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

Percentage Accurate: 97.3% → 98.9%

Time: 12.5s

Alternatives: 16

Speedup: 1.0×

• 33.3% 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: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.1%

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

   1. associate-+l- 98.1%

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

   2. associate--l+ 98.1%

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

   3. fma-def 98.9%

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

   4. associate-*l/ 98.9%

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

   5. fma-neg 98.9%

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

   6. sub-neg 98.9%

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

   7. distribute-neg-in 98.9%

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

   8. remove-double-neg 98.9%

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

   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: 98.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.1%

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

   1. sub-neg 98.1%

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

   2. associate-+l+ 98.1%

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

   3. fma-def 98.9%

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

   4. associate-*l/ 98.9%

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

   5. distribute-frac-neg 98.9%

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

   6. distribute-rgt-neg-out 98.9%

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

   7. associate-/l* 99.2%

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

   8. neg-mul-1 99.2%

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

   9. associate-/r* 99.2%

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

   10. metadata-eval 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 3: 64.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := c + t_1\\ t_3 := c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -1.25 \cdot 10^{+77}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.45 \cdot 10^{-43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{-79}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 2.7 \cdot 10^{-46}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (+ c t_1)) (t_3 (+ c (* a (* b -0.25)))))
   (if (<= (* x y) -1.25e+77)
     (+ c (* x y))
     (if (<= (* x y) -1.45e-43)
       t_2
       (if (<= (* x y) -5.5e-79)
         t_3
         (if (<= (* x y) 0.0)
           t_2
           (if (<= (* x y) 2.7e-46) t_3 (+ (* x y) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = c + t_1;
	double t_3 = c + (a * (b * -0.25));
	double tmp;
	if ((x * y) <= -1.25e+77) {
		tmp = c + (x * y);
	} else if ((x * y) <= -1.45e-43) {
		tmp = t_2;
	} else if ((x * y) <= -5.5e-79) {
		tmp = t_3;
	} else if ((x * y) <= 0.0) {
		tmp = t_2;
	} else if ((x * y) <= 2.7e-46) {
		tmp = t_3;
	} else {
		tmp = (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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    t_2 = c + t_1
    t_3 = c + (a * (b * (-0.25d0)))
    if ((x * y) <= (-1.25d+77)) then
        tmp = c + (x * y)
    else if ((x * y) <= (-1.45d-43)) then
        tmp = t_2
    else if ((x * y) <= (-5.5d-79)) then
        tmp = t_3
    else if ((x * y) <= 0.0d0) then
        tmp = t_2
    else if ((x * y) <= 2.7d-46) then
        tmp = t_3
    else
        tmp = (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 = 0.0625 * (z * t);
	double t_2 = c + t_1;
	double t_3 = c + (a * (b * -0.25));
	double tmp;
	if ((x * y) <= -1.25e+77) {
		tmp = c + (x * y);
	} else if ((x * y) <= -1.45e-43) {
		tmp = t_2;
	} else if ((x * y) <= -5.5e-79) {
		tmp = t_3;
	} else if ((x * y) <= 0.0) {
		tmp = t_2;
	} else if ((x * y) <= 2.7e-46) {
		tmp = t_3;
	} else {
		tmp = (x * y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = c + t_1
	t_3 = c + (a * (b * -0.25))
	tmp = 0
	if (x * y) <= -1.25e+77:
		tmp = c + (x * y)
	elif (x * y) <= -1.45e-43:
		tmp = t_2
	elif (x * y) <= -5.5e-79:
		tmp = t_3
	elif (x * y) <= 0.0:
		tmp = t_2
	elif (x * y) <= 2.7e-46:
		tmp = t_3
	else:
		tmp = (x * y) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(c + t_1)
	t_3 = Float64(c + Float64(a * Float64(b * -0.25)))
	tmp = 0.0
	if (Float64(x * y) <= -1.25e+77)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(x * y) <= -1.45e-43)
		tmp = t_2;
	elseif (Float64(x * y) <= -5.5e-79)
		tmp = t_3;
	elseif (Float64(x * y) <= 0.0)
		tmp = t_2;
	elseif (Float64(x * y) <= 2.7e-46)
		tmp = t_3;
	else
		tmp = Float64(Float64(x * y) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	t_2 = c + t_1;
	t_3 = c + (a * (b * -0.25));
	tmp = 0.0;
	if ((x * y) <= -1.25e+77)
		tmp = c + (x * y);
	elseif ((x * y) <= -1.45e-43)
		tmp = t_2;
	elseif ((x * y) <= -5.5e-79)
		tmp = t_3;
	elseif ((x * y) <= 0.0)
		tmp = t_2;
	elseif ((x * y) <= 2.7e-46)
		tmp = t_3;
	else
		tmp = (x * y) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.25e+77], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.45e-43], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -5.5e-79], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 0.0], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2.7e-46], t$95$3, N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.25000000000000001e77

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0 94.4%

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

   3. Taylor expanded in a around 0 86.2%

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

   if -1.25000000000000001e77 < (*.f64 x y) < -1.4500000000000001e-43 or -5.4999999999999997e-79 < (*.f64 x y) < 0.0

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 99.0%

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

   3. Taylor expanded in a around 0 73.3%

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

   if -1.4500000000000001e-43 < (*.f64 x y) < -5.4999999999999997e-79 or 0.0 < (*.f64 x y) < 2.7e-46

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 78.0%

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

      1. *-commutative 78.0%

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

      2. associate-*r* 78.0%

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

   4. Simplified 78.0%

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

   if 2.7e-46 < (*.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. Step-by-step derivation

      1. associate-+l- 94.9%

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

      2. associate--l+ 94.9%

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

      3. fma-def 97.6%

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

      4. associate-*l/ 97.6%

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

      5. fma-neg 97.6%

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

      6. sub-neg 97.6%

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

      7. distribute-neg-in 97.6%

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

      8. remove-double-neg 97.6%

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

      9. associate-/l* 98.6%

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

      10. distribute-frac-neg 98.6%

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

      11. associate-/r/ 98.7%

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

      12. fma-def 98.7%

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

      13. neg-mul-1 98.7%

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

      14. *-commutative 98.7%

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

      15. associate-/l* 98.7%

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

      16. metadata-eval 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in a around 0 82.6%

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

   5. Taylor expanded in c around 0 74.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.25 \cdot 10^{+77}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.45 \cdot 10^{-43}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{-79}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2.7 \cdot 10^{-46}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 4: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.2 \cdot 10^{+132}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 4.8 \cdot 10^{+137}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - 0.25 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + \frac{a}{\frac{-4}{b}}\right) + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -8.2e+132)
   (+ c (* x y))
   (if (<= (* x y) 4.8e+137)
     (- (+ c (* 0.0625 (* z t))) (* 0.25 (* a b)))
     (+ (+ c (/ a (/ -4.0 b))) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -8.2e+132) {
		tmp = c + (x * y);
	} else if ((x * y) <= 4.8e+137) {
		tmp = (c + (0.0625 * (z * t))) - (0.25 * (a * b));
	} else {
		tmp = (c + (a / (-4.0 / b))) + (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) <= (-8.2d+132)) then
        tmp = c + (x * y)
    else if ((x * y) <= 4.8d+137) then
        tmp = (c + (0.0625d0 * (z * t))) - (0.25d0 * (a * b))
    else
        tmp = (c + (a / ((-4.0d0) / b))) + (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) <= -8.2e+132) {
		tmp = c + (x * y);
	} else if ((x * y) <= 4.8e+137) {
		tmp = (c + (0.0625 * (z * t))) - (0.25 * (a * b));
	} else {
		tmp = (c + (a / (-4.0 / b))) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -8.2e+132:
		tmp = c + (x * y)
	elif (x * y) <= 4.8e+137:
		tmp = (c + (0.0625 * (z * t))) - (0.25 * (a * b))
	else:
		tmp = (c + (a / (-4.0 / b))) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -8.2e+132)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(x * y) <= 4.8e+137)
		tmp = Float64(Float64(c + Float64(0.0625 * Float64(z * t))) - Float64(0.25 * Float64(a * b)));
	else
		tmp = Float64(Float64(c + Float64(a / Float64(-4.0 / b))) + 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) <= -8.2e+132)
		tmp = c + (x * y);
	elseif ((x * y) <= 4.8e+137)
		tmp = (c + (0.0625 * (z * t))) - (0.25 * (a * b));
	else
		tmp = (c + (a / (-4.0 / b))) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -8.2e+132], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.8e+137], N[(N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(a / N[(-4.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.19999999999999983e132

   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 z around 0 96.3%

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

   3. Taylor expanded in a around 0 96.3%

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

   if -8.19999999999999983e132 < (*.f64 x y) < 4.79999999999999966e137

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 94.6%

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

   if 4.79999999999999966e137 < (*.f64 x y)

   1. Initial program 93.0%

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

      1. sub-neg 93.0%

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

      2. associate-+l+ 93.0%

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

      3. fma-def 97.7%

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

      4. associate-*l/ 97.7%

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

      5. distribute-frac-neg 97.7%

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

      6. distribute-rgt-neg-out 97.7%

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

      7. associate-/l* 97.7%

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

      8. neg-mul-1 97.7%

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

      9. associate-/r* 97.7%

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

      10. metadata-eval 97.7%

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

   3. Simplified 97.7%

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

      1. fma-udef 93.0%

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

      2. *-commutative 93.0%

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

      3. div-inv 93.0%

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

      4. metadata-eval 93.0%

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

   5. Applied egg-rr 93.0%

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

   6. Taylor expanded in x around inf 93.2%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.2 \cdot 10^{+132}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 4.8 \cdot 10^{+137}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - 0.25 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + \frac{a}{\frac{-4}{b}}\right) + x \cdot y\\ \end{array} \]

Alternative 5: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+45} \lor \neg \left(a \cdot b \leq 10^{+30}\right):\\ \;\;\;\;\left(c + \frac{a}{\frac{-4}{b}}\right) + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e+45) (not (<= (* a b) 1e+30)))
   (+ (+ c (/ a (/ -4.0 b))) (* x y))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+45) || !((a * b) <= 1e+30)) {
		tmp = (c + (a / (-4.0 / b))) + (x * y);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((a * b) <= (-5d+45)) .or. (.not. ((a * b) <= 1d+30))) then
        tmp = (c + (a / ((-4.0d0) / b))) + (x * y)
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+45) || !((a * b) <= 1e+30)) {
		tmp = (c + (a / (-4.0 / b))) + (x * y);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -5e+45) or not ((a * b) <= 1e+30):
		tmp = (c + (a / (-4.0 / b))) + (x * y)
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -5e+45) || !(Float64(a * b) <= 1e+30))
		tmp = Float64(Float64(c + Float64(a / Float64(-4.0 / b))) + Float64(x * y));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -5e+45) || ~(((a * b) <= 1e+30)))
		tmp = (c + (a / (-4.0 / b))) + (x * y);
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e+45], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1e+30]], $MachinePrecision]], N[(N[(c + N[(a / N[(-4.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5e45 or 1e30 < (*.f64 a b)

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. associate-+l+ 98.4%

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

      3. fma-def 98.4%

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

      4. associate-*l/ 98.4%

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

      5. distribute-frac-neg 98.4%

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

      6. distribute-rgt-neg-out 98.4%

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

      7. associate-/l* 99.0%

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

      8. neg-mul-1 99.0%

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

      9. associate-/r* 99.0%

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

      10. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

      1. fma-udef 99.0%

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

      2. *-commutative 99.0%

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

      3. div-inv 99.0%

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

      4. metadata-eval 99.0%

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

   5. Applied egg-rr 99.0%

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

   6. Taylor expanded in x around inf 88.7%

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

   if -5e45 < (*.f64 a b) < 1e30

   1. Initial program 97.9%

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

   2. Taylor expanded in a around 0 95.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+45} \lor \neg \left(a \cdot b \leq 10^{+30}\right):\\ \;\;\;\;\left(c + \frac{a}{\frac{-4}{b}}\right) + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 6: 85.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+214}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+30}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - 0.25 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -5e+214)
   (+ c (* a (* b -0.25)))
   (if (<= (* a b) 1e+30)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (- (* x y) (* 0.25 (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -5e+214) {
		tmp = c + (a * (b * -0.25));
	} else if ((a * b) <= 1e+30) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (x * y) - (0.25 * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a * b) <= (-5d+214)) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((a * b) <= 1d+30) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = (x * y) - (0.25d0 * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -5e+214) {
		tmp = c + (a * (b * -0.25));
	} else if ((a * b) <= 1e+30) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (x * y) - (0.25 * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -5e+214:
		tmp = c + (a * (b * -0.25))
	elif (a * b) <= 1e+30:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = (x * y) - (0.25 * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -5e+214)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(a * b) <= 1e+30)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(Float64(x * y) - Float64(0.25 * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -5e+214)
		tmp = c + (a * (b * -0.25));
	elseif ((a * b) <= 1e+30)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = (x * y) - (0.25 * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -5e+214], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+30], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - N[(0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.99999999999999953e214

   1. Initial program 97.3%

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

   2. Taylor expanded in a around inf 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-*r* 94.1%

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

   4. Simplified 94.1%

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

   if -4.99999999999999953e214 < (*.f64 a b) < 1e30

   1. Initial program 98.3%

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

   2. Taylor expanded in a around 0 91.3%

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

   if 1e30 < (*.f64 a b)

   1. Initial program 97.8%

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

   2. Taylor expanded in z around 0 91.5%

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

   3. Taylor expanded in c around 0 84.0%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+214}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+30}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - 0.25 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 7: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+45}:\\ \;\;\;\;\left(c + \frac{a}{\frac{-4}{b}}\right) + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 10^{+30}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -5e+45)
   (+ (+ c (/ a (/ -4.0 b))) (* x y))
   (if (<= (* a b) 1e+30)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (- (+ c (* x y)) (* 0.25 (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -5e+45) {
		tmp = (c + (a / (-4.0 / b))) + (x * y);
	} else if ((a * b) <= 1e+30) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (c + (x * y)) - (0.25 * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a * b) <= (-5d+45)) then
        tmp = (c + (a / ((-4.0d0) / b))) + (x * y)
    else if ((a * b) <= 1d+30) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = (c + (x * y)) - (0.25d0 * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -5e+45) {
		tmp = (c + (a / (-4.0 / b))) + (x * y);
	} else if ((a * b) <= 1e+30) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (c + (x * y)) - (0.25 * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -5e+45:
		tmp = (c + (a / (-4.0 / b))) + (x * y)
	elif (a * b) <= 1e+30:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = (c + (x * y)) - (0.25 * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -5e+45)
		tmp = Float64(Float64(c + Float64(a / Float64(-4.0 / b))) + Float64(x * y));
	elseif (Float64(a * b) <= 1e+30)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(0.25 * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -5e+45)
		tmp = (c + (a / (-4.0 / b))) + (x * y);
	elseif ((a * b) <= 1e+30)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = (c + (x * y)) - (0.25 * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -5e+45], N[(N[(c + N[(a / N[(-4.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+30], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5e45

   1. Initial program 98.7%

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

      1. sub-neg 98.7%

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

      2. associate-+l+ 98.7%

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

      3. fma-def 98.7%

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

      4. associate-*l/ 98.7%

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

      5. distribute-frac-neg 98.7%

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

      6. distribute-rgt-neg-out 98.7%

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

      7. associate-/l* 99.8%

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

      8. neg-mul-1 99.8%

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

      9. associate-/r* 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

      2. *-commutative 99.8%

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

      3. div-inv 99.8%

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

      4. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 86.7%

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

   if -5e45 < (*.f64 a b) < 1e30

   1. Initial program 97.9%

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

   2. Taylor expanded in a around 0 95.9%

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

   if 1e30 < (*.f64 a b)

   1. Initial program 97.8%

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

   2. Taylor expanded in z around 0 91.5%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+45}:\\ \;\;\;\;\left(c + \frac{a}{\frac{-4}{b}}\right) + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 10^{+30}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 8: 43.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+131}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -0.0029:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 4.5 \cdot 10^{+206}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -2e+131)
   (* x y)
   (if (<= (* x y) -0.0029)
     c
     (if (<= (* x y) 4.5e+206) (* a (* b -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) <= -2e+131) {
		tmp = x * y;
	} else if ((x * y) <= -0.0029) {
		tmp = c;
	} else if ((x * y) <= 4.5e+206) {
		tmp = a * (b * -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) <= (-2d+131)) then
        tmp = x * y
    else if ((x * y) <= (-0.0029d0)) then
        tmp = c
    else if ((x * y) <= 4.5d+206) then
        tmp = a * (b * (-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) <= -2e+131) {
		tmp = x * y;
	} else if ((x * y) <= -0.0029) {
		tmp = c;
	} else if ((x * y) <= 4.5e+206) {
		tmp = a * (b * -0.25);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -2e+131:
		tmp = x * y
	elif (x * y) <= -0.0029:
		tmp = c
	elif (x * y) <= 4.5e+206:
		tmp = a * (b * -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) <= -2e+131)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -0.0029)
		tmp = c;
	elseif (Float64(x * y) <= 4.5e+206)
		tmp = Float64(a * Float64(b * -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) <= -2e+131)
		tmp = x * y;
	elseif ((x * y) <= -0.0029)
		tmp = c;
	elseif ((x * y) <= 4.5e+206)
		tmp = a * (b * -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], -2e+131], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -0.0029], c, If[LessEqual[N[(x * y), $MachinePrecision], 4.5e+206], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.9999999999999998e131 or 4.50000000000000018e206 < (*.f64 x y)

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 93.5%

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

   3. Taylor expanded in c around 0 91.4%

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

   4. Taylor expanded in x around inf 89.9%

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

   if -1.9999999999999998e131 < (*.f64 x y) < -0.0029

   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 46.4%

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

   if -0.0029 < (*.f64 x y) < 4.50000000000000018e206

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. associate-+l+ 99.5%

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

      3. fma-def 99.5%

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

      4. associate-*l/ 99.5%

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

      5. distribute-frac-neg 99.5%

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

      6. distribute-rgt-neg-out 99.5%

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

      7. associate-/l* 99.9%

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

      8. neg-mul-1 99.9%

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

      9. associate-/r* 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. *-commutative 99.9%

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

      3. div-inv 99.9%

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

      4. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around inf 36.8%

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

      1. associate-*r* 37.3%

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

      2. *-commutative 37.3%

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

      3. associate-*l* 37.3%

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

   8. Simplified 37.3%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+131}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -0.0029:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 4.5 \cdot 10^{+206}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 9: 97.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (c + (a / (-4.0 / b))) + ((x * y) + (t * (z * 0.0625)));
}

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 + (a / ((-4.0d0) / b))) + ((x * y) + (t * (z * 0.0625d0)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (c + (a / (-4.0 / b))) + ((x * y) + (t * (z * 0.0625)));
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(c + N[(a / N[(-4.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.1%

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

   1. sub-neg 98.1%

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

   2. associate-+l+ 98.1%

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

   3. fma-def 98.9%

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

   4. associate-*l/ 98.9%

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

   5. distribute-frac-neg 98.9%

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

   6. distribute-rgt-neg-out 98.9%

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

   7. associate-/l* 99.2%

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

   8. neg-mul-1 99.2%

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

   9. associate-/r* 99.2%

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

   10. metadata-eval 99.2%

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

3. Simplified 99.2%

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

   1. fma-udef 98.4%

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

   2. *-commutative 98.4%

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

   3. div-inv 98.4%

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

   4. metadata-eval 98.4%

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

5. Applied egg-rr 98.4%

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

6. Final simplification 98.4%

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

Alternative 10: 61.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - 0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -9 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-279}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-29}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* x y) (* 0.25 (* a b)))))
   (if (<= x -9e+97)
     t_1
     (if (<= x -6.8e-279)
       (+ c (* 0.0625 (* z t)))
       (if (<= x 7.8e-29) (+ c (* a (* b -0.25))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) - (0.25 * (a * b));
	double tmp;
	if (x <= -9e+97) {
		tmp = t_1;
	} else if (x <= -6.8e-279) {
		tmp = c + (0.0625 * (z * t));
	} else if (x <= 7.8e-29) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (0.25d0 * (a * b))
    if (x <= (-9d+97)) then
        tmp = t_1
    else if (x <= (-6.8d-279)) then
        tmp = c + (0.0625d0 * (z * t))
    else if (x <= 7.8d-29) then
        tmp = c + (a * (b * (-0.25d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) - (0.25 * (a * b));
	double tmp;
	if (x <= -9e+97) {
		tmp = t_1;
	} else if (x <= -6.8e-279) {
		tmp = c + (0.0625 * (z * t));
	} else if (x <= 7.8e-29) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) - (0.25 * (a * b))
	tmp = 0
	if x <= -9e+97:
		tmp = t_1
	elif x <= -6.8e-279:
		tmp = c + (0.0625 * (z * t))
	elif x <= 7.8e-29:
		tmp = c + (a * (b * -0.25))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) - Float64(0.25 * Float64(a * b)))
	tmp = 0.0
	if (x <= -9e+97)
		tmp = t_1;
	elseif (x <= -6.8e-279)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (x <= 7.8e-29)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) - (0.25 * (a * b));
	tmp = 0.0;
	if (x <= -9e+97)
		tmp = t_1;
	elseif (x <= -6.8e-279)
		tmp = c + (0.0625 * (z * t));
	elseif (x <= 7.8e-29)
		tmp = c + (a * (b * -0.25));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9e+97], t$95$1, If[LessEqual[x, -6.8e-279], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e-29], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.99999999999999952e97 or 7.7999999999999995e-29 < x

   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 z around 0 83.3%

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

   3. Taylor expanded in c around 0 70.1%

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

   if -8.99999999999999952e97 < x < -6.8000000000000003e-279

   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 89.7%

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

   3. Taylor expanded in a around 0 65.7%

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

   if -6.8000000000000003e-279 < x < 7.7999999999999995e-29

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 69.3%

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

      1. *-commutative 69.3%

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

      2. associate-*r* 69.3%

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

   4. Simplified 69.3%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+97}:\\ \;\;\;\;x \cdot y - 0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-279}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-29}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - 0.25 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 11: 64.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.5 \cdot 10^{+75} \lor \neg \left(x \cdot y \leq 3.1 \cdot 10^{+170}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -6.5e+75) (not (<= (* x y) 3.1e+170)))
   (+ c (* x y))
   (+ c (* 0.0625 (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -6.5e+75) || !((x * y) <= 3.1e+170)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-6.5d+75)) .or. (.not. ((x * y) <= 3.1d+170))) then
        tmp = c + (x * y)
    else
        tmp = c + (0.0625d0 * (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -6.5e+75) || !((x * y) <= 3.1e+170)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -6.5e+75) or not ((x * y) <= 3.1e+170):
		tmp = c + (x * y)
	else:
		tmp = c + (0.0625 * (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -6.5e+75) || !(Float64(x * y) <= 3.1e+170))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -6.5e+75) || ~(((x * y) <= 3.1e+170)))
		tmp = c + (x * y);
	else
		tmp = c + (0.0625 * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -6.5e+75], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.1e+170]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -6.4999999999999998e75 or 3.1e170 < (*.f64 x y)

   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 z around 0 93.6%

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

   3. Taylor expanded in a around 0 83.0%

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

   if -6.4999999999999998e75 < (*.f64 x y) < 3.1e170

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 94.9%

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

   3. Taylor expanded in a around 0 63.8%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.5 \cdot 10^{+75} \lor \neg \left(x \cdot y \leq 3.1 \cdot 10^{+170}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 12: 48.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-240}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+222}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* t (* z 0.0625))))
   (if (<= t -5.8e-114)
     t_2
     (if (<= t 6.5e-278)
       t_1
       (if (<= t 3e-240) (* a (* b -0.25)) (if (<= t 8.2e+222) 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 (t <= -5.8e-114) {
		tmp = t_2;
	} else if (t <= 6.5e-278) {
		tmp = t_1;
	} else if (t <= 3e-240) {
		tmp = a * (b * -0.25);
	} else if (t <= 8.2e+222) {
		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 (t <= (-5.8d-114)) then
        tmp = t_2
    else if (t <= 6.5d-278) then
        tmp = t_1
    else if (t <= 3d-240) then
        tmp = a * (b * (-0.25d0))
    else if (t <= 8.2d+222) 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 (t <= -5.8e-114) {
		tmp = t_2;
	} else if (t <= 6.5e-278) {
		tmp = t_1;
	} else if (t <= 3e-240) {
		tmp = a * (b * -0.25);
	} else if (t <= 8.2e+222) {
		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 t <= -5.8e-114:
		tmp = t_2
	elif t <= 6.5e-278:
		tmp = t_1
	elif t <= 3e-240:
		tmp = a * (b * -0.25)
	elif t <= 8.2e+222:
		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 (t <= -5.8e-114)
		tmp = t_2;
	elseif (t <= 6.5e-278)
		tmp = t_1;
	elseif (t <= 3e-240)
		tmp = Float64(a * Float64(b * -0.25));
	elseif (t <= 8.2e+222)
		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 (t <= -5.8e-114)
		tmp = t_2;
	elseif (t <= 6.5e-278)
		tmp = t_1;
	elseif (t <= 3e-240)
		tmp = a * (b * -0.25);
	elseif (t <= 8.2e+222)
		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[t, -5.8e-114], t$95$2, If[LessEqual[t, 6.5e-278], t$95$1, If[LessEqual[t, 3e-240], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e+222], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.79999999999999993e-114 or 8.19999999999999974e222 < t

   1. Initial program 97.1%

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

   2. Taylor expanded in x around 0 78.4%

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

   3. Taylor expanded in a around 0 78.4%

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

      1. +-commutative 78.4%

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

      2. *-commutative 78.4%

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

      3. associate-*r* 78.4%

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

      4. *-commutative 78.4%

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

      5. associate-*r* 78.4%

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

      6. associate-+r+ 78.4%

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

      7. associate-*r* 78.4%

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

      8. *-commutative 78.4%

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

      9. fma-udef 78.4%

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

      10. fma-def 78.4%

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

      11. fma-udef 78.4%

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

      12. associate-*r* 78.4%

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

      13. fma-udef 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in t around inf 47.5%

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

      1. associate-*r* 47.5%

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

      2. *-commutative 47.5%

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

      3. associate-*l* 47.5%

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

   8. Simplified 47.5%

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

   if -5.79999999999999993e-114 < t < 6.5e-278 or 2.99999999999999991e-240 < t < 8.19999999999999974e222

   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 z around 0 82.5%

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

   3. Taylor expanded in a around 0 54.2%

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

   if 6.5e-278 < t < 2.99999999999999991e-240

   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. sub-neg 100.0%

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

      2. associate-+l+ 100.0%

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

      3. fma-def 100.0%

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

      4. associate-*l/ 100.0%

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

      5. distribute-frac-neg 100.0%

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

      6. distribute-rgt-neg-out 100.0%

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

      7. associate-/l* 100.0%

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

      8. neg-mul-1 100.0%

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

      9. associate-/r* 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. *-commutative 100.0%

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

      3. div-inv 100.0%

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

      4. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in a around inf 80.5%

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

      1. associate-*r* 80.5%

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

      2. *-commutative 80.5%

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

      3. associate-*l* 80.5%

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

   8. Simplified 80.5%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-278}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-240}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+222}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]

Alternative 13: 59.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-278}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-5}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))))
   (if (<= x -4.2e+112)
     t_1
     (if (<= x -1.25e-278)
       (+ c (* 0.0625 (* z t)))
       (if (<= x 5e-5) (+ c (* a (* b -0.25))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if (x <= -4.2e+112) {
		tmp = t_1;
	} else if (x <= -1.25e-278) {
		tmp = c + (0.0625 * (z * t));
	} else if (x <= 5e-5) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c + (x * y)
    if (x <= (-4.2d+112)) then
        tmp = t_1
    else if (x <= (-1.25d-278)) then
        tmp = c + (0.0625d0 * (z * t))
    else if (x <= 5d-5) then
        tmp = c + (a * (b * (-0.25d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if (x <= -4.2e+112) {
		tmp = t_1;
	} else if (x <= -1.25e-278) {
		tmp = c + (0.0625 * (z * t));
	} else if (x <= 5e-5) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	tmp = 0
	if x <= -4.2e+112:
		tmp = t_1
	elif x <= -1.25e-278:
		tmp = c + (0.0625 * (z * t))
	elif x <= 5e-5:
		tmp = c + (a * (b * -0.25))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (x <= -4.2e+112)
		tmp = t_1;
	elseif (x <= -1.25e-278)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (x <= 5e-5)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	tmp = 0.0;
	if (x <= -4.2e+112)
		tmp = t_1;
	elseif (x <= -1.25e-278)
		tmp = c + (0.0625 * (z * t));
	elseif (x <= 5e-5)
		tmp = c + (a * (b * -0.25));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+112], t$95$1, If[LessEqual[x, -1.25e-278], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e-5], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.1999999999999998e112 or 5.00000000000000024e-5 < x

   1. Initial program 96.2%

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

   2. Taylor expanded in z around 0 83.7%

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

   3. Taylor expanded in a around 0 65.4%

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

   if -4.1999999999999998e112 < x < -1.24999999999999996e-278

   1. Initial program 98.9%

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

   2. Taylor expanded in x around 0 87.9%

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

   3. Taylor expanded in a around 0 63.8%

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

   if -1.24999999999999996e-278 < x < 5.00000000000000024e-5

   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 67.2%

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

      1. *-commutative 67.2%

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

      2. associate-*r* 67.2%

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

   4. Simplified 67.2%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+112}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-278}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-5}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 14: 39.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+112}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-256}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \leq 0.00011:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -1.9e+112)
   (* x y)
   (if (<= x -5.1e-256)
     (* t (* z 0.0625))
     (if (<= x 0.00011) (* a (* b -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 <= -1.9e+112) {
		tmp = x * y;
	} else if (x <= -5.1e-256) {
		tmp = t * (z * 0.0625);
	} else if (x <= 0.00011) {
		tmp = a * (b * -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 <= (-1.9d+112)) then
        tmp = x * y
    else if (x <= (-5.1d-256)) then
        tmp = t * (z * 0.0625d0)
    else if (x <= 0.00011d0) then
        tmp = a * (b * (-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 <= -1.9e+112) {
		tmp = x * y;
	} else if (x <= -5.1e-256) {
		tmp = t * (z * 0.0625);
	} else if (x <= 0.00011) {
		tmp = a * (b * -0.25);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -1.9e+112:
		tmp = x * y
	elif x <= -5.1e-256:
		tmp = t * (z * 0.0625)
	elif x <= 0.00011:
		tmp = a * (b * -0.25)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -1.9e+112)
		tmp = Float64(x * y);
	elseif (x <= -5.1e-256)
		tmp = Float64(t * Float64(z * 0.0625));
	elseif (x <= 0.00011)
		tmp = Float64(a * Float64(b * -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 <= -1.9e+112)
		tmp = x * y;
	elseif (x <= -5.1e-256)
		tmp = t * (z * 0.0625);
	elseif (x <= 0.00011)
		tmp = a * (b * -0.25);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -1.9e+112], N[(x * y), $MachinePrecision], If[LessEqual[x, -5.1e-256], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.00011], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.90000000000000004e112 or 1.10000000000000004e-4 < x

   1. Initial program 96.2%

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

   2. Taylor expanded in z around 0 83.7%

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

   3. Taylor expanded in c around 0 69.3%

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

   4. Taylor expanded in x around inf 51.7%

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

   if -1.90000000000000004e112 < x < -5.10000000000000011e-256

   1. Initial program 98.8%

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

   2. Taylor expanded in x around 0 86.5%

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

   3. Taylor expanded in a around 0 86.5%

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

      1. +-commutative 86.5%

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

      2. *-commutative 86.5%

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

      3. associate-*r* 86.5%

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

      4. *-commutative 86.5%

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

      5. associate-*r* 86.5%

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

      6. associate-+r+ 86.5%

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

      7. associate-*r* 86.5%

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

      8. *-commutative 86.5%

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

      9. fma-udef 86.5%

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

      10. fma-def 86.5%

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

      11. fma-udef 86.5%

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

      12. associate-*r* 86.5%

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

      13. fma-udef 86.5%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in t around inf 40.1%

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

      1. associate-*r* 40.1%

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

      2. *-commutative 40.1%

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

      3. associate-*l* 40.1%

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

   8. Simplified 40.1%

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

   if -5.10000000000000011e-256 < x < 1.10000000000000004e-4

   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. sub-neg 100.0%

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

      2. associate-+l+ 100.0%

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

      3. fma-def 100.0%

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

      4. associate-*l/ 100.0%

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

      5. distribute-frac-neg 100.0%

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

      6. distribute-rgt-neg-out 100.0%

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

      7. associate-/l* 100.0%

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

      8. neg-mul-1 100.0%

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

      9. associate-/r* 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 99.9%

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

      2. *-commutative 99.9%

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

      3. div-inv 99.9%

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

      4. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around inf 39.9%

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

      1. associate-*r* 39.9%

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

      2. *-commutative 39.9%

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

      3. associate-*l* 39.9%

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

   8. Simplified 39.9%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+112}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-256}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \leq 0.00011:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 15: 40.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.4 \cdot 10^{+130} \lor \neg \left(x \cdot y \leq 6 \cdot 10^{-43}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2.4e+130) (not (<= (* x y) 6e-43))) (* 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) <= -2.4e+130) || !((x * y) <= 6e-43)) {
		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) <= (-2.4d+130)) .or. (.not. ((x * y) <= 6d-43))) 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) <= -2.4e+130) || !((x * y) <= 6e-43)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -2.4e+130) or not ((x * y) <= 6e-43):
		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) <= -2.4e+130) || !(Float64(x * y) <= 6e-43))
		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) <= -2.4e+130) || ~(((x * y) <= 6e-43)))
		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], -2.4e+130], N[Not[LessEqual[N[(x * y), $MachinePrecision], 6e-43]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.40000000000000024e130 or 6.00000000000000007e-43 < (*.f64 x y)

   1. Initial program 95.2%

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

   2. Taylor expanded in z around 0 80.6%

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

   3. Taylor expanded in c around 0 75.5%

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

   4. Taylor expanded in x around inf 62.8%

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

   if -2.40000000000000024e130 < (*.f64 x y) < 6.00000000000000007e-43

   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 31.4%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.4 \cdot 10^{+130} \lor \neg \left(x \cdot y \leq 6 \cdot 10^{-43}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 16: 21.6% 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 98.1%

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

2. Taylor expanded in c around inf 21.5%

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

3. Final simplification 21.5%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023310 
(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))