tmp = t_2
    else if ((a * b) <= 2d+247) then
        tmp = t_1
    else
        tmp = a * (b * (-0.25d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + ((x * y) + (0.0625 * (z * t)));
	double t_2 = c + ((x * y) - ((a * b) * 0.25));
	double tmp;
	if ((a * b) <= -2e+105) {
		tmp = t_2;
	} else if ((a * b) <= 1e+21) {
		tmp = t_1;
	} else if ((a * b) <= 5e+211) {
		tmp = t_2;
	} else if ((a * b) <= 2e+247) {
		tmp = t_1;
	} else {
		tmp = a * (b * -0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + ((x * y) + (0.0625 * (z * t)))
	t_2 = c + ((x * y) - ((a * b) * 0.25))
	tmp = 0
	if (a * b) <= -2e+105:
		tmp = t_2
	elif (a * b) <= 1e+21:
		tmp = t_1
	elif (a * b) <= 5e+211:
		tmp = t_2
	elif (a * b) <= 2e+247:
		tmp = t_1
	else:
		tmp = a * (b * -0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))))
	t_2 = Float64(c + Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25)))
	tmp = 0.0
	if (Float64(a * b) <= -2e+105)
		tmp = t_2;
	elseif (Float64(a * b) <= 1e+21)
		tmp = t_1;
	elseif (Float64(a * b) <= 5e+211)
		tmp = t_2;
	elseif (Float64(a * b) <= 2e+247)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(b * -0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + ((x * y) + (0.0625 * (z * t)));
	t_2 = c + ((x * y) - ((a * b) * 0.25));
	tmp = 0.0;
	if ((a * b) <= -2e+105)
		tmp = t_2;
	elseif ((a * b) <= 1e+21)
		tmp = t_1;
	elseif ((a * b) <= 5e+211)
		tmp = t_2;
	elseif ((a * b) <= 2e+247)
		tmp = t_1;
	else
		tmp = a * (b * -0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+105], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 1e+21], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 5e+211], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 2e+247], t$95$1, N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.9999999999999999e105 or 1e21 < (*.f64 a b) < 4.9999999999999995e211

   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 z around 0 89.2%

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

   if -1.9999999999999999e105 < (*.f64 a b) < 1e21 or 4.9999999999999995e211 < (*.f64 a b) < 1.9999999999999999e247

   1. Initial program 99.3%

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

   3. Taylor expanded in a around 0 96.2%

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

   if 1.9999999999999999e247 < (*.f64 a b)

   1. Initial program 84.0%

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

   3. Taylor expanded in a around inf 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*r* 92.4%

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

   5. Simplified 92.4%

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

   6. Taylor expanded in a around inf 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*r* 92.4%

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

      3. *-commutative 92.4%

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

   8. Simplified 92.4%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+105}:\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+21}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+211}:\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+247}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;c + t\_1\\ \mathbf{else}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\right)\\ \end{array} \end{array} \]

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 (- (* 0.0625 (* z t)) (* (* 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 + ((0.0625 * (z * t)) - ((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 + ((0.0625 * (z * t)) - ((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 + ((0.0625 * (z * t)) - ((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(c + Float64(Float64(0.0625 * Float64(z * t)) - 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 + ((0.0625 * (z * t)) - ((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[(c + N[(N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   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

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

   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 x around 0 75.0%

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

4. Final simplification 99.2%

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

Alternative 5: 36.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.95 \cdot 10^{+95}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+95} \lor \neg \left(a \leq -3.5 \cdot 10^{+64}\right) \land \left(a \leq -3.1 \cdot 10^{+23} \lor \neg \left(a \leq 2.2 \cdot 10^{-25}\right)\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))))
   (if (<= a -3.5e+163)
     t_1
     (if (<= a -4.95e+95)
       c
       (if (or (<= a -1.8e+95)
               (and (not (<= a -3.5e+64))
                    (or (<= a -3.1e+23) (not (<= a 2.2e-25)))))
         t_1
         (* z (* t 0.0625)))))))

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 (a <= -3.5e+163) {
		tmp = t_1;
	} else if (a <= -4.95e+95) {
		tmp = c;
	} else if ((a <= -1.8e+95) || (!(a <= -3.5e+64) && ((a <= -3.1e+23) || !(a <= 2.2e-25)))) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = a * (b * (-0.25d0))
    if (a <= (-3.5d+163)) then
        tmp = t_1
    else if (a <= (-4.95d+95)) then
        tmp = c
    else if ((a <= (-1.8d+95)) .or. (.not. (a <= (-3.5d+64))) .and. (a <= (-3.1d+23)) .or. (.not. (a <= 2.2d-25))) then
        tmp = t_1
    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 t_1 = a * (b * -0.25);
	double tmp;
	if (a <= -3.5e+163) {
		tmp = t_1;
	} else if (a <= -4.95e+95) {
		tmp = c;
	} else if ((a <= -1.8e+95) || (!(a <= -3.5e+64) && ((a <= -3.1e+23) || !(a <= 2.2e-25)))) {
		tmp = t_1;
	} else {
		tmp = z * (t * 0.0625);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	tmp = 0
	if a <= -3.5e+163:
		tmp = t_1
	elif a <= -4.95e+95:
		tmp = c
	elif (a <= -1.8e+95) or (not (a <= -3.5e+64) and ((a <= -3.1e+23) or not (a <= 2.2e-25))):
		tmp = t_1
	else:
		tmp = z * (t * 0.0625)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (a <= -3.5e+163)
		tmp = t_1;
	elseif (a <= -4.95e+95)
		tmp = c;
	elseif ((a <= -1.8e+95) || (!(a <= -3.5e+64) && ((a <= -3.1e+23) || !(a <= 2.2e-25))))
		tmp = t_1;
	else
		tmp = Float64(z * Float64(t * 0.0625));
	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 (a <= -3.5e+163)
		tmp = t_1;
	elseif (a <= -4.95e+95)
		tmp = c;
	elseif ((a <= -1.8e+95) || (~((a <= -3.5e+64)) && ((a <= -3.1e+23) || ~((a <= 2.2e-25)))))
		tmp = t_1;
	else
		tmp = z * (t * 0.0625);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+163], t$95$1, If[LessEqual[a, -4.95e+95], c, If[Or[LessEqual[a, -1.8e+95], And[N[Not[LessEqual[a, -3.5e+64]], $MachinePrecision], Or[LessEqual[a, -3.1e+23], N[Not[LessEqual[a, 2.2e-25]], $MachinePrecision]]]], t$95$1, N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.5000000000000003e163 or -4.9499999999999998e95 < a < -1.79999999999999989e95 or -3.4999999999999999e64 < a < -3.09999999999999971e23 or 2.2000000000000002e-25 < a

   1. Initial program 94.5%

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

   3. Taylor expanded in a around inf 62.9%

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

      1. *-commutative 62.9%

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

      2. associate-*r* 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in a around inf 51.1%

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

      1. *-commutative 51.1%

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

      2. associate-*r* 51.1%

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

      3. *-commutative 51.1%

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

   8. Simplified 51.1%

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

   if -3.5000000000000003e163 < a < -4.9499999999999998e95

   1. Initial program 94.0%

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

   3. Taylor expanded in z around inf 48.3%

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

      1. *-commutative 48.3%

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

      2. *-commutative 48.3%

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

      3. associate-*r* 48.3%

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

      4. *-commutative 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in z around 0 13.7%

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

   if -1.79999999999999989e95 < a < -3.4999999999999999e64 or -3.09999999999999971e23 < a < 2.2000000000000002e-25

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 50.7%

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

      1. *-commutative 50.7%

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

      2. *-commutative 50.7%

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

      3. associate-*r* 50.7%

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

      4. *-commutative 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in z around inf 27.2%

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

      1. associate-*r* 27.2%

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

      2. *-commutative 27.2%

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

   8. Simplified 27.2%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+163}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \leq -4.95 \cdot 10^{+95}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+95} \lor \neg \left(a \leq -3.5 \cdot 10^{+64}\right) \land \left(a \leq -3.1 \cdot 10^{+23} \lor \neg \left(a \leq 2.2 \cdot 10^{-25}\right)\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -7.4 \cdot 10^{+229}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -3.5 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2.8 \cdot 10^{-248}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 3.15 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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) -7.4e+229)
     t_2
     (if (<= (* x y) -3.5e-86)
       t_1
       (if (<= (* x y) -2.8e-248)
         (* z (* t 0.0625))
         (if (<= (* x y) 3.15e+128) 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) <= -7.4e+229) {
		tmp = t_2;
	} else if ((x * y) <= -3.5e-86) {
		tmp = t_1;
	} else if ((x * y) <= -2.8e-248) {
		tmp = z * (t * 0.0625);
	} else if ((x * y) <= 3.15e+128) {
		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) <= (-7.4d+229)) then
        tmp = t_2
    else if ((x * y) <= (-3.5d-86)) then
        tmp = t_1
    else if ((x * y) <= (-2.8d-248)) then
        tmp = z * (t * 0.0625d0)
    else if ((x * y) <= 3.15d+128) 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) <= -7.4e+229) {
		tmp = t_2;
	} else if ((x * y) <= -3.5e-86) {
		tmp = t_1;
	} else if ((x * y) <= -2.8e-248) {
		tmp = z * (t * 0.0625);
	} else if ((x * y) <= 3.15e+128) {
		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) <= -7.4e+229:
		tmp = t_2
	elif (x * y) <= -3.5e-86:
		tmp = t_1
	elif (x * y) <= -2.8e-248:
		tmp = z * (t * 0.0625)
	elif (x * y) <= 3.15e+128:
		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) <= -7.4e+229)
		tmp = t_2;
	elseif (Float64(x * y) <= -3.5e-86)
		tmp = t_1;
	elseif (Float64(x * y) <= -2.8e-248)
		tmp = Float64(z * Float64(t * 0.0625));
	elseif (Float64(x * y) <= 3.15e+128)
		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) <= -7.4e+229)
		tmp = t_2;
	elseif ((x * y) <= -3.5e-86)
		tmp = t_1;
	elseif ((x * y) <= -2.8e-248)
		tmp = z * (t * 0.0625);
	elseif ((x * y) <= 3.15e+128)
		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], -7.4e+229], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -3.5e-86], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2.8e-248], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.15e+128], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -7.40000000000000005e229 or 3.1499999999999999e128 < (*.f64 x y)

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 84.3%

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

   if -7.40000000000000005e229 < (*.f64 x y) < -3.50000000000000021e-86 or -2.8000000000000001e-248 < (*.f64 x y) < 3.1499999999999999e128

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 61.1%

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

      1. *-commutative 61.1%

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

      2. associate-*r* 61.1%

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

   5. Simplified 61.1%

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

   if -3.50000000000000021e-86 < (*.f64 x y) < -2.8000000000000001e-248

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 79.8%

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

      1. *-commutative 79.8%

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

      2. *-commutative 79.8%

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

      3. associate-*r* 79.8%

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

      4. *-commutative 79.8%

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

   5. Simplified 79.8%

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

   6. Taylor expanded in z around inf 68.6%

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

      1. associate-*r* 68.6%

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

      2. *-commutative 68.6%

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

   8. Simplified 68.6%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.4 \cdot 10^{+229}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.5 \cdot 10^{-86}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -2.8 \cdot 10^{-248}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 3.15 \cdot 10^{+128}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -8 \cdot 10^{+229}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -2.4 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2.15 \cdot 10^{-248}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 2.06 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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) -8e+229)
     t_2
     (if (<= (* x y) -2.4e+46)
       t_1
       (if (<= (* x y) -2.15e-248)
         (+ c (* z (* t 0.0625)))
         (if (<= (* x y) 2.06e+129) 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) <= -8e+229) {
		tmp = t_2;
	} else if ((x * y) <= -2.4e+46) {
		tmp = t_1;
	} else if ((x * y) <= -2.15e-248) {
		tmp = c + (z * (t * 0.0625));
	} else if ((x * y) <= 2.06e+129) {
		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) <= (-8d+229)) then
        tmp = t_2
    else if ((x * y) <= (-2.4d+46)) then
        tmp = t_1
    else if ((x * y) <= (-2.15d-248)) then
        tmp = c + (z * (t * 0.0625d0))
    else if ((x * y) <= 2.06d+129) 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) <= -8e+229) {
		tmp = t_2;
	} else if ((x * y) <= -2.4e+46) {
		tmp = t_1;
	} else if ((x * y) <= -2.15e-248) {
		tmp = c + (z * (t * 0.0625));
	} else if ((x * y) <= 2.06e+129) {
		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) <= -8e+229:
		tmp = t_2
	elif (x * y) <= -2.4e+46:
		tmp = t_1
	elif (x * y) <= -2.15e-248:
		tmp = c + (z * (t * 0.0625))
	elif (x * y) <= 2.06e+129:
		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) <= -8e+229)
		tmp = t_2;
	elseif (Float64(x * y) <= -2.4e+46)
		tmp = t_1;
	elseif (Float64(x * y) <= -2.15e-248)
		tmp = Float64(c + Float64(z * Float64(t * 0.0625)));
	elseif (Float64(x * y) <= 2.06e+129)
		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) <= -8e+229)
		tmp = t_2;
	elseif ((x * y) <= -2.4e+46)
		tmp = t_1;
	elseif ((x * y) <= -2.15e-248)
		tmp = c + (z * (t * 0.0625));
	elseif ((x * y) <= 2.06e+129)
		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], -8e+229], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -2.4e+46], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2.15e-248], N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.06e+129], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -7.9999999999999999e229 or 2.06e129 < (*.f64 x y)

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 84.3%

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

   if -7.9999999999999999e229 < (*.f64 x y) < -2.40000000000000008e46 or -2.1500000000000002e-248 < (*.f64 x y) < 2.06e129

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 61.7%

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

      1. *-commutative 61.7%

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

      2. associate-*r* 61.7%

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

   5. Simplified 61.7%

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

   if -2.40000000000000008e46 < (*.f64 x y) < -2.1500000000000002e-248

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 81.9%

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

      1. *-commutative 81.9%

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

      2. *-commutative 81.9%

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

      3. associate-*r* 81.9%

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

      4. *-commutative 81.9%

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

   5. Simplified 81.9%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8 \cdot 10^{+229}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.4 \cdot 10^{+46}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -2.15 \cdot 10^{-248}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 2.06 \cdot 10^{+129}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+105}:\\ \;\;\;\;c + \left(x \cdot y - t\_1\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+125}:\\ \;\;\;\;c + \left(x \cdot y + t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(t\_2 - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* 0.0625 (* z t))))
   (if (<= (* a b) -2e+105)
     (+ c (- (* x y) t_1))
     (if (<= (* a b) 2e+125) (+ c (+ (* x y) t_2)) (+ c (- t_2 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 t_2 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -2e+105) {
		tmp = c + ((x * y) - t_1);
	} else if ((a * b) <= 2e+125) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = c + (t_2 - 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) :: t_2
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    t_2 = 0.0625d0 * (z * t)
    if ((a * b) <= (-2d+105)) then
        tmp = c + ((x * y) - t_1)
    else if ((a * b) <= 2d+125) then
        tmp = c + ((x * y) + t_2)
    else
        tmp = c + (t_2 - 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 t_2 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -2e+105) {
		tmp = c + ((x * y) - t_1);
	} else if ((a * b) <= 2e+125) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = c + (t_2 - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -2e+105:
		tmp = c + ((x * y) - t_1)
	elif (a * b) <= 2e+125:
		tmp = c + ((x * y) + t_2)
	else:
		tmp = c + (t_2 - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	t_2 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -2e+105)
		tmp = Float64(c + Float64(Float64(x * y) - t_1));
	elseif (Float64(a * b) <= 2e+125)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	else
		tmp = Float64(c + Float64(t_2 - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	t_2 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((a * b) <= -2e+105)
		tmp = c + ((x * y) - t_1);
	elseif ((a * b) <= 2e+125)
		tmp = c + ((x * y) + t_2);
	else
		tmp = c + (t_2 - 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]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+105], N[(c + N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+125], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(c + N[(t$95$2 - t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.9999999999999999e105

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0 91.9%

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

   if -1.9999999999999999e105 < (*.f64 a b) < 1.9999999999999998e125

   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 94.6%

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

   if 1.9999999999999998e125 < (*.f64 a b)

   1. Initial program 89.8%

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

   3. Taylor expanded in x around 0 88.3%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+105}:\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+125}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+34} \lor \neg \left(b \leq 7.5 \cdot 10^{+74}\right) \land \left(b \leq 3.8 \cdot 10^{+118} \lor \neg \left(b \leq 2.05 \cdot 10^{+178}\right)\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -6.4e+34)
         (and (not (<= b 7.5e+74))
              (or (<= b 3.8e+118) (not (<= b 2.05e+178)))))
   (* 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 ((b <= -6.4e+34) || (!(b <= 7.5e+74) && ((b <= 3.8e+118) || !(b <= 2.05e+178)))) {
		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 ((b <= (-6.4d+34)) .or. (.not. (b <= 7.5d+74)) .and. (b <= 3.8d+118) .or. (.not. (b <= 2.05d+178))) 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 ((b <= -6.4e+34) || (!(b <= 7.5e+74) && ((b <= 3.8e+118) || !(b <= 2.05e+178)))) {
		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 (b <= -6.4e+34) or (not (b <= 7.5e+74) and ((b <= 3.8e+118) or not (b <= 2.05e+178))):
		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 ((b <= -6.4e+34) || (!(b <= 7.5e+74) && ((b <= 3.8e+118) || !(b <= 2.05e+178))))
		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 ((b <= -6.4e+34) || (~((b <= 7.5e+74)) && ((b <= 3.8e+118) || ~((b <= 2.05e+178)))))
		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[b, -6.4e+34], And[N[Not[LessEqual[b, 7.5e+74]], $MachinePrecision], Or[LessEqual[b, 3.8e+118], N[Not[LessEqual[b, 2.05e+178]], $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 b < -6.3999999999999997e34 or 7.5e74 < b < 3.80000000000000016e118 or 2.04999999999999998e178 < b

   1. Initial program 93.0%

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

   3. Taylor expanded in a around inf 69.8%

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

      1. *-commutative 69.8%

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

      2. associate-*r* 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in a around inf 55.1%

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

      1. *-commutative 55.1%

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

      2. associate-*r* 55.1%

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

      3. *-commutative 55.1%

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

   8. Simplified 55.1%

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

   if -6.3999999999999997e34 < b < 7.5e74 or 3.80000000000000016e118 < b < 2.04999999999999998e178

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf 61.1%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+34} \lor \neg \left(b \leq 7.5 \cdot 10^{+74}\right) \land \left(b \leq 3.8 \cdot 10^{+118} \lor \neg \left(b \leq 2.05 \cdot 10^{+178}\right)\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+24} \lor \neg \left(b \leq 2 \cdot 10^{+179}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -1e+24) (not (<= b 2e+179)))
   (+ c (* 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 ((b <= -1e+24) || !(b <= 2e+179)) {
		tmp = c + (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 ((b <= (-1d+24)) .or. (.not. (b <= 2d+179))) then
        tmp = c + (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 ((b <= -1e+24) || !(b <= 2e+179)) {
		tmp = c + (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 (b <= -1e+24) or not (b <= 2e+179):
		tmp = c + (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 ((b <= -1e+24) || !(b <= 2e+179))
		tmp = Float64(c + Float64(a * Float64(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 ((b <= -1e+24) || ~((b <= 2e+179)))
		tmp = c + (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[b, -1e+24], N[Not[LessEqual[b, 2e+179]], $MachinePrecision]], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $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 b < -9.9999999999999998e23 or 1.99999999999999996e179 < b

   1. Initial program 93.3%

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

   3. Taylor expanded in a around inf 74.0%

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

      1. *-commutative 74.0%

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

      2. associate-*r* 74.0%

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

   5. Simplified 74.0%

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

   if -9.9999999999999998e23 < b < 1.99999999999999996e179

   1. Initial program 98.8%

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

   3. Taylor expanded in a around 0 87.4%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+24} \lor \neg \left(b \leq 2 \cdot 10^{+179}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-84} \lor \neg \left(b \leq 8.8 \cdot 10^{+64}\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -2e-84) (not (<= b 8.8e+64))) (* 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 ((b <= -2e-84) || !(b <= 8.8e+64)) {
		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 ((b <= (-2d-84)) .or. (.not. (b <= 8.8d+64))) 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 ((b <= -2e-84) || !(b <= 8.8e+64)) {
		tmp = a * (b * -0.25);
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -2e-84) or not (b <= 8.8e+64):
		tmp = a * (b * -0.25)
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -2e-84) || !(b <= 8.8e+64))
		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 ((b <= -2e-84) || ~((b <= 8.8e+64)))
		tmp = a * (b * -0.25);
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -2e-84], N[Not[LessEqual[b, 8.8e+64]], $MachinePrecision]], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if b < -2.0000000000000001e-84 or 8.80000000000000007e64 < 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 a around inf 62.9%

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

      1. *-commutative 62.9%

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

      2. associate-*r* 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in a around inf 46.9%

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

      1. *-commutative 46.9%

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

      2. associate-*r* 46.9%

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

      3. *-commutative 46.9%

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

   8. Simplified 46.9%

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

   if -2.0000000000000001e-84 < b < 8.80000000000000007e64

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 55.0%

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

      1. *-commutative 55.0%

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

      2. *-commutative 55.0%

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

      3. associate-*r* 55.0%

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

      4. *-commutative 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in z around 0 22.3%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-84} \lor \neg \left(b \leq 8.8 \cdot 10^{+64}\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 22.4% 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 96.9%

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

3. Taylor expanded in z around inf 43.1%

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

   1. *-commutative 43.1%

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

   2. *-commutative 43.1%

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

   3. associate-*r* 43.1%

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

   4. *-commutative 43.1%

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

5. Simplified 43.1%

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

6. Taylor expanded in z around 0 20.1%

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

7. Final simplification 20.1%

   \[\leadsto c \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024050 
(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))