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

Percentage Accurate: 97.5% → 99.0%

Time: 9.3s

Alternatives: 14

Speedup: 0.5×

• 33.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.5% 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: 99.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. associate-+l- 97.6%

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

   2. associate--l+ 97.6%

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

   3. fma-def 98.0%

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

   4. associate-*l/ 98.0%

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

   5. fma-neg 99.2%

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

   6. sub-neg 99.2%

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

   7. distribute-neg-in 99.2%

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

   8. remove-double-neg 99.2%

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

   9. associate-/l* 99.2%

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

   10. distribute-frac-neg 99.2%

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

   11. associate-/r/ 99.2%

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

   12. fma-def 99.2%

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

   13. neg-mul-1 99.2%

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

   14. *-commutative 99.2%

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

   15. associate-/l* 99.2%

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

   16. metadata-eval 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 98.9% accurate, 0.1× speedup

Math

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

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) (fma (* z 0.0625) 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 = fma((z * 0.0625), 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 = fma(Float64(z * 0.0625), t, Float64(a * Float64(b * -0.25)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(c + t$95$1), $MachinePrecision], N[(N[(z * 0.0625), $MachinePrecision] * t + N[(a * N[(b * -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%

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

   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. Taylor expanded in x around 0 16.7%

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

   3. Taylor expanded in c around 0 16.7%

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

      1. *-commutative 16.7%

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

      2. associate-*r* 16.7%

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

      3. fma-neg 66.7%

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

      4. *-commutative 66.7%

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

      5. *-commutative 66.7%

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

      6. distribute-rgt-neg-in 66.7%

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

      7. metadata-eval 66.7%

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

      8. associate-*r* 66.7%

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

      9. *-commutative 66.7%

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

   5. Applied egg-rr 66.7%

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

4. Final simplification 99.2%

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

Alternative 3: 98.5% accurate, 0.5× speedup

Math

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

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) (* b (* a -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 = b * (a * -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 = b * (a * -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 = b * (a * -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(b * Float64(a * -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 = b * (a * -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[(b * N[(a * -0.25), $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%

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

   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. Taylor expanded in x around 0 16.7%

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

   3. Taylor expanded in a around inf 66.7%

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

      1. *-commutative 66.7%

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

      2. *-commutative 66.7%

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

      3. associate-*l* 66.7%

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

   5. Simplified 66.7%

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

4. Final simplification 99.2%

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

Alternative 4: 43.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{if}\;x \cdot y \leq -2.25 \cdot 10^{+108}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.1 \cdot 10^{-46}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq -4.5 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1.5 \cdot 10^{-261}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 6.4 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* z 0.0625))))
   (if (<= (* x y) -2.25e+108)
     (* x y)
     (if (<= (* x y) -3.1e-46)
       c
       (if (<= (* x y) -4.5e-142)
         t_1
         (if (<= (* x y) -1.5e-261)
           (* b (* a -0.25))
           (if (<= (* x y) 6.4e+52) t_1 (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (z * 0.0625);
	double tmp;
	if ((x * y) <= -2.25e+108) {
		tmp = x * y;
	} else if ((x * y) <= -3.1e-46) {
		tmp = c;
	} else if ((x * y) <= -4.5e-142) {
		tmp = t_1;
	} else if ((x * y) <= -1.5e-261) {
		tmp = b * (a * -0.25);
	} else if ((x * y) <= 6.4e+52) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (z * 0.0625d0)
    if ((x * y) <= (-2.25d+108)) then
        tmp = x * y
    else if ((x * y) <= (-3.1d-46)) then
        tmp = c
    else if ((x * y) <= (-4.5d-142)) then
        tmp = t_1
    else if ((x * y) <= (-1.5d-261)) then
        tmp = b * (a * (-0.25d0))
    else if ((x * y) <= 6.4d+52) then
        tmp = t_1
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (z * 0.0625);
	double tmp;
	if ((x * y) <= -2.25e+108) {
		tmp = x * y;
	} else if ((x * y) <= -3.1e-46) {
		tmp = c;
	} else if ((x * y) <= -4.5e-142) {
		tmp = t_1;
	} else if ((x * y) <= -1.5e-261) {
		tmp = b * (a * -0.25);
	} else if ((x * y) <= 6.4e+52) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = t * (z * 0.0625)
	tmp = 0
	if (x * y) <= -2.25e+108:
		tmp = x * y
	elif (x * y) <= -3.1e-46:
		tmp = c
	elif (x * y) <= -4.5e-142:
		tmp = t_1
	elif (x * y) <= -1.5e-261:
		tmp = b * (a * -0.25)
	elif (x * y) <= 6.4e+52:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(z * 0.0625))
	tmp = 0.0
	if (Float64(x * y) <= -2.25e+108)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -3.1e-46)
		tmp = c;
	elseif (Float64(x * y) <= -4.5e-142)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.5e-261)
		tmp = Float64(b * Float64(a * -0.25));
	elseif (Float64(x * y) <= 6.4e+52)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (z * 0.0625);
	tmp = 0.0;
	if ((x * y) <= -2.25e+108)
		tmp = x * y;
	elseif ((x * y) <= -3.1e-46)
		tmp = c;
	elseif ((x * y) <= -4.5e-142)
		tmp = t_1;
	elseif ((x * y) <= -1.5e-261)
		tmp = b * (a * -0.25);
	elseif ((x * y) <= 6.4e+52)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.25e+108], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.1e-46], c, If[LessEqual[N[(x * y), $MachinePrecision], -4.5e-142], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.5e-261], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.4e+52], t$95$1, N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2.25e108 or 6.4e52 < (*.f64 x y)

   1. Initial program 95.0%

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

   2. Taylor expanded in a around 0 81.5%

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

   3. Taylor expanded in x around inf 66.8%

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

   if -2.25e108 < (*.f64 x y) < -3.1000000000000001e-46

   1. Initial program 100.0%

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

   2. Taylor expanded in c around inf 46.7%

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

   if -3.1000000000000001e-46 < (*.f64 x y) < -4.50000000000000019e-142 or -1.5e-261 < (*.f64 x y) < 6.4e52

   1. Initial program 99.0%

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

   2. Taylor expanded in a around 0 73.5%

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

   3. Taylor expanded in t around inf 42.9%

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

      1. *-commutative 42.9%

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

      2. associate-*l* 42.9%

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

      3. *-commutative 42.9%

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

   5. Simplified 42.9%

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

   if -4.50000000000000019e-142 < (*.f64 x y) < -1.5e-261

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in a around inf 57.1%

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

      1. *-commutative 57.1%

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

      2. *-commutative 57.1%

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

      3. associate-*l* 57.1%

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

   5. Simplified 57.1%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.25 \cdot 10^{+108}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.1 \cdot 10^{-46}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq -4.5 \cdot 10^{-142}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -1.5 \cdot 10^{-261}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 6.4 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 5: 65.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -9.5 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -8.5 \cdot 10^{-121}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 2.9 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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) -2.7e+140)
     t_2
     (if (<= (* x y) -9.5e-91)
       t_1
       (if (<= (* x y) -8.5e-121)
         (* t (* z 0.0625))
         (if (<= (* x y) 2.9e+55) 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) <= -2.7e+140) {
		tmp = t_2;
	} else if ((x * y) <= -9.5e-91) {
		tmp = t_1;
	} else if ((x * y) <= -8.5e-121) {
		tmp = t * (z * 0.0625);
	} else if ((x * y) <= 2.9e+55) {
		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) <= (-2.7d+140)) then
        tmp = t_2
    else if ((x * y) <= (-9.5d-91)) then
        tmp = t_1
    else if ((x * y) <= (-8.5d-121)) then
        tmp = t * (z * 0.0625d0)
    else if ((x * y) <= 2.9d+55) 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) <= -2.7e+140) {
		tmp = t_2;
	} else if ((x * y) <= -9.5e-91) {
		tmp = t_1;
	} else if ((x * y) <= -8.5e-121) {
		tmp = t * (z * 0.0625);
	} else if ((x * y) <= 2.9e+55) {
		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) <= -2.7e+140:
		tmp = t_2
	elif (x * y) <= -9.5e-91:
		tmp = t_1
	elif (x * y) <= -8.5e-121:
		tmp = t * (z * 0.0625)
	elif (x * y) <= 2.9e+55:
		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) <= -2.7e+140)
		tmp = t_2;
	elseif (Float64(x * y) <= -9.5e-91)
		tmp = t_1;
	elseif (Float64(x * y) <= -8.5e-121)
		tmp = Float64(t * Float64(z * 0.0625));
	elseif (Float64(x * y) <= 2.9e+55)
		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) <= -2.7e+140)
		tmp = t_2;
	elseif ((x * y) <= -9.5e-91)
		tmp = t_1;
	elseif ((x * y) <= -8.5e-121)
		tmp = t * (z * 0.0625);
	elseif ((x * y) <= 2.9e+55)
		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], -2.7e+140], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -9.5e-91], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -8.5e-121], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.9e+55], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.70000000000000018e140 or 2.8999999999999999e55 < (*.f64 x y)

   1. Initial program 95.6%

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

   2. Taylor expanded in x around inf 73.9%

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

   if -2.70000000000000018e140 < (*.f64 x y) < -9.5e-91 or -8.50000000000000025e-121 < (*.f64 x y) < 2.8999999999999999e55

   1. Initial program 98.7%

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

   2. Taylor expanded in a around inf 62.3%

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

      1. *-commutative 62.3%

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

      2. associate-*r* 62.3%

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

   4. Simplified 62.3%

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

   if -9.5e-91 < (*.f64 x y) < -8.50000000000000025e-121

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 100.0%

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

   3. Taylor expanded in t around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l* 100.0%

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

      3. *-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+140}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -9.5 \cdot 10^{-91}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -8.5 \cdot 10^{-121}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 2.9 \cdot 10^{+55}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 6: 64.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + z \cdot \left(t \cdot 0.0625\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -2.5 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -2.5 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-260}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 4.6 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* z (* t 0.0625)))) (t_2 (+ c (* x y))))
   (if (<= (* x y) -2.5e+58)
     t_2
     (if (<= (* x y) -2.5e-136)
       t_1
       (if (<= (* x y) -1e-260)
         (+ c (* a (* b -0.25)))
         (if (<= (* x y) 4.6e+47) 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 + (z * (t * 0.0625));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -2.5e+58) {
		tmp = t_2;
	} else if ((x * y) <= -2.5e-136) {
		tmp = t_1;
	} else if ((x * y) <= -1e-260) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 4.6e+47) {
		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 + (z * (t * 0.0625d0))
    t_2 = c + (x * y)
    if ((x * y) <= (-2.5d+58)) then
        tmp = t_2
    else if ((x * y) <= (-2.5d-136)) then
        tmp = t_1
    else if ((x * y) <= (-1d-260)) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((x * y) <= 4.6d+47) 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 + (z * (t * 0.0625));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -2.5e+58) {
		tmp = t_2;
	} else if ((x * y) <= -2.5e-136) {
		tmp = t_1;
	} else if ((x * y) <= -1e-260) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 4.6e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (z * (t * 0.0625))
	t_2 = c + (x * y)
	tmp = 0
	if (x * y) <= -2.5e+58:
		tmp = t_2
	elif (x * y) <= -2.5e-136:
		tmp = t_1
	elif (x * y) <= -1e-260:
		tmp = c + (a * (b * -0.25))
	elif (x * y) <= 4.6e+47:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(z * Float64(t * 0.0625)))
	t_2 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -2.5e+58)
		tmp = t_2;
	elseif (Float64(x * y) <= -2.5e-136)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e-260)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 4.6e+47)
		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 + (z * (t * 0.0625));
	t_2 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -2.5e+58)
		tmp = t_2;
	elseif ((x * y) <= -2.5e-136)
		tmp = t_1;
	elseif ((x * y) <= -1e-260)
		tmp = c + (a * (b * -0.25));
	elseif ((x * y) <= 4.6e+47)
		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[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.5e+58], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -2.5e-136], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e-260], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.6e+47], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.49999999999999993e58 or 4.5999999999999997e47 < (*.f64 x y)

   1. Initial program 95.5%

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

   2. Taylor expanded in x around inf 70.3%

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

   if -2.49999999999999993e58 < (*.f64 x y) < -2.5000000000000001e-136 or -9.99999999999999961e-261 < (*.f64 x y) < 4.5999999999999997e47

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 69.9%

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

      1. associate-*r* 69.9%

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

      2. *-commutative 69.9%

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

   4. Simplified 69.9%

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

   if -2.5000000000000001e-136 < (*.f64 x y) < -9.99999999999999961e-261

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 94.1%

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

      1. *-commutative 94.1%

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

      2. associate-*r* 94.1%

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

   4. Simplified 94.1%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.5 \cdot 10^{+58}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.5 \cdot 10^{-136}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-260}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 4.6 \cdot 10^{+47}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 7: 88.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+119} \lor \neg \left(a \cdot b \leq 10^{-22}\right):\\ \;\;\;\;\left(c + t_1\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* z t) 0.0625)))
   (if (or (<= (* a b) -5e+119) (not (<= (* a b) 1e-22)))
     (- (+ c t_1) (* (* a b) 0.25))
     (+ 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 = (z * t) * 0.0625;
	double tmp;
	if (((a * b) <= -5e+119) || !((a * b) <= 1e-22)) {
		tmp = (c + t_1) - ((a * b) * 0.25);
	} 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 = (z * t) * 0.0625d0
    if (((a * b) <= (-5d+119)) .or. (.not. ((a * b) <= 1d-22))) then
        tmp = (c + t_1) - ((a * b) * 0.25d0)
    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 = (z * t) * 0.0625;
	double tmp;
	if (((a * b) <= -5e+119) || !((a * b) <= 1e-22)) {
		tmp = (c + t_1) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (z * t) * 0.0625
	tmp = 0
	if ((a * b) <= -5e+119) or not ((a * b) <= 1e-22):
		tmp = (c + t_1) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(z * t) * 0.0625)
	tmp = 0.0
	if ((Float64(a * b) <= -5e+119) || !(Float64(a * b) <= 1e-22))
		tmp = Float64(Float64(c + t_1) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (z * t) * 0.0625;
	tmp = 0.0;
	if (((a * b) <= -5e+119) || ~(((a * b) <= 1e-22)))
		tmp = (c + t_1) - ((a * b) * 0.25);
	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[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]}, If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e+119], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1e-22]], $MachinePrecision]], N[(N[(c + t$95$1), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.9999999999999999e119 or 1e-22 < (*.f64 a b)

   1. Initial program 94.5%

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

   2. Taylor expanded in x around 0 82.9%

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

   if -4.9999999999999999e119 < (*.f64 a b) < 1e-22

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 97.4%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+119} \lor \neg \left(a \cdot b \leq 10^{-22}\right):\\ \;\;\;\;\left(c + \left(z \cdot t\right) \cdot 0.0625\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 8: 87.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+134} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+160}\right):\\ \;\;\;\;t_1 - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* z t) 0.0625)))
   (if (or (<= (* a b) -1e+134) (not (<= (* a b) 5e+160)))
     (- t_1 (* (* a b) 0.25))
     (+ 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 = (z * t) * 0.0625;
	double tmp;
	if (((a * b) <= -1e+134) || !((a * b) <= 5e+160)) {
		tmp = t_1 - ((a * b) * 0.25);
	} 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 = (z * t) * 0.0625d0
    if (((a * b) <= (-1d+134)) .or. (.not. ((a * b) <= 5d+160))) then
        tmp = t_1 - ((a * b) * 0.25d0)
    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 = (z * t) * 0.0625;
	double tmp;
	if (((a * b) <= -1e+134) || !((a * b) <= 5e+160)) {
		tmp = t_1 - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (z * t) * 0.0625
	tmp = 0
	if ((a * b) <= -1e+134) or not ((a * b) <= 5e+160):
		tmp = t_1 - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(z * t) * 0.0625)
	tmp = 0.0
	if ((Float64(a * b) <= -1e+134) || !(Float64(a * b) <= 5e+160))
		tmp = Float64(t_1 - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (z * t) * 0.0625;
	tmp = 0.0;
	if (((a * b) <= -1e+134) || ~(((a * b) <= 5e+160)))
		tmp = t_1 - ((a * b) * 0.25);
	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[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]}, If[Or[LessEqual[N[(a * b), $MachinePrecision], -1e+134], N[Not[LessEqual[N[(a * b), $MachinePrecision], 5e+160]], $MachinePrecision]], N[(t$95$1 - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -9.99999999999999921e133 or 5.0000000000000002e160 < (*.f64 a b)

   1. Initial program 91.6%

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

   2. Taylor expanded in x around 0 85.1%

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

   3. Taylor expanded in c around 0 81.2%

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

   if -9.99999999999999921e133 < (*.f64 a b) < 5.0000000000000002e160

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 91.4%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+134} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+160}\right):\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625 - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 9: 60.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{-116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-98}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25)))) (t_2 (+ (* x y) (* (* z t) 0.0625))))
   (if (<= z -2.9e-116)
     t_2
     (if (<= z 1.9e-190)
       t_1
       (if (<= z 2.15e-98) (+ c (* x y)) (if (<= z 1.3e+47) 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 = (x * y) + ((z * t) * 0.0625);
	double tmp;
	if (z <= -2.9e-116) {
		tmp = t_2;
	} else if (z <= 1.9e-190) {
		tmp = t_1;
	} else if (z <= 2.15e-98) {
		tmp = c + (x * y);
	} else if (z <= 1.3e+47) {
		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 = (x * y) + ((z * t) * 0.0625d0)
    if (z <= (-2.9d-116)) then
        tmp = t_2
    else if (z <= 1.9d-190) then
        tmp = t_1
    else if (z <= 2.15d-98) then
        tmp = c + (x * y)
    else if (z <= 1.3d+47) 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 = (x * y) + ((z * t) * 0.0625);
	double tmp;
	if (z <= -2.9e-116) {
		tmp = t_2;
	} else if (z <= 1.9e-190) {
		tmp = t_1;
	} else if (z <= 2.15e-98) {
		tmp = c + (x * y);
	} else if (z <= 1.3e+47) {
		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 = (x * y) + ((z * t) * 0.0625)
	tmp = 0
	if z <= -2.9e-116:
		tmp = t_2
	elif z <= 1.9e-190:
		tmp = t_1
	elif z <= 2.15e-98:
		tmp = c + (x * y)
	elif z <= 1.3e+47:
		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(Float64(x * y) + Float64(Float64(z * t) * 0.0625))
	tmp = 0.0
	if (z <= -2.9e-116)
		tmp = t_2;
	elseif (z <= 1.9e-190)
		tmp = t_1;
	elseif (z <= 2.15e-98)
		tmp = Float64(c + Float64(x * y));
	elseif (z <= 1.3e+47)
		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 = (x * y) + ((z * t) * 0.0625);
	tmp = 0.0;
	if (z <= -2.9e-116)
		tmp = t_2;
	elseif (z <= 1.9e-190)
		tmp = t_1;
	elseif (z <= 2.15e-98)
		tmp = c + (x * y);
	elseif (z <= 1.3e+47)
		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[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e-116], t$95$2, If[LessEqual[z, 1.9e-190], t$95$1, If[LessEqual[z, 2.15e-98], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+47], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8999999999999998e-116 or 1.30000000000000002e47 < z

   1. Initial program 96.3%

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

   2. Taylor expanded in a around 0 83.0%

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

   3. Taylor expanded in c around 0 67.9%

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

   if -2.8999999999999998e-116 < z < 1.8999999999999999e-190 or 2.14999999999999994e-98 < z < 1.30000000000000002e47

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 61.7%

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

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

   4. Simplified 61.7%

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

   if 1.8999999999999999e-190 < z < 2.14999999999999994e-98

   1. Initial program 94.7%

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

   2. Taylor expanded in x around inf 77.8%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-116}:\\ \;\;\;\;x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-190}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-98}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+47}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \end{array} \]

Alternative 10: 44.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{+108}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.7 \cdot 10^{-125}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.45 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -7e+108)
   (* x y)
   (if (<= (* x y) -2.7e-125)
     c
     (if (<= (* x y) 1.45e+55) (* b (* a -0.25)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -7e+108) {
		tmp = x * y;
	} else if ((x * y) <= -2.7e-125) {
		tmp = c;
	} else if ((x * y) <= 1.45e+55) {
		tmp = b * (a * -0.25);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x * y) <= (-7d+108)) then
        tmp = x * y
    else if ((x * y) <= (-2.7d-125)) then
        tmp = c
    else if ((x * y) <= 1.45d+55) then
        tmp = b * (a * (-0.25d0))
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -7e+108) {
		tmp = x * y;
	} else if ((x * y) <= -2.7e-125) {
		tmp = c;
	} else if ((x * y) <= 1.45e+55) {
		tmp = b * (a * -0.25);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -7e+108:
		tmp = x * y
	elif (x * y) <= -2.7e-125:
		tmp = c
	elif (x * y) <= 1.45e+55:
		tmp = b * (a * -0.25)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -7e+108)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -2.7e-125)
		tmp = c;
	elseif (Float64(x * y) <= 1.45e+55)
		tmp = Float64(b * Float64(a * -0.25));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -7e+108)
		tmp = x * y;
	elseif ((x * y) <= -2.7e-125)
		tmp = c;
	elseif ((x * y) <= 1.45e+55)
		tmp = b * (a * -0.25);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -7e+108], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.7e-125], c, If[LessEqual[N[(x * y), $MachinePrecision], 1.45e+55], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -7.0000000000000005e108 or 1.4499999999999999e55 < (*.f64 x y)

   1. Initial program 94.9%

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

   2. Taylor expanded in a around 0 82.3%

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

   3. Taylor expanded in x around inf 67.5%

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

   if -7.0000000000000005e108 < (*.f64 x y) < -2.6999999999999998e-125

   1. Initial program 100.0%

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

   2. Taylor expanded in c around inf 41.9%

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

   if -2.6999999999999998e-125 < (*.f64 x y) < 1.4499999999999999e55

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0 94.4%

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

   3. Taylor expanded in a around inf 34.9%

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

      1. *-commutative 34.9%

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

      2. *-commutative 34.9%

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

      3. associate-*l* 34.9%

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

   5. Simplified 34.9%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{+108}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.7 \cdot 10^{-125}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.45 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 11: 78.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+217}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -6.2e+147)
   (* b (* a -0.25))
   (if (<= b 3.8e+217)
     (+ c (+ (* x y) (* (* z t) 0.0625)))
     (+ 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 (b <= -6.2e+147) {
		tmp = b * (a * -0.25);
	} else if (b <= 3.8e+217) {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	} 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 (b <= (-6.2d+147)) then
        tmp = b * (a * (-0.25d0))
    else if (b <= 3.8d+217) then
        tmp = c + ((x * y) + ((z * t) * 0.0625d0))
    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 (b <= -6.2e+147) {
		tmp = b * (a * -0.25);
	} else if (b <= 3.8e+217) {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -6.2e+147:
		tmp = b * (a * -0.25)
	elif b <= 3.8e+217:
		tmp = c + ((x * y) + ((z * t) * 0.0625))
	else:
		tmp = c + (a * (b * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -6.2e+147)
		tmp = Float64(b * Float64(a * -0.25));
	elseif (b <= 3.8e+217)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625)));
	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 (b <= -6.2e+147)
		tmp = b * (a * -0.25);
	elseif (b <= 3.8e+217)
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	else
		tmp = c + (a * (b * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -6.2e+147], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e+217], N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.2000000000000001e147

   1. Initial program 93.0%

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

   2. Taylor expanded in x around 0 83.1%

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

   3. Taylor expanded in a around inf 56.8%

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

      1. *-commutative 56.8%

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

      2. *-commutative 56.8%

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

      3. associate-*l* 56.8%

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

   5. Simplified 56.8%

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

   if -6.2000000000000001e147 < b < 3.80000000000000002e217

   1. Initial program 99.0%

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

   2. Taylor expanded in a around 0 83.3%

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

   if 3.80000000000000002e217 < b

   1. Initial program 91.3%

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

   2. Taylor expanded in a around inf 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-*r* 79.4%

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

   4. Simplified 79.4%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+217}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]

Alternative 12: 54.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-277}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;z \leq 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* t (* z 0.0625))))
   (if (<= z -3.7e+114)
     t_2
     (if (<= z 1.45e-298)
       t_1
       (if (<= z 1.56e-277) (* b (* a -0.25)) (if (<= z 1e+46) 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 + (x * y);
	double t_2 = t * (z * 0.0625);
	double tmp;
	if (z <= -3.7e+114) {
		tmp = t_2;
	} else if (z <= 1.45e-298) {
		tmp = t_1;
	} else if (z <= 1.56e-277) {
		tmp = b * (a * -0.25);
	} else if (z <= 1e+46) {
		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 + (x * y)
    t_2 = t * (z * 0.0625d0)
    if (z <= (-3.7d+114)) then
        tmp = t_2
    else if (z <= 1.45d-298) then
        tmp = t_1
    else if (z <= 1.56d-277) then
        tmp = b * (a * (-0.25d0))
    else if (z <= 1d+46) 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 + (x * y);
	double t_2 = t * (z * 0.0625);
	double tmp;
	if (z <= -3.7e+114) {
		tmp = t_2;
	} else if (z <= 1.45e-298) {
		tmp = t_1;
	} else if (z <= 1.56e-277) {
		tmp = b * (a * -0.25);
	} else if (z <= 1e+46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = t * (z * 0.0625)
	tmp = 0
	if z <= -3.7e+114:
		tmp = t_2
	elif z <= 1.45e-298:
		tmp = t_1
	elif z <= 1.56e-277:
		tmp = b * (a * -0.25)
	elif z <= 1e+46:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(t * Float64(z * 0.0625))
	tmp = 0.0
	if (z <= -3.7e+114)
		tmp = t_2;
	elseif (z <= 1.45e-298)
		tmp = t_1;
	elseif (z <= 1.56e-277)
		tmp = Float64(b * Float64(a * -0.25));
	elseif (z <= 1e+46)
		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 + (x * y);
	t_2 = t * (z * 0.0625);
	tmp = 0.0;
	if (z <= -3.7e+114)
		tmp = t_2;
	elseif (z <= 1.45e-298)
		tmp = t_1;
	elseif (z <= 1.56e-277)
		tmp = b * (a * -0.25);
	elseif (z <= 1e+46)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e+114], t$95$2, If[LessEqual[z, 1.45e-298], t$95$1, If[LessEqual[z, 1.56e-277], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+46], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7000000000000001e114 or 9.9999999999999999e45 < z

   1. Initial program 95.6%

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

   2. Taylor expanded in a around 0 85.9%

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

   3. Taylor expanded in t around inf 53.1%

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

      1. *-commutative 53.1%

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

      2. associate-*l* 53.1%

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

      3. *-commutative 53.1%

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

   5. Simplified 53.1%

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

   if -3.7000000000000001e114 < z < 1.45000000000000007e-298 or 1.56e-277 < z < 9.9999999999999999e45

   1. Initial program 98.7%

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

   2. Taylor expanded in x around inf 61.5%

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

   if 1.45000000000000007e-298 < z < 1.56e-277

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 90.8%

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

   3. Taylor expanded in a around inf 70.9%

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

      1. *-commutative 70.9%

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

      2. *-commutative 70.9%

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

      3. associate-*l* 70.9%

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

   5. Simplified 70.9%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-298}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-277}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;z \leq 10^{+46}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]

Alternative 13: 41.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.9 \cdot 10^{+109} \lor \neg \left(x \cdot y \leq 1.25 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2.9e+109) (not (<= (* x y) 1.25e+34))) (* 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) <= -2.9e+109) || !((x * y) <= 1.25e+34)) {
		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) <= (-2.9d+109)) .or. (.not. ((x * y) <= 1.25d+34))) 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) <= -2.9e+109) || !((x * y) <= 1.25e+34)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -2.9e+109) or not ((x * y) <= 1.25e+34):
		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) <= -2.9e+109) || !(Float64(x * y) <= 1.25e+34))
		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) <= -2.9e+109) || ~(((x * y) <= 1.25e+34)))
		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], -2.9e+109], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.25e+34]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.9e109 or 1.25e34 < (*.f64 x y)

   1. Initial program 95.1%

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

   2. Taylor expanded in a around 0 82.1%

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

   3. Taylor expanded in x around inf 65.9%

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

   if -2.9e109 < (*.f64 x y) < 1.25e34

   1. Initial program 99.3%

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

   2. Taylor expanded in c around inf 32.7%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.9 \cdot 10^{+109} \lor \neg \left(x \cdot y \leq 1.25 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 14: 22.2% 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 97.6%

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

2. Taylor expanded in c around inf 22.2%

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

3. Final simplification 22.2%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023332 
(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))