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

Percentage Accurate: 97.7% → 99.0%

Time: 7.1s

Alternatives: 13

Speedup: 0.5×

• 32.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. associate-+l- 97.7%

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

   2. associate--l+ 97.7%

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

   3. fma-def 99.2%

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

   4. associate-*l/ 99.2%

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

   5. fma-neg 99.6%

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

   6. sub-neg 99.6%

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

   7. distribute-neg-in 99.6%

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

   8. remove-double-neg 99.6%

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

   9. associate-/l* 99.5%

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

   10. distribute-frac-neg 99.5%

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

   11. associate-/r/ 99.6%

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

   12. fma-def 99.6%

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

   13. neg-mul-1 99.6%

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

   14. *-commutative 99.6%

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

   15. associate-/l* 99.6%

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

   16. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 98.1% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. associate-+l- 97.7%

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

   2. fma-def 98.8%

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

   3. *-commutative 98.8%

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

   4. associate-/l* 98.8%

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

   5. associate-/l* 98.7%

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

3. Simplified 98.7%

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

4. Final simplification 98.7%

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

Alternative 3: 98.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
   (if (<= t_1 INFINITY)
     (+ c t_1)
     (- (+ c (* (* z t) 0.0625)) (* (* a b) 0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = c + t_1;
	} else {
		tmp = (c + ((z * t) * 0.0625)) - ((a * b) * 0.25);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = c + t_1;
	} else {
		tmp = (c + ((z * t) * 0.0625)) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)
	tmp = 0
	if t_1 <= math.inf:
		tmp = c + t_1
	else:
		tmp = (c + ((z * t) * 0.0625)) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(c + t_1);
	else
		tmp = Float64(Float64(c + Float64(Float64(z * t) * 0.0625)) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = c + t_1;
	else
		tmp = (c + ((z * t) * 0.0625)) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(c + t$95$1), $MachinePrecision], N[(N[(c + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. fma-def 50.0%

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

      3. *-commutative 50.0%

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

      4. associate-/l* 50.0%

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

      5. associate-/l* 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in x around 0 66.7%

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

4. Final simplification 99.2%

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

Alternative 4: 64.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + \left(z \cdot t\right) \cdot 0.0625\\ t_2 := c + a \cdot \left(b \cdot -0.25\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-201}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \cdot b \leq 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \cdot b \leq 10:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* (* z t) 0.0625)))
        (t_2 (+ c (* a (* b -0.25))))
        (t_3 (+ c (* x y))))
   (if (<= (* a b) -2e+78)
     t_2
     (if (<= (* a b) -4e-79)
       t_1
       (if (<= (* a b) -2e-201)
         t_3
         (if (<= (* a b) 1e-192)
           t_1
           (if (<= (* a b) 2e-123) t_3 (if (<= (* a b) 10.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + ((z * t) * 0.0625);
	double t_2 = c + (a * (b * -0.25));
	double t_3 = c + (x * y);
	double tmp;
	if ((a * b) <= -2e+78) {
		tmp = t_2;
	} else if ((a * b) <= -4e-79) {
		tmp = t_1;
	} else if ((a * b) <= -2e-201) {
		tmp = t_3;
	} else if ((a * b) <= 1e-192) {
		tmp = t_1;
	} else if ((a * b) <= 2e-123) {
		tmp = t_3;
	} else if ((a * b) <= 10.0) {
		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) :: t_3
    real(8) :: tmp
    t_1 = c + ((z * t) * 0.0625d0)
    t_2 = c + (a * (b * (-0.25d0)))
    t_3 = c + (x * y)
    if ((a * b) <= (-2d+78)) then
        tmp = t_2
    else if ((a * b) <= (-4d-79)) then
        tmp = t_1
    else if ((a * b) <= (-2d-201)) then
        tmp = t_3
    else if ((a * b) <= 1d-192) then
        tmp = t_1
    else if ((a * b) <= 2d-123) then
        tmp = t_3
    else if ((a * b) <= 10.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + ((z * t) * 0.0625);
	double t_2 = c + (a * (b * -0.25));
	double t_3 = c + (x * y);
	double tmp;
	if ((a * b) <= -2e+78) {
		tmp = t_2;
	} else if ((a * b) <= -4e-79) {
		tmp = t_1;
	} else if ((a * b) <= -2e-201) {
		tmp = t_3;
	} else if ((a * b) <= 1e-192) {
		tmp = t_1;
	} else if ((a * b) <= 2e-123) {
		tmp = t_3;
	} else if ((a * b) <= 10.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + ((z * t) * 0.0625)
	t_2 = c + (a * (b * -0.25))
	t_3 = c + (x * y)
	tmp = 0
	if (a * b) <= -2e+78:
		tmp = t_2
	elif (a * b) <= -4e-79:
		tmp = t_1
	elif (a * b) <= -2e-201:
		tmp = t_3
	elif (a * b) <= 1e-192:
		tmp = t_1
	elif (a * b) <= 2e-123:
		tmp = t_3
	elif (a * b) <= 10.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(Float64(z * t) * 0.0625))
	t_2 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(a * b) <= -2e+78)
		tmp = t_2;
	elseif (Float64(a * b) <= -4e-79)
		tmp = t_1;
	elseif (Float64(a * b) <= -2e-201)
		tmp = t_3;
	elseif (Float64(a * b) <= 1e-192)
		tmp = t_1;
	elseif (Float64(a * b) <= 2e-123)
		tmp = t_3;
	elseif (Float64(a * b) <= 10.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + ((z * t) * 0.0625);
	t_2 = c + (a * (b * -0.25));
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((a * b) <= -2e+78)
		tmp = t_2;
	elseif ((a * b) <= -4e-79)
		tmp = t_1;
	elseif ((a * b) <= -2e-201)
		tmp = t_3;
	elseif ((a * b) <= 1e-192)
		tmp = t_1;
	elseif ((a * b) <= 2e-123)
		tmp = t_3;
	elseif ((a * b) <= 10.0)
		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[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+78], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -4e-79], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -2e-201], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 1e-192], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2e-123], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 10.0], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.00000000000000002e78 or 10 < (*.f64 a b)

   1. Initial program 97.0%

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

   2. Taylor expanded in a around inf 71.9%

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

      1. *-commutative 71.9%

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

      2. associate-*l* 71.9%

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

   4. Simplified 71.9%

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

   if -2.00000000000000002e78 < (*.f64 a b) < -4e-79 or -1.99999999999999989e-201 < (*.f64 a b) < 1.0000000000000001e-192 or 2.0000000000000001e-123 < (*.f64 a b) < 10

   1. Initial program 97.5%

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

      1. associate-+l- 97.5%

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

      2. fma-def 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 99.9%

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

      5. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 88.6%

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

   5. Taylor expanded in t around inf 70.1%

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

   if -4e-79 < (*.f64 a b) < -1.99999999999999989e-201 or 1.0000000000000001e-192 < (*.f64 a b) < 2.0000000000000001e-123

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. fma-def 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 100.0%

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

      5. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 87.0%

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

   5. Taylor expanded in a around 0 84.4%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+78}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{-79}:\\ \;\;\;\;c + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-201}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 10^{-192}:\\ \;\;\;\;c + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-123}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 10:\\ \;\;\;\;c + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]

Alternative 5: 89.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot t\right) \cdot 0.0625\\ t_2 := \left(a \cdot b\right) \cdot 0.25\\ t_3 := \left(c + x \cdot y\right) - t_2\\ t_4 := c + \left(x \cdot y + t_1\right)\\ \mathbf{if}\;x \cdot y \leq -3.4 \cdot 10^{+128}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \cdot y \leq -4.5 \cdot 10^{+66}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -0.0053:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \cdot y \leq 1.65 \cdot 10^{+75}:\\ \;\;\;\;\left(c + t_1\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* z t) 0.0625))
        (t_2 (* (* a b) 0.25))
        (t_3 (- (+ c (* x y)) t_2))
        (t_4 (+ c (+ (* x y) t_1))))
   (if (<= (* x y) -3.4e+128)
     t_4
     (if (<= (* x y) -4.5e+66)
       t_3
       (if (<= (* x y) -0.0053)
         t_4
         (if (<= (* x y) 1.65e+75) (- (+ c t_1) t_2) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) * 0.0625;
	double t_2 = (a * b) * 0.25;
	double t_3 = (c + (x * y)) - t_2;
	double t_4 = c + ((x * y) + t_1);
	double tmp;
	if ((x * y) <= -3.4e+128) {
		tmp = t_4;
	} else if ((x * y) <= -4.5e+66) {
		tmp = t_3;
	} else if ((x * y) <= -0.0053) {
		tmp = t_4;
	} else if ((x * y) <= 1.65e+75) {
		tmp = (c + t_1) - t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = (z * t) * 0.0625d0
    t_2 = (a * b) * 0.25d0
    t_3 = (c + (x * y)) - t_2
    t_4 = c + ((x * y) + t_1)
    if ((x * y) <= (-3.4d+128)) then
        tmp = t_4
    else if ((x * y) <= (-4.5d+66)) then
        tmp = t_3
    else if ((x * y) <= (-0.0053d0)) then
        tmp = t_4
    else if ((x * y) <= 1.65d+75) then
        tmp = (c + t_1) - t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) * 0.0625;
	double t_2 = (a * b) * 0.25;
	double t_3 = (c + (x * y)) - t_2;
	double t_4 = c + ((x * y) + t_1);
	double tmp;
	if ((x * y) <= -3.4e+128) {
		tmp = t_4;
	} else if ((x * y) <= -4.5e+66) {
		tmp = t_3;
	} else if ((x * y) <= -0.0053) {
		tmp = t_4;
	} else if ((x * y) <= 1.65e+75) {
		tmp = (c + t_1) - t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (z * t) * 0.0625
	t_2 = (a * b) * 0.25
	t_3 = (c + (x * y)) - t_2
	t_4 = c + ((x * y) + t_1)
	tmp = 0
	if (x * y) <= -3.4e+128:
		tmp = t_4
	elif (x * y) <= -4.5e+66:
		tmp = t_3
	elif (x * y) <= -0.0053:
		tmp = t_4
	elif (x * y) <= 1.65e+75:
		tmp = (c + t_1) - t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(z * t) * 0.0625)
	t_2 = Float64(Float64(a * b) * 0.25)
	t_3 = Float64(Float64(c + Float64(x * y)) - t_2)
	t_4 = Float64(c + Float64(Float64(x * y) + t_1))
	tmp = 0.0
	if (Float64(x * y) <= -3.4e+128)
		tmp = t_4;
	elseif (Float64(x * y) <= -4.5e+66)
		tmp = t_3;
	elseif (Float64(x * y) <= -0.0053)
		tmp = t_4;
	elseif (Float64(x * y) <= 1.65e+75)
		tmp = Float64(Float64(c + t_1) - t_2);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (z * t) * 0.0625;
	t_2 = (a * b) * 0.25;
	t_3 = (c + (x * y)) - t_2;
	t_4 = c + ((x * y) + t_1);
	tmp = 0.0;
	if ((x * y) <= -3.4e+128)
		tmp = t_4;
	elseif ((x * y) <= -4.5e+66)
		tmp = t_3;
	elseif ((x * y) <= -0.0053)
		tmp = t_4;
	elseif ((x * y) <= 1.65e+75)
		tmp = (c + t_1) - t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.4e+128], t$95$4, If[LessEqual[N[(x * y), $MachinePrecision], -4.5e+66], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -0.0053], t$95$4, If[LessEqual[N[(x * y), $MachinePrecision], 1.65e+75], N[(N[(c + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.3999999999999999e128 or -4.4999999999999998e66 < (*.f64 x y) < -0.00530000000000000002

   1. Initial program 95.9%

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

      1. associate-+l- 95.9%

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

      2. fma-def 98.0%

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

      3. *-commutative 98.0%

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

      4. associate-/l* 97.9%

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

      5. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in a around 0 93.8%

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

   if -3.3999999999999999e128 < (*.f64 x y) < -4.4999999999999998e66 or 1.64999999999999999e75 < (*.f64 x y)

   1. Initial program 95.3%

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

      1. associate-+l- 95.3%

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

      2. fma-def 98.4%

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

      3. *-commutative 98.4%

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

      4. associate-/l* 98.4%

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

      5. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in t around 0 95.2%

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

   if -0.00530000000000000002 < (*.f64 x y) < 1.64999999999999999e75

   1. Initial program 99.3%

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

      1. associate-+l- 99.3%

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

      2. fma-def 99.3%

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

      3. *-commutative 99.3%

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

      4. associate-/l* 99.2%

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

      5. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around 0 94.7%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.4 \cdot 10^{+128}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -4.5 \cdot 10^{+66}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq -0.0053:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 1.65 \cdot 10^{+75}:\\ \;\;\;\;\left(c + \left(z \cdot t\right) \cdot 0.0625\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 6: 64.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.5 \cdot 10^{+205} \lor \neg \left(x \cdot y \leq -2.7 \cdot 10^{+130} \lor \neg \left(x \cdot y \leq -6.4 \cdot 10^{+36}\right) \land x \cdot y \leq 8.5 \cdot 10^{+69}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + \left(z \cdot t\right) \cdot 0.0625\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -9.5e+205)
         (not
          (or (<= (* x y) -2.7e+130)
              (and (not (<= (* x y) -6.4e+36)) (<= (* x y) 8.5e+69)))))
   (+ c (* x y))
   (+ c (* (* z t) 0.0625))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -9.5e+205) || !(((x * y) <= -2.7e+130) || (!((x * y) <= -6.4e+36) && ((x * y) <= 8.5e+69)))) {
		tmp = c + (x * y);
	} else {
		tmp = c + ((z * t) * 0.0625);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-9.5d+205)) .or. (.not. ((x * y) <= (-2.7d+130)) .or. (.not. ((x * y) <= (-6.4d+36))) .and. ((x * y) <= 8.5d+69))) then
        tmp = c + (x * y)
    else
        tmp = c + ((z * t) * 0.0625d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -9.5e+205) || !(((x * y) <= -2.7e+130) || (!((x * y) <= -6.4e+36) && ((x * y) <= 8.5e+69)))) {
		tmp = c + (x * y);
	} else {
		tmp = c + ((z * t) * 0.0625);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -9.5e+205) or not (((x * y) <= -2.7e+130) or (not ((x * y) <= -6.4e+36) and ((x * y) <= 8.5e+69))):
		tmp = c + (x * y)
	else:
		tmp = c + ((z * t) * 0.0625)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -9.5e+205) || !((Float64(x * y) <= -2.7e+130) || (!(Float64(x * y) <= -6.4e+36) && (Float64(x * y) <= 8.5e+69))))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(Float64(z * t) * 0.0625));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -9.5e+205) || ~((((x * y) <= -2.7e+130) || (~(((x * y) <= -6.4e+36)) && ((x * y) <= 8.5e+69)))))
		tmp = c + (x * y);
	else
		tmp = c + ((z * t) * 0.0625);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -9.5e+205], N[Not[Or[LessEqual[N[(x * y), $MachinePrecision], -2.7e+130], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -6.4e+36]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 8.5e+69]]]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.4999999999999997e205 or -2.6999999999999998e130 < (*.f64 x y) < -6.3999999999999998e36 or 8.5000000000000002e69 < (*.f64 x y)

   1. Initial program 94.8%

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

      1. associate-+l- 94.8%

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

      2. fma-def 97.9%

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

      3. *-commutative 97.9%

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

      4. associate-/l* 97.9%

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

      5. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in t around 0 92.8%

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

   5. Taylor expanded in a around 0 77.4%

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

   if -9.4999999999999997e205 < (*.f64 x y) < -2.6999999999999998e130 or -6.3999999999999998e36 < (*.f64 x y) < 8.5000000000000002e69

   1. Initial program 99.4%

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

      1. associate-+l- 99.4%

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

      2. fma-def 99.4%

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

      3. *-commutative 99.4%

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

      4. associate-/l* 99.3%

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

      5. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in a around 0 67.6%

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

   5. Taylor expanded in t around inf 61.4%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.5 \cdot 10^{+205} \lor \neg \left(x \cdot y \leq -2.7 \cdot 10^{+130} \lor \neg \left(x \cdot y \leq -6.4 \cdot 10^{+36}\right) \land x \cdot y \leq 8.5 \cdot 10^{+69}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + \left(z \cdot t\right) \cdot 0.0625\\ \end{array} \]

Alternative 7: 88.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+100} \lor \neg \left(a \cdot b \leq 10\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -1e+100) (not (<= (* a b) 10.0)))
   (- (+ c (* x y)) (* (* a b) 0.25))
   (+ c (+ (* x y) (* (* z t) 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -1e+100) || !((a * b) <= 10.0)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((a * b) <= (-1d+100)) .or. (.not. ((a * b) <= 10.0d0))) then
        tmp = (c + (x * y)) - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + ((z * t) * 0.0625d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -1e+100) || !((a * b) <= 10.0)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -1e+100) or not ((a * b) <= 10.0):
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + ((z * t) * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -1e+100) || !(Float64(a * b) <= 10.0))
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -1e+100) || ~(((a * b) <= 10.0)))
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1e+100], N[Not[LessEqual[N[(a * b), $MachinePrecision], 10.0]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.00000000000000002e100 or 10 < (*.f64 a b)

   1. Initial program 97.0%

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

      1. associate-+l- 97.0%

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

      2. fma-def 97.0%

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

      3. *-commutative 97.0%

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

      4. associate-/l* 97.0%

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

      5. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in t around 0 87.6%

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

   if -1.00000000000000002e100 < (*.f64 a b) < 10

   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. fma-def 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 99.9%

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

      5. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 90.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+100} \lor \neg \left(a \cdot b \leq 10\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 8: 86.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+100}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+139}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -1e+100)
   (+ c (* a (* b -0.25)))
   (if (<= (* a b) 1e+139)
     (+ c (+ (* x y) (* (* z t) 0.0625)))
     (- (* x y) (* (* a b) 0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -1e+100) {
		tmp = c + (a * (b * -0.25));
	} else if ((a * b) <= 1e+139) {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a * b) <= (-1d+100)) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((a * b) <= 1d+139) then
        tmp = c + ((x * y) + ((z * t) * 0.0625d0))
    else
        tmp = (x * y) - ((a * b) * 0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -1e+100) {
		tmp = c + (a * (b * -0.25));
	} else if ((a * b) <= 1e+139) {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -1e+100:
		tmp = c + (a * (b * -0.25))
	elif (a * b) <= 1e+139:
		tmp = c + ((x * y) + ((z * t) * 0.0625))
	else:
		tmp = (x * y) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -1e+100)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(a * b) <= 1e+139)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625)));
	else
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -1e+100)
		tmp = c + (a * (b * -0.25));
	elseif ((a * b) <= 1e+139)
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	else
		tmp = (x * y) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -1e+100], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+139], N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.00000000000000002e100

   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 a around inf 83.5%

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

      1. *-commutative 83.5%

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

      2. associate-*l* 83.5%

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

   4. Simplified 83.5%

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

   if -1.00000000000000002e100 < (*.f64 a b) < 1.00000000000000003e139

   1. Initial program 98.4%

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

      1. associate-+l- 98.4%

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

      2. fma-def 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 99.9%

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

      5. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 88.6%

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

   if 1.00000000000000003e139 < (*.f64 a b)

   1. Initial program 94.7%

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

      1. associate-+l- 94.7%

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

      2. fma-def 94.7%

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

      3. *-commutative 94.7%

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

      4. associate-/l* 94.7%

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

      5. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in t around 0 84.8%

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

   5. Taylor expanded in c around 0 84.8%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+100}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+139}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 9: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ t_2 := c + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-139}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 1.536 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* a b) 0.25))) (t_2 (+ c (* (* z t) 0.0625))))
   (if (<= t -3.7e-97)
     t_2
     (if (<= t 3.7e-237)
       t_1
       (if (<= t 2.7e-139)
         (+ c (* a (* b -0.25)))
         (if (<= t 1.536e+84) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) - ((a * b) * 0.25);
	double t_2 = c + ((z * t) * 0.0625);
	double tmp;
	if (t <= -3.7e-97) {
		tmp = t_2;
	} else if (t <= 3.7e-237) {
		tmp = t_1;
	} else if (t <= 2.7e-139) {
		tmp = c + (a * (b * -0.25));
	} else if (t <= 1.536e+84) {
		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 = (x * y) - ((a * b) * 0.25d0)
    t_2 = c + ((z * t) * 0.0625d0)
    if (t <= (-3.7d-97)) then
        tmp = t_2
    else if (t <= 3.7d-237) then
        tmp = t_1
    else if (t <= 2.7d-139) then
        tmp = c + (a * (b * (-0.25d0)))
    else if (t <= 1.536d+84) 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 = (x * y) - ((a * b) * 0.25);
	double t_2 = c + ((z * t) * 0.0625);
	double tmp;
	if (t <= -3.7e-97) {
		tmp = t_2;
	} else if (t <= 3.7e-237) {
		tmp = t_1;
	} else if (t <= 2.7e-139) {
		tmp = c + (a * (b * -0.25));
	} else if (t <= 1.536e+84) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) - ((a * b) * 0.25)
	t_2 = c + ((z * t) * 0.0625)
	tmp = 0
	if t <= -3.7e-97:
		tmp = t_2
	elif t <= 3.7e-237:
		tmp = t_1
	elif t <= 2.7e-139:
		tmp = c + (a * (b * -0.25))
	elif t <= 1.536e+84:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25))
	t_2 = Float64(c + Float64(Float64(z * t) * 0.0625))
	tmp = 0.0
	if (t <= -3.7e-97)
		tmp = t_2;
	elseif (t <= 3.7e-237)
		tmp = t_1;
	elseif (t <= 2.7e-139)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (t <= 1.536e+84)
		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 = (x * y) - ((a * b) * 0.25);
	t_2 = c + ((z * t) * 0.0625);
	tmp = 0.0;
	if (t <= -3.7e-97)
		tmp = t_2;
	elseif (t <= 3.7e-237)
		tmp = t_1;
	elseif (t <= 2.7e-139)
		tmp = c + (a * (b * -0.25));
	elseif (t <= 1.536e+84)
		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[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e-97], t$95$2, If[LessEqual[t, 3.7e-237], t$95$1, If[LessEqual[t, 2.7e-139], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.536e+84], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.69999999999999976e-97 or 1.53599999999999999e84 < t

   1. Initial program 96.3%

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

      1. associate-+l- 96.3%

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

      2. fma-def 98.5%

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

      3. *-commutative 98.5%

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

      4. associate-/l* 98.4%

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

      5. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in a around 0 80.5%

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

   5. Taylor expanded in t around inf 63.5%

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

   if -3.69999999999999976e-97 < t < 3.7000000000000001e-237 or 2.6999999999999998e-139 < t < 1.53599999999999999e84

   1. Initial program 99.0%

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

      1. associate-+l- 99.0%

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

      2. fma-def 99.0%

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

      3. *-commutative 99.0%

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

      4. associate-/l* 99.0%

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

      5. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in t around 0 90.0%

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

   5. Taylor expanded in c around 0 67.5%

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

   if 3.7000000000000001e-237 < t < 2.6999999999999998e-139

   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 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-*l* 80.3%

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

   4. Simplified 80.3%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-97}:\\ \;\;\;\;c + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-237}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-139}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 1.536 \cdot 10^{+84}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(z \cdot t\right) \cdot 0.0625\\ \end{array} \]

Alternative 10: 36.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{+118}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{+37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \leq -11500000000:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-223}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+47}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -1e+118)
   c
   (if (<= c -1.4e+37)
     (* x y)
     (if (<= c -11500000000.0)
       c
       (if (<= c 1.85e-223)
         (* (* a b) -0.25)
         (if (<= c 1.15e+47) (* x y) c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -1e+118) {
		tmp = c;
	} else if (c <= -1.4e+37) {
		tmp = x * y;
	} else if (c <= -11500000000.0) {
		tmp = c;
	} else if (c <= 1.85e-223) {
		tmp = (a * b) * -0.25;
	} else if (c <= 1.15e+47) {
		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 (c <= (-1d+118)) then
        tmp = c
    else if (c <= (-1.4d+37)) then
        tmp = x * y
    else if (c <= (-11500000000.0d0)) then
        tmp = c
    else if (c <= 1.85d-223) then
        tmp = (a * b) * (-0.25d0)
    else if (c <= 1.15d+47) 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 (c <= -1e+118) {
		tmp = c;
	} else if (c <= -1.4e+37) {
		tmp = x * y;
	} else if (c <= -11500000000.0) {
		tmp = c;
	} else if (c <= 1.85e-223) {
		tmp = (a * b) * -0.25;
	} else if (c <= 1.15e+47) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -1e+118:
		tmp = c
	elif c <= -1.4e+37:
		tmp = x * y
	elif c <= -11500000000.0:
		tmp = c
	elif c <= 1.85e-223:
		tmp = (a * b) * -0.25
	elif c <= 1.15e+47:
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -1e+118)
		tmp = c;
	elseif (c <= -1.4e+37)
		tmp = Float64(x * y);
	elseif (c <= -11500000000.0)
		tmp = c;
	elseif (c <= 1.85e-223)
		tmp = Float64(Float64(a * b) * -0.25);
	elseif (c <= 1.15e+47)
		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 (c <= -1e+118)
		tmp = c;
	elseif (c <= -1.4e+37)
		tmp = x * y;
	elseif (c <= -11500000000.0)
		tmp = c;
	elseif (c <= 1.85e-223)
		tmp = (a * b) * -0.25;
	elseif (c <= 1.15e+47)
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -1e+118], c, If[LessEqual[c, -1.4e+37], N[(x * y), $MachinePrecision], If[LessEqual[c, -11500000000.0], c, If[LessEqual[c, 1.85e-223], N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision], If[LessEqual[c, 1.15e+47], N[(x * y), $MachinePrecision], c]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -9.99999999999999967e117 or -1.3999999999999999e37 < c < -1.15e10 or 1.1499999999999999e47 < c

   1. Initial program 95.9%

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

      1. associate-+l- 95.9%

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

      2. fma-def 99.0%

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

      3. *-commutative 99.0%

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

      4. associate-/l* 99.0%

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

      5. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in c around inf 56.4%

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

   if -9.99999999999999967e117 < c < -1.3999999999999999e37 or 1.8499999999999999e-223 < c < 1.1499999999999999e47

   1. Initial program 98.4%

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

      1. associate-+l- 98.4%

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

      2. fma-def 98.4%

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

      3. *-commutative 98.4%

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

      4. associate-/l* 98.3%

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

      5. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around 0 70.0%

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

   5. Taylor expanded in x around inf 50.6%

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

   if -1.15e10 < c < 1.8499999999999999e-223

   1. Initial program 98.9%

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

      1. associate-+l- 98.9%

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

      2. fma-def 98.9%

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

      3. *-commutative 98.9%

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

      4. associate-/l* 98.9%

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

      5. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in t around 0 66.9%

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

   5. Taylor expanded in a around inf 43.6%

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

      1. *-commutative 43.6%

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

   7. Simplified 43.6%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{+118}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{+37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \leq -11500000000:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-223}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+47}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 11: 62.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.8 \cdot 10^{+169} \lor \neg \left(a \cdot b \leq 9 \cdot 10^{+141}\right):\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -1.8e+169) (not (<= (* a b) 9e+141)))
   (* (* a b) -0.25)
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -1.8e+169) || !((a * b) <= 9e+141)) {
		tmp = (a * b) * -0.25;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((a * b) <= (-1.8d+169)) .or. (.not. ((a * b) <= 9d+141))) then
        tmp = (a * b) * (-0.25d0)
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -1.8e+169) || !((a * b) <= 9e+141)) {
		tmp = (a * b) * -0.25;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -1.8e+169) or not ((a * b) <= 9e+141):
		tmp = (a * b) * -0.25
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -1.8e+169) || !(Float64(a * b) <= 9e+141))
		tmp = Float64(Float64(a * b) * -0.25);
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -1.8e+169) || ~(((a * b) <= 9e+141)))
		tmp = (a * b) * -0.25;
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.8e+169], N[Not[LessEqual[N[(a * b), $MachinePrecision], 9e+141]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.80000000000000005e169 or 9.0000000000000003e141 < (*.f64 a b)

   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. fma-def 94.9%

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

      3. *-commutative 94.9%

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

      4. associate-/l* 94.9%

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

      5. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in t around 0 90.0%

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

   5. Taylor expanded in a around inf 81.5%

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

      1. *-commutative 81.5%

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

   7. Simplified 81.5%

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

   if -1.80000000000000005e169 < (*.f64 a b) < 9.0000000000000003e141

   1. Initial program 98.5%

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

      1. associate-+l- 98.5%

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

      2. fma-def 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 99.9%

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

      5. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 70.9%

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

   5. Taylor expanded in a around 0 59.4%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.8 \cdot 10^{+169} \lor \neg \left(a \cdot b \leq 9 \cdot 10^{+141}\right):\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 12: 37.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.1 \cdot 10^{+114}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+44}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -3.1e+114) c (if (<= c 1.45e+44) (* x y) c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -3.1e+114) {
		tmp = c;
	} else if (c <= 1.45e+44) {
		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 (c <= (-3.1d+114)) then
        tmp = c
    else if (c <= 1.45d+44) 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 (c <= -3.1e+114) {
		tmp = c;
	} else if (c <= 1.45e+44) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -3.1e+114:
		tmp = c
	elif c <= 1.45e+44:
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -3.1e+114)
		tmp = c;
	elseif (c <= 1.45e+44)
		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 (c <= -3.1e+114)
		tmp = c;
	elseif (c <= 1.45e+44)
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -3.1e+114], c, If[LessEqual[c, 1.45e+44], N[(x * y), $MachinePrecision], c]]

Derivation

1. Split input into 2 regimes

2. if c < -3.1e114 or 1.4500000000000001e44 < c

   1. Initial program 96.7%

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

      1. associate-+l- 96.7%

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

      2. fma-def 98.9%

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

      3. *-commutative 98.9%

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

      4. associate-/l* 98.9%

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

      5. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in c around inf 57.3%

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

   if -3.1e114 < c < 1.4500000000000001e44

   1. Initial program 98.2%

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

      1. associate-+l- 98.2%

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

      2. fma-def 98.8%

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

      3. *-commutative 98.8%

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

      4. associate-/l* 98.7%

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

      5. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in t around 0 67.1%

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

   5. Taylor expanded in x around inf 33.1%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.1 \cdot 10^{+114}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+44}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 13: 22.4% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ c \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 c)

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return c;
}

Python

def code(x, y, z, t, a, b, c):
	return c

Julia

function code(x, y, z, t, a, b, c)
	return c
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = c;
end

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. associate-+l- 97.7%

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

   2. fma-def 98.8%

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

   3. *-commutative 98.8%

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

   4. associate-/l* 98.8%

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

   5. associate-/l* 98.7%

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

3. Simplified 98.7%

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

4. Taylor expanded in c around inf 23.5%

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

5. Final simplification 23.5%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023290 
(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))