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

Percentage Accurate: 97.8% → 98.9%

Time: 7.7s

Alternatives: 15

Speedup: 0.5×

• 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: 97.8% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.6%

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

   1. associate-+l- 96.6%

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

   2. +-commutative 96.6%

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

   3. associate--l+ 96.6%

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

   4. associate-*l/ 96.6%

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

   5. *-commutative 96.6%

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

   6. fma-def 97.0%

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

   7. fma-neg 99.0%

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

   8. neg-sub0 99.0%

      \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \color{blue}{0 - \left(\frac{a \cdot b}{4} - c\right)}\right)\right) \]

   9. associate-+l- 99.0%

      \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \color{blue}{\left(0 - \frac{a \cdot b}{4}\right) + c}\right)\right) \]

   10. neg-sub0 99.0%

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

   11. +-commutative 99.0%

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

   12. unsub-neg 99.0%

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

   13. *-commutative 99.0%

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

   14. associate-*r/ 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 98.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(N[(N[(N[(t * z), $MachinePrecision] / 16.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(x * y + N[(t * N[(z / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c - N[(b * N[(a / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $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 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. associate-*l/ 99.3%

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

      4. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   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 14.3%

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

      3. associate-*l/ 14.3%

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

      4. associate-*l/ 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in x around 0 85.7%

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

   5. Taylor expanded in c around 0 85.7%

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

4. Final simplification 99.6%

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

Alternative 3: 64.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + 0.0625 \cdot \left(t \cdot z\right)\\ t_2 := c + b \cdot \left(a \cdot -0.25\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-141}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-48}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot a \leq 4 \cdot 10^{+62}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{+139}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* 0.0625 (* t z))))
        (t_2 (+ c (* b (* a -0.25))))
        (t_3 (+ c (* x y))))
   (if (<= (* b a) -1e+148)
     t_2
     (if (<= (* b a) -2e+15)
       t_1
       (if (<= (* b a) -1e-141)
         t_3
         (if (<= (* b a) -1e-305)
           t_1
           (if (<= (* b a) 5e-48)
             t_3
             (if (<= (* b a) 4e+62)
               (- (* x y) (* (* b a) 0.25))
               (if (<= (* b a) 5e+139) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (0.0625 * (t * z));
	double t_2 = c + (b * (a * -0.25));
	double t_3 = c + (x * y);
	double tmp;
	if ((b * a) <= -1e+148) {
		tmp = t_2;
	} else if ((b * a) <= -2e+15) {
		tmp = t_1;
	} else if ((b * a) <= -1e-141) {
		tmp = t_3;
	} else if ((b * a) <= -1e-305) {
		tmp = t_1;
	} else if ((b * a) <= 5e-48) {
		tmp = t_3;
	} else if ((b * a) <= 4e+62) {
		tmp = (x * y) - ((b * a) * 0.25);
	} else if ((b * a) <= 5e+139) {
		tmp = t_3;
	} 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 + (0.0625d0 * (t * z))
    t_2 = c + (b * (a * (-0.25d0)))
    t_3 = c + (x * y)
    if ((b * a) <= (-1d+148)) then
        tmp = t_2
    else if ((b * a) <= (-2d+15)) then
        tmp = t_1
    else if ((b * a) <= (-1d-141)) then
        tmp = t_3
    else if ((b * a) <= (-1d-305)) then
        tmp = t_1
    else if ((b * a) <= 5d-48) then
        tmp = t_3
    else if ((b * a) <= 4d+62) then
        tmp = (x * y) - ((b * a) * 0.25d0)
    else if ((b * a) <= 5d+139) then
        tmp = t_3
    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 + (0.0625 * (t * z));
	double t_2 = c + (b * (a * -0.25));
	double t_3 = c + (x * y);
	double tmp;
	if ((b * a) <= -1e+148) {
		tmp = t_2;
	} else if ((b * a) <= -2e+15) {
		tmp = t_1;
	} else if ((b * a) <= -1e-141) {
		tmp = t_3;
	} else if ((b * a) <= -1e-305) {
		tmp = t_1;
	} else if ((b * a) <= 5e-48) {
		tmp = t_3;
	} else if ((b * a) <= 4e+62) {
		tmp = (x * y) - ((b * a) * 0.25);
	} else if ((b * a) <= 5e+139) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (0.0625 * (t * z))
	t_2 = c + (b * (a * -0.25))
	t_3 = c + (x * y)
	tmp = 0
	if (b * a) <= -1e+148:
		tmp = t_2
	elif (b * a) <= -2e+15:
		tmp = t_1
	elif (b * a) <= -1e-141:
		tmp = t_3
	elif (b * a) <= -1e-305:
		tmp = t_1
	elif (b * a) <= 5e-48:
		tmp = t_3
	elif (b * a) <= 4e+62:
		tmp = (x * y) - ((b * a) * 0.25)
	elif (b * a) <= 5e+139:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(0.0625 * Float64(t * z)))
	t_2 = Float64(c + Float64(b * Float64(a * -0.25)))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(b * a) <= -1e+148)
		tmp = t_2;
	elseif (Float64(b * a) <= -2e+15)
		tmp = t_1;
	elseif (Float64(b * a) <= -1e-141)
		tmp = t_3;
	elseif (Float64(b * a) <= -1e-305)
		tmp = t_1;
	elseif (Float64(b * a) <= 5e-48)
		tmp = t_3;
	elseif (Float64(b * a) <= 4e+62)
		tmp = Float64(Float64(x * y) - Float64(Float64(b * a) * 0.25));
	elseif (Float64(b * a) <= 5e+139)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (0.0625 * (t * z));
	t_2 = c + (b * (a * -0.25));
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((b * a) <= -1e+148)
		tmp = t_2;
	elseif ((b * a) <= -2e+15)
		tmp = t_1;
	elseif ((b * a) <= -1e-141)
		tmp = t_3;
	elseif ((b * a) <= -1e-305)
		tmp = t_1;
	elseif ((b * a) <= 5e-48)
		tmp = t_3;
	elseif ((b * a) <= 4e+62)
		tmp = (x * y) - ((b * a) * 0.25);
	elseif ((b * a) <= 5e+139)
		tmp = t_3;
	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[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -1e+148], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -2e+15], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -1e-141], t$95$3, If[LessEqual[N[(b * a), $MachinePrecision], -1e-305], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 5e-48], t$95$3, If[LessEqual[N[(b * a), $MachinePrecision], 4e+62], N[(N[(x * y), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 5e+139], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -1e148 or 5.0000000000000003e139 < (*.f64 a b)

   1. Initial program 91.2%

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

   2. Taylor expanded in a around inf 83.6%

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

      1. *-commutative 83.6%

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

      2. *-commutative 83.6%

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

      3. associate-*l* 85.7%

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

   4. Simplified 85.7%

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

   if -1e148 < (*.f64 a b) < -2e15 or -1e-141 < (*.f64 a b) < -9.99999999999999996e-306

   1. Initial program 97.7%

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

   2. Taylor expanded in z around inf 78.9%

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

   if -2e15 < (*.f64 a b) < -1e-141 or -9.99999999999999996e-306 < (*.f64 a b) < 4.9999999999999999e-48 or 4.00000000000000014e62 < (*.f64 a b) < 5.0000000000000003e139

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 73.3%

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

   if 4.9999999999999999e-48 < (*.f64 a b) < 4.00000000000000014e62

   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. associate-*l/ 100.0%

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

      4. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 88.4%

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

   5. Taylor expanded in c around 0 82.2%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+148}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{+15}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-141}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-305}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-48}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 4 \cdot 10^{+62}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{+139}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 4: 98.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(t * z), $MachinePrecision] / 16.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(c + t$95$1), $MachinePrecision], N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $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 99.3%

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

   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 14.3%

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

      3. associate-*l/ 14.3%

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

      4. associate-*l/ 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in x around 0 85.7%

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

   5. Taylor expanded in c around 0 85.7%

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

4. Final simplification 99.0%

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

Alternative 5: 88.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ t_2 := \left(b \cdot a\right) \cdot 0.25\\ t_3 := c + \left(t_1 + x \cdot y\right)\\ t_4 := \left(c + t_1\right) - t_2\\ \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+102}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-30}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot a \leq 4 \cdot 10^{+62}:\\ \;\;\;\;\left(c + x \cdot y\right) - t_2\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{+139}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* t z)))
        (t_2 (* (* b a) 0.25))
        (t_3 (+ c (+ t_1 (* x y))))
        (t_4 (- (+ c t_1) t_2)))
   (if (<= (* b a) -5e+102)
     t_4
     (if (<= (* b a) 5e-30)
       t_3
       (if (<= (* b a) 4e+62)
         (- (+ c (* x y)) t_2)
         (if (<= (* b a) 5e+139) t_3 t_4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (t * z);
	double t_2 = (b * a) * 0.25;
	double t_3 = c + (t_1 + (x * y));
	double t_4 = (c + t_1) - t_2;
	double tmp;
	if ((b * a) <= -5e+102) {
		tmp = t_4;
	} else if ((b * a) <= 5e-30) {
		tmp = t_3;
	} else if ((b * a) <= 4e+62) {
		tmp = (c + (x * y)) - t_2;
	} else if ((b * a) <= 5e+139) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	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 = 0.0625d0 * (t * z)
    t_2 = (b * a) * 0.25d0
    t_3 = c + (t_1 + (x * y))
    t_4 = (c + t_1) - t_2
    if ((b * a) <= (-5d+102)) then
        tmp = t_4
    else if ((b * a) <= 5d-30) then
        tmp = t_3
    else if ((b * a) <= 4d+62) then
        tmp = (c + (x * y)) - t_2
    else if ((b * a) <= 5d+139) then
        tmp = t_3
    else
        tmp = t_4
    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 * (t * z);
	double t_2 = (b * a) * 0.25;
	double t_3 = c + (t_1 + (x * y));
	double t_4 = (c + t_1) - t_2;
	double tmp;
	if ((b * a) <= -5e+102) {
		tmp = t_4;
	} else if ((b * a) <= 5e-30) {
		tmp = t_3;
	} else if ((b * a) <= 4e+62) {
		tmp = (c + (x * y)) - t_2;
	} else if ((b * a) <= 5e+139) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (t * z)
	t_2 = (b * a) * 0.25
	t_3 = c + (t_1 + (x * y))
	t_4 = (c + t_1) - t_2
	tmp = 0
	if (b * a) <= -5e+102:
		tmp = t_4
	elif (b * a) <= 5e-30:
		tmp = t_3
	elif (b * a) <= 4e+62:
		tmp = (c + (x * y)) - t_2
	elif (b * a) <= 5e+139:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(t * z))
	t_2 = Float64(Float64(b * a) * 0.25)
	t_3 = Float64(c + Float64(t_1 + Float64(x * y)))
	t_4 = Float64(Float64(c + t_1) - t_2)
	tmp = 0.0
	if (Float64(b * a) <= -5e+102)
		tmp = t_4;
	elseif (Float64(b * a) <= 5e-30)
		tmp = t_3;
	elseif (Float64(b * a) <= 4e+62)
		tmp = Float64(Float64(c + Float64(x * y)) - t_2);
	elseif (Float64(b * a) <= 5e+139)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (t * z);
	t_2 = (b * a) * 0.25;
	t_3 = c + (t_1 + (x * y));
	t_4 = (c + t_1) - t_2;
	tmp = 0.0;
	if ((b * a) <= -5e+102)
		tmp = t_4;
	elseif ((b * a) <= 5e-30)
		tmp = t_3;
	elseif ((b * a) <= 4e+62)
		tmp = (c + (x * y)) - t_2;
	elseif ((b * a) <= 5e+139)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(t$95$1 + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -5e+102], t$95$4, If[LessEqual[N[(b * a), $MachinePrecision], 5e-30], t$95$3, If[LessEqual[N[(b * a), $MachinePrecision], 4e+62], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 5e+139], t$95$3, t$95$4]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5e102 or 5.0000000000000003e139 < (*.f64 a b)

   1. Initial program 92.1%

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

      1. associate-+l- 92.1%

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

      2. fma-def 92.1%

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

      3. associate-*l/ 92.1%

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

      4. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in x around 0 90.1%

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

   if -5e102 < (*.f64 a b) < 4.99999999999999972e-30 or 4.00000000000000014e62 < (*.f64 a b) < 5.0000000000000003e139

   1. Initial program 98.7%

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

   2. Taylor expanded in a around 0 96.3%

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

   if 4.99999999999999972e-30 < (*.f64 a b) < 4.00000000000000014e62

   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. associate-*l/ 100.0%

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

      4. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 93.4%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+102}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-30}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \mathbf{elif}\;b \cdot a \leq 4 \cdot 10^{+62}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{+139}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 6: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ t_2 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+191}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 4 \cdot 10^{+62}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (+ (* 0.0625 (* t z)) (* x y))))
        (t_2 (+ c (* b (* a -0.25)))))
   (if (<= (* b a) -1e+191)
     t_2
     (if (<= (* b a) 5e-30)
       t_1
       (if (<= (* b a) 4e+62)
         (- (* x y) (* (* b a) 0.25))
         (if (<= (* b a) 5e+139) 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 + ((0.0625 * (t * z)) + (x * y));
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if ((b * a) <= -1e+191) {
		tmp = t_2;
	} else if ((b * a) <= 5e-30) {
		tmp = t_1;
	} else if ((b * a) <= 4e+62) {
		tmp = (x * y) - ((b * a) * 0.25);
	} else if ((b * a) <= 5e+139) {
		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 + ((0.0625d0 * (t * z)) + (x * y))
    t_2 = c + (b * (a * (-0.25d0)))
    if ((b * a) <= (-1d+191)) then
        tmp = t_2
    else if ((b * a) <= 5d-30) then
        tmp = t_1
    else if ((b * a) <= 4d+62) then
        tmp = (x * y) - ((b * a) * 0.25d0)
    else if ((b * a) <= 5d+139) 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 + ((0.0625 * (t * z)) + (x * y));
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if ((b * a) <= -1e+191) {
		tmp = t_2;
	} else if ((b * a) <= 5e-30) {
		tmp = t_1;
	} else if ((b * a) <= 4e+62) {
		tmp = (x * y) - ((b * a) * 0.25);
	} else if ((b * a) <= 5e+139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + ((0.0625 * (t * z)) + (x * y))
	t_2 = c + (b * (a * -0.25))
	tmp = 0
	if (b * a) <= -1e+191:
		tmp = t_2
	elif (b * a) <= 5e-30:
		tmp = t_1
	elif (b * a) <= 4e+62:
		tmp = (x * y) - ((b * a) * 0.25)
	elif (b * a) <= 5e+139:
		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(0.0625 * Float64(t * z)) + Float64(x * y)))
	t_2 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (Float64(b * a) <= -1e+191)
		tmp = t_2;
	elseif (Float64(b * a) <= 5e-30)
		tmp = t_1;
	elseif (Float64(b * a) <= 4e+62)
		tmp = Float64(Float64(x * y) - Float64(Float64(b * a) * 0.25));
	elseif (Float64(b * a) <= 5e+139)
		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 + ((0.0625 * (t * z)) + (x * y));
	t_2 = c + (b * (a * -0.25));
	tmp = 0.0;
	if ((b * a) <= -1e+191)
		tmp = t_2;
	elseif ((b * a) <= 5e-30)
		tmp = t_1;
	elseif ((b * a) <= 4e+62)
		tmp = (x * y) - ((b * a) * 0.25);
	elseif ((b * a) <= 5e+139)
		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[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -1e+191], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 5e-30], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 4e+62], N[(N[(x * y), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 5e+139], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.00000000000000007e191 or 5.0000000000000003e139 < (*.f64 a b)

   1. Initial program 90.7%

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

   2. Taylor expanded in a around inf 86.6%

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

      1. *-commutative 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-*l* 88.8%

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

   4. Simplified 88.8%

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

   if -1.00000000000000007e191 < (*.f64 a b) < 4.99999999999999972e-30 or 4.00000000000000014e62 < (*.f64 a b) < 5.0000000000000003e139

   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 a around 0 94.9%

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

   if 4.99999999999999972e-30 < (*.f64 a b) < 4.00000000000000014e62

   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. associate-*l/ 100.0%

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

      4. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 93.4%

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

   5. Taylor expanded in c around 0 86.3%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+191}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-30}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \mathbf{elif}\;b \cdot a \leq 4 \cdot 10^{+62}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{+139}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 7: 83.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(t \cdot z\right)\\ t_3 := c + \left(t_2 + x \cdot y\right)\\ \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+191}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-30}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot a \leq 4 \cdot 10^{+62}:\\ \;\;\;\;x \cdot y - t_1\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{+139}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) 0.25))
        (t_2 (* 0.0625 (* t z)))
        (t_3 (+ c (+ t_2 (* x y)))))
   (if (<= (* b a) -1e+191)
     (- t_2 t_1)
     (if (<= (* b a) 5e-30)
       t_3
       (if (<= (* b a) 4e+62)
         (- (* x y) t_1)
         (if (<= (* b a) 5e+139) t_3 (+ c (* b (* a -0.25)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * 0.25;
	double t_2 = 0.0625 * (t * z);
	double t_3 = c + (t_2 + (x * y));
	double tmp;
	if ((b * a) <= -1e+191) {
		tmp = t_2 - t_1;
	} else if ((b * a) <= 5e-30) {
		tmp = t_3;
	} else if ((b * a) <= 4e+62) {
		tmp = (x * y) - t_1;
	} else if ((b * a) <= 5e+139) {
		tmp = t_3;
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b * a) * 0.25d0
    t_2 = 0.0625d0 * (t * z)
    t_3 = c + (t_2 + (x * y))
    if ((b * a) <= (-1d+191)) then
        tmp = t_2 - t_1
    else if ((b * a) <= 5d-30) then
        tmp = t_3
    else if ((b * a) <= 4d+62) then
        tmp = (x * y) - t_1
    else if ((b * a) <= 5d+139) then
        tmp = t_3
    else
        tmp = c + (b * (a * (-0.25d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * 0.25;
	double t_2 = 0.0625 * (t * z);
	double t_3 = c + (t_2 + (x * y));
	double tmp;
	if ((b * a) <= -1e+191) {
		tmp = t_2 - t_1;
	} else if ((b * a) <= 5e-30) {
		tmp = t_3;
	} else if ((b * a) <= 4e+62) {
		tmp = (x * y) - t_1;
	} else if ((b * a) <= 5e+139) {
		tmp = t_3;
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * 0.25
	t_2 = 0.0625 * (t * z)
	t_3 = c + (t_2 + (x * y))
	tmp = 0
	if (b * a) <= -1e+191:
		tmp = t_2 - t_1
	elif (b * a) <= 5e-30:
		tmp = t_3
	elif (b * a) <= 4e+62:
		tmp = (x * y) - t_1
	elif (b * a) <= 5e+139:
		tmp = t_3
	else:
		tmp = c + (b * (a * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * 0.25)
	t_2 = Float64(0.0625 * Float64(t * z))
	t_3 = Float64(c + Float64(t_2 + Float64(x * y)))
	tmp = 0.0
	if (Float64(b * a) <= -1e+191)
		tmp = Float64(t_2 - t_1);
	elseif (Float64(b * a) <= 5e-30)
		tmp = t_3;
	elseif (Float64(b * a) <= 4e+62)
		tmp = Float64(Float64(x * y) - t_1);
	elseif (Float64(b * a) <= 5e+139)
		tmp = t_3;
	else
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b * a) * 0.25;
	t_2 = 0.0625 * (t * z);
	t_3 = c + (t_2 + (x * y));
	tmp = 0.0;
	if ((b * a) <= -1e+191)
		tmp = t_2 - t_1;
	elseif ((b * a) <= 5e-30)
		tmp = t_3;
	elseif ((b * a) <= 4e+62)
		tmp = (x * y) - t_1;
	elseif ((b * a) <= 5e+139)
		tmp = t_3;
	else
		tmp = c + (b * (a * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(t$95$2 + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -1e+191], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 5e-30], t$95$3, If[LessEqual[N[(b * a), $MachinePrecision], 4e+62], N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 5e+139], t$95$3, N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -1.00000000000000007e191

   1. Initial program 89.1%

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

      1. associate-+l- 89.1%

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

      2. fma-def 89.1%

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

      3. associate-*l/ 89.1%

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

      4. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in x around 0 88.9%

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

   5. Taylor expanded in c around 0 85.9%

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

   if -1.00000000000000007e191 < (*.f64 a b) < 4.99999999999999972e-30 or 4.00000000000000014e62 < (*.f64 a b) < 5.0000000000000003e139

   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 a around 0 94.9%

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

   if 4.99999999999999972e-30 < (*.f64 a b) < 4.00000000000000014e62

   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. associate-*l/ 100.0%

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

      4. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 93.4%

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

   5. Taylor expanded in c around 0 86.3%

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

   if 5.0000000000000003e139 < (*.f64 a b)

   1. Initial program 92.1%

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

   2. Taylor expanded in a around inf 92.1%

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

      1. *-commutative 92.1%

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

      2. *-commutative 92.1%

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

      3. associate-*l* 92.1%

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

   4. Simplified 92.1%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+191}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-30}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \mathbf{elif}\;b \cdot a \leq 4 \cdot 10^{+62}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{+139}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 8: 59.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + b \cdot \left(a \cdot -0.25\right)\\ t_3 := c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;b \leq -18500000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y)))
        (t_2 (+ c (* b (* a -0.25))))
        (t_3 (+ c (* 0.0625 (* t z)))))
   (if (<= b -18500000.0)
     t_2
     (if (<= b 4.4e-213)
       t_1
       (if (<= b 6.2e-99)
         t_3
         (if (<= b 1.25e-45)
           t_1
           (if (<= b 1.9e+34) t_3 (if (<= b 5.6e+90) 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 = c + (b * (a * -0.25));
	double t_3 = c + (0.0625 * (t * z));
	double tmp;
	if (b <= -18500000.0) {
		tmp = t_2;
	} else if (b <= 4.4e-213) {
		tmp = t_1;
	} else if (b <= 6.2e-99) {
		tmp = t_3;
	} else if (b <= 1.25e-45) {
		tmp = t_1;
	} else if (b <= 1.9e+34) {
		tmp = t_3;
	} else if (b <= 5.6e+90) {
		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 + (x * y)
    t_2 = c + (b * (a * (-0.25d0)))
    t_3 = c + (0.0625d0 * (t * z))
    if (b <= (-18500000.0d0)) then
        tmp = t_2
    else if (b <= 4.4d-213) then
        tmp = t_1
    else if (b <= 6.2d-99) then
        tmp = t_3
    else if (b <= 1.25d-45) then
        tmp = t_1
    else if (b <= 1.9d+34) then
        tmp = t_3
    else if (b <= 5.6d+90) 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 = c + (b * (a * -0.25));
	double t_3 = c + (0.0625 * (t * z));
	double tmp;
	if (b <= -18500000.0) {
		tmp = t_2;
	} else if (b <= 4.4e-213) {
		tmp = t_1;
	} else if (b <= 6.2e-99) {
		tmp = t_3;
	} else if (b <= 1.25e-45) {
		tmp = t_1;
	} else if (b <= 1.9e+34) {
		tmp = t_3;
	} else if (b <= 5.6e+90) {
		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 = c + (b * (a * -0.25))
	t_3 = c + (0.0625 * (t * z))
	tmp = 0
	if b <= -18500000.0:
		tmp = t_2
	elif b <= 4.4e-213:
		tmp = t_1
	elif b <= 6.2e-99:
		tmp = t_3
	elif b <= 1.25e-45:
		tmp = t_1
	elif b <= 1.9e+34:
		tmp = t_3
	elif b <= 5.6e+90:
		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(c + Float64(b * Float64(a * -0.25)))
	t_3 = Float64(c + Float64(0.0625 * Float64(t * z)))
	tmp = 0.0
	if (b <= -18500000.0)
		tmp = t_2;
	elseif (b <= 4.4e-213)
		tmp = t_1;
	elseif (b <= 6.2e-99)
		tmp = t_3;
	elseif (b <= 1.25e-45)
		tmp = t_1;
	elseif (b <= 1.9e+34)
		tmp = t_3;
	elseif (b <= 5.6e+90)
		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 = c + (b * (a * -0.25));
	t_3 = c + (0.0625 * (t * z));
	tmp = 0.0;
	if (b <= -18500000.0)
		tmp = t_2;
	elseif (b <= 4.4e-213)
		tmp = t_1;
	elseif (b <= 6.2e-99)
		tmp = t_3;
	elseif (b <= 1.25e-45)
		tmp = t_1;
	elseif (b <= 1.9e+34)
		tmp = t_3;
	elseif (b <= 5.6e+90)
		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[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -18500000.0], t$95$2, If[LessEqual[b, 4.4e-213], t$95$1, If[LessEqual[b, 6.2e-99], t$95$3, If[LessEqual[b, 1.25e-45], t$95$1, If[LessEqual[b, 1.9e+34], t$95$3, If[LessEqual[b, 5.6e+90], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.85e7 or 5.6000000000000001e90 < b

   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 a around inf 63.2%

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

      1. *-commutative 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*l* 64.6%

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

   4. Simplified 64.6%

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

   if -1.85e7 < b < 4.40000000000000019e-213 or 6.1999999999999997e-99 < b < 1.24999999999999994e-45 or 1.9000000000000001e34 < b < 5.6000000000000001e90

   1. Initial program 99.0%

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

   2. Taylor expanded in x around inf 63.6%

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

   if 4.40000000000000019e-213 < b < 6.1999999999999997e-99 or 1.24999999999999994e-45 < b < 1.9000000000000001e34

   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 z around inf 64.6%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -18500000:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-213}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-99}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-45}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+34}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+90}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 9: 87.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+191}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-30}:\\ \;\;\;\;c + \left(t_2 + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) 0.25)) (t_2 (* 0.0625 (* t z))))
   (if (<= (* b a) -1e+191)
     (- t_2 t_1)
     (if (<= (* b a) 5e-30) (+ c (+ t_2 (* x y))) (- (+ c (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * 0.25;
	double t_2 = 0.0625 * (t * z);
	double tmp;
	if ((b * a) <= -1e+191) {
		tmp = t_2 - t_1;
	} else if ((b * a) <= 5e-30) {
		tmp = c + (t_2 + (x * y));
	} else {
		tmp = (c + (x * y)) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * a) * 0.25d0
    t_2 = 0.0625d0 * (t * z)
    if ((b * a) <= (-1d+191)) then
        tmp = t_2 - t_1
    else if ((b * a) <= 5d-30) then
        tmp = c + (t_2 + (x * y))
    else
        tmp = (c + (x * y)) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * 0.25;
	double t_2 = 0.0625 * (t * z);
	double tmp;
	if ((b * a) <= -1e+191) {
		tmp = t_2 - t_1;
	} else if ((b * a) <= 5e-30) {
		tmp = c + (t_2 + (x * y));
	} else {
		tmp = (c + (x * y)) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * 0.25
	t_2 = 0.0625 * (t * z)
	tmp = 0
	if (b * a) <= -1e+191:
		tmp = t_2 - t_1
	elif (b * a) <= 5e-30:
		tmp = c + (t_2 + (x * y))
	else:
		tmp = (c + (x * y)) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * 0.25)
	t_2 = Float64(0.0625 * Float64(t * z))
	tmp = 0.0
	if (Float64(b * a) <= -1e+191)
		tmp = Float64(t_2 - t_1);
	elseif (Float64(b * a) <= 5e-30)
		tmp = Float64(c + Float64(t_2 + Float64(x * y)));
	else
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b * a) * 0.25;
	t_2 = 0.0625 * (t * z);
	tmp = 0.0;
	if ((b * a) <= -1e+191)
		tmp = t_2 - t_1;
	elseif ((b * a) <= 5e-30)
		tmp = c + (t_2 + (x * y));
	else
		tmp = (c + (x * y)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -1e+191], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 5e-30], N[(c + N[(t$95$2 + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.00000000000000007e191

   1. Initial program 89.1%

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

      1. associate-+l- 89.1%

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

      2. fma-def 89.1%

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

      3. associate-*l/ 89.1%

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

      4. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in x around 0 88.9%

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

   5. Taylor expanded in c around 0 85.9%

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

   if -1.00000000000000007e191 < (*.f64 a b) < 4.99999999999999972e-30

   1. Initial program 98.7%

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

   2. Taylor expanded in a around 0 94.9%

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

   if 4.99999999999999972e-30 < (*.f64 a b)

   1. Initial program 95.7%

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

      1. associate-+l- 95.7%

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

      2. fma-def 95.7%

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

      3. associate-*l/ 95.7%

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

      4. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around 0 88.7%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+191}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-30}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 10: 39.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ t_2 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;b \leq -4 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-190}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-49}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+90}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* t z))) (t_2 (* b (* a -0.25))))
   (if (<= b -4e-45)
     t_2
     (if (<= b 9e-190)
       (* x y)
       (if (<= b 2.2e-146)
         t_1
         (if (<= b 3.9e-49)
           c
           (if (<= b 7e+34) t_1 (if (<= b 3.7e+90) (* x y) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (t * z);
	double t_2 = b * (a * -0.25);
	double tmp;
	if (b <= -4e-45) {
		tmp = t_2;
	} else if (b <= 9e-190) {
		tmp = x * y;
	} else if (b <= 2.2e-146) {
		tmp = t_1;
	} else if (b <= 3.9e-49) {
		tmp = c;
	} else if (b <= 7e+34) {
		tmp = t_1;
	} else if (b <= 3.7e+90) {
		tmp = x * y;
	} 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 = 0.0625d0 * (t * z)
    t_2 = b * (a * (-0.25d0))
    if (b <= (-4d-45)) then
        tmp = t_2
    else if (b <= 9d-190) then
        tmp = x * y
    else if (b <= 2.2d-146) then
        tmp = t_1
    else if (b <= 3.9d-49) then
        tmp = c
    else if (b <= 7d+34) then
        tmp = t_1
    else if (b <= 3.7d+90) then
        tmp = x * y
    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 = 0.0625 * (t * z);
	double t_2 = b * (a * -0.25);
	double tmp;
	if (b <= -4e-45) {
		tmp = t_2;
	} else if (b <= 9e-190) {
		tmp = x * y;
	} else if (b <= 2.2e-146) {
		tmp = t_1;
	} else if (b <= 3.9e-49) {
		tmp = c;
	} else if (b <= 7e+34) {
		tmp = t_1;
	} else if (b <= 3.7e+90) {
		tmp = x * y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (t * z)
	t_2 = b * (a * -0.25)
	tmp = 0
	if b <= -4e-45:
		tmp = t_2
	elif b <= 9e-190:
		tmp = x * y
	elif b <= 2.2e-146:
		tmp = t_1
	elif b <= 3.9e-49:
		tmp = c
	elif b <= 7e+34:
		tmp = t_1
	elif b <= 3.7e+90:
		tmp = x * y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(t * z))
	t_2 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (b <= -4e-45)
		tmp = t_2;
	elseif (b <= 9e-190)
		tmp = Float64(x * y);
	elseif (b <= 2.2e-146)
		tmp = t_1;
	elseif (b <= 3.9e-49)
		tmp = c;
	elseif (b <= 7e+34)
		tmp = t_1;
	elseif (b <= 3.7e+90)
		tmp = Float64(x * y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (t * z);
	t_2 = b * (a * -0.25);
	tmp = 0.0;
	if (b <= -4e-45)
		tmp = t_2;
	elseif (b <= 9e-190)
		tmp = x * y;
	elseif (b <= 2.2e-146)
		tmp = t_1;
	elseif (b <= 3.9e-49)
		tmp = c;
	elseif (b <= 7e+34)
		tmp = t_1;
	elseif (b <= 3.7e+90)
		tmp = x * y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4e-45], t$95$2, If[LessEqual[b, 9e-190], N[(x * y), $MachinePrecision], If[LessEqual[b, 2.2e-146], t$95$1, If[LessEqual[b, 3.9e-49], c, If[LessEqual[b, 7e+34], t$95$1, If[LessEqual[b, 3.7e+90], N[(x * y), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.99999999999999994e-45 or 3.7e90 < b

   1. Initial program 94.0%

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

      1. associate-+l- 94.0%

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

      2. fma-def 94.0%

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

      3. associate-*l/ 94.0%

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

      4. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around 0 79.0%

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

   5. Taylor expanded in a around inf 43.7%

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

      1. *-commutative 43.7%

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

      2. *-commutative 43.7%

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

      3. associate-*r* 45.0%

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

   7. Simplified 45.0%

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

   if -3.99999999999999994e-45 < b < 9.00000000000000042e-190 or 6.99999999999999996e34 < b < 3.7e90

   1. Initial program 98.8%

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

      1. associate-+l- 98.8%

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

      2. fma-def 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. associate-*l/ 100.0%

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

      4. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 71.7%

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

   5. Taylor expanded in y around inf 35.0%

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

   if 9.00000000000000042e-190 < b < 2.2e-146 or 3.90000000000000011e-49 < b < 6.99999999999999996e34

   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. associate-*l/ 100.0%

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

      4. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 75.0%

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

   5. Taylor expanded in t around inf 46.5%

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

   if 2.2e-146 < b < 3.90000000000000011e-49

   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. associate-*l/ 100.0%

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

      4. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in c around inf 55.0%

      \[\leadsto \color{blue}{c} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-45}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-190}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-146}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-49}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+34}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+90}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 11: 52.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + 0.0625 \cdot \left(t \cdot z\right)\\ t_3 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;b \leq -8600:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y)))
        (t_2 (+ c (* 0.0625 (* t z))))
        (t_3 (* b (* a -0.25))))
   (if (<= b -8600.0)
     t_3
     (if (<= b 1.15e-212)
       t_1
       (if (<= b 5e-99)
         t_2
         (if (<= b 1.5e-41)
           t_1
           (if (<= b 8.5e+34) t_2 (if (<= b 9e+199) t_1 t_3))))))))

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 = c + (0.0625 * (t * z));
	double t_3 = b * (a * -0.25);
	double tmp;
	if (b <= -8600.0) {
		tmp = t_3;
	} else if (b <= 1.15e-212) {
		tmp = t_1;
	} else if (b <= 5e-99) {
		tmp = t_2;
	} else if (b <= 1.5e-41) {
		tmp = t_1;
	} else if (b <= 8.5e+34) {
		tmp = t_2;
	} else if (b <= 9e+199) {
		tmp = t_1;
	} 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) :: tmp
    t_1 = c + (x * y)
    t_2 = c + (0.0625d0 * (t * z))
    t_3 = b * (a * (-0.25d0))
    if (b <= (-8600.0d0)) then
        tmp = t_3
    else if (b <= 1.15d-212) then
        tmp = t_1
    else if (b <= 5d-99) then
        tmp = t_2
    else if (b <= 1.5d-41) then
        tmp = t_1
    else if (b <= 8.5d+34) then
        tmp = t_2
    else if (b <= 9d+199) then
        tmp = t_1
    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 = c + (x * y);
	double t_2 = c + (0.0625 * (t * z));
	double t_3 = b * (a * -0.25);
	double tmp;
	if (b <= -8600.0) {
		tmp = t_3;
	} else if (b <= 1.15e-212) {
		tmp = t_1;
	} else if (b <= 5e-99) {
		tmp = t_2;
	} else if (b <= 1.5e-41) {
		tmp = t_1;
	} else if (b <= 8.5e+34) {
		tmp = t_2;
	} else if (b <= 9e+199) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = c + (0.0625 * (t * z))
	t_3 = b * (a * -0.25)
	tmp = 0
	if b <= -8600.0:
		tmp = t_3
	elif b <= 1.15e-212:
		tmp = t_1
	elif b <= 5e-99:
		tmp = t_2
	elif b <= 1.5e-41:
		tmp = t_1
	elif b <= 8.5e+34:
		tmp = t_2
	elif b <= 9e+199:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(c + Float64(0.0625 * Float64(t * z)))
	t_3 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (b <= -8600.0)
		tmp = t_3;
	elseif (b <= 1.15e-212)
		tmp = t_1;
	elseif (b <= 5e-99)
		tmp = t_2;
	elseif (b <= 1.5e-41)
		tmp = t_1;
	elseif (b <= 8.5e+34)
		tmp = t_2;
	elseif (b <= 9e+199)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = c + (0.0625 * (t * z));
	t_3 = b * (a * -0.25);
	tmp = 0.0;
	if (b <= -8600.0)
		tmp = t_3;
	elseif (b <= 1.15e-212)
		tmp = t_1;
	elseif (b <= 5e-99)
		tmp = t_2;
	elseif (b <= 1.5e-41)
		tmp = t_1;
	elseif (b <= 8.5e+34)
		tmp = t_2;
	elseif (b <= 9e+199)
		tmp = t_1;
	else
		tmp = t_3;
	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[(c + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8600.0], t$95$3, If[LessEqual[b, 1.15e-212], t$95$1, If[LessEqual[b, 5e-99], t$95$2, If[LessEqual[b, 1.5e-41], t$95$1, If[LessEqual[b, 8.5e+34], t$95$2, If[LessEqual[b, 9e+199], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8600 or 8.9999999999999994e199 < b

   1. Initial program 93.0%

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

      1. associate-+l- 93.0%

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

      2. fma-def 93.0%

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

      3. associate-*l/ 93.0%

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

      4. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in z around 0 78.9%

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

   5. Taylor expanded in a around inf 48.3%

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

      1. *-commutative 48.3%

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

      2. *-commutative 48.3%

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

      3. associate-*r* 50.0%

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

   7. Simplified 50.0%

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

   if -8600 < b < 1.15e-212 or 4.99999999999999969e-99 < b < 1.49999999999999994e-41 or 8.5000000000000003e34 < b < 8.9999999999999994e199

   1. Initial program 98.4%

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

   2. Taylor expanded in x around inf 61.7%

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

   if 1.15e-212 < b < 4.99999999999999969e-99 or 1.49999999999999994e-41 < b < 8.5000000000000003e34

   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 z around inf 64.6%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8600:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-212}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-99}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-41}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+34}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+199}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 12: 52.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;b \leq -55000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.56 \cdot 10^{+31}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+200}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* b (* a -0.25))))
   (if (<= b -55000000.0)
     t_2
     (if (<= b 1.55e-41)
       t_1
       (if (<= b 1.56e+31) (* 0.0625 (* t z)) (if (<= b 1.4e+200) 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 = b * (a * -0.25);
	double tmp;
	if (b <= -55000000.0) {
		tmp = t_2;
	} else if (b <= 1.55e-41) {
		tmp = t_1;
	} else if (b <= 1.56e+31) {
		tmp = 0.0625 * (t * z);
	} else if (b <= 1.4e+200) {
		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 = b * (a * (-0.25d0))
    if (b <= (-55000000.0d0)) then
        tmp = t_2
    else if (b <= 1.55d-41) then
        tmp = t_1
    else if (b <= 1.56d+31) then
        tmp = 0.0625d0 * (t * z)
    else if (b <= 1.4d+200) 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 = b * (a * -0.25);
	double tmp;
	if (b <= -55000000.0) {
		tmp = t_2;
	} else if (b <= 1.55e-41) {
		tmp = t_1;
	} else if (b <= 1.56e+31) {
		tmp = 0.0625 * (t * z);
	} else if (b <= 1.4e+200) {
		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 = b * (a * -0.25)
	tmp = 0
	if b <= -55000000.0:
		tmp = t_2
	elif b <= 1.55e-41:
		tmp = t_1
	elif b <= 1.56e+31:
		tmp = 0.0625 * (t * z)
	elif b <= 1.4e+200:
		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(b * Float64(a * -0.25))
	tmp = 0.0
	if (b <= -55000000.0)
		tmp = t_2;
	elseif (b <= 1.55e-41)
		tmp = t_1;
	elseif (b <= 1.56e+31)
		tmp = Float64(0.0625 * Float64(t * z));
	elseif (b <= 1.4e+200)
		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 = b * (a * -0.25);
	tmp = 0.0;
	if (b <= -55000000.0)
		tmp = t_2;
	elseif (b <= 1.55e-41)
		tmp = t_1;
	elseif (b <= 1.56e+31)
		tmp = 0.0625 * (t * z);
	elseif (b <= 1.4e+200)
		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[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -55000000.0], t$95$2, If[LessEqual[b, 1.55e-41], t$95$1, If[LessEqual[b, 1.56e+31], N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e+200], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.5e7 or 1.39999999999999992e200 < b

   1. Initial program 93.0%

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

      1. associate-+l- 93.0%

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

      2. fma-def 93.0%

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

      3. associate-*l/ 93.0%

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

      4. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in z around 0 78.7%

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

   5. Taylor expanded in a around inf 48.8%

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

      1. *-commutative 48.8%

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

      2. *-commutative 48.8%

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

      3. associate-*r* 50.5%

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

   7. Simplified 50.5%

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

   if -5.5e7 < b < 1.55e-41 or 1.56000000000000004e31 < b < 1.39999999999999992e200

   1. Initial program 98.6%

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

   2. Taylor expanded in x around inf 61.8%

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

   if 1.55e-41 < b < 1.56000000000000004e31

   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. associate-*l/ 100.0%

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

      4. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 85.5%

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

   5. Taylor expanded in t around inf 54.8%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -55000000:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-41}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 1.56 \cdot 10^{+31}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+200}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 13: 35.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-115}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 7.7 \cdot 10^{-28}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+148}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -3.2e-115)
   (* x y)
   (if (<= y 7.7e-28) c (if (<= y 8.6e+148) (* 0.0625 (* t z)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -3.2e-115) {
		tmp = x * y;
	} else if (y <= 7.7e-28) {
		tmp = c;
	} else if (y <= 8.6e+148) {
		tmp = 0.0625 * (t * z);
	} 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 (y <= (-3.2d-115)) then
        tmp = x * y
    else if (y <= 7.7d-28) then
        tmp = c
    else if (y <= 8.6d+148) then
        tmp = 0.0625d0 * (t * z)
    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 (y <= -3.2e-115) {
		tmp = x * y;
	} else if (y <= 7.7e-28) {
		tmp = c;
	} else if (y <= 8.6e+148) {
		tmp = 0.0625 * (t * z);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -3.2e-115:
		tmp = x * y
	elif y <= 7.7e-28:
		tmp = c
	elif y <= 8.6e+148:
		tmp = 0.0625 * (t * z)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -3.2e-115)
		tmp = Float64(x * y);
	elseif (y <= 7.7e-28)
		tmp = c;
	elseif (y <= 8.6e+148)
		tmp = Float64(0.0625 * Float64(t * z));
	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 (y <= -3.2e-115)
		tmp = x * y;
	elseif (y <= 7.7e-28)
		tmp = c;
	elseif (y <= 8.6e+148)
		tmp = 0.0625 * (t * z);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -3.2e-115], N[(x * y), $MachinePrecision], If[LessEqual[y, 7.7e-28], c, If[LessEqual[y, 8.6e+148], N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2e-115 or 8.6000000000000003e148 < y

   1. Initial program 94.4%

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

      1. associate-+l- 94.4%

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

      2. fma-def 95.2%

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

      3. associate-*l/ 95.2%

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

      4. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 81.5%

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

   5. Taylor expanded in y around inf 41.3%

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

   if -3.2e-115 < y < 7.7000000000000001e-28

   1. Initial program 99.1%

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

      1. associate-+l- 99.1%

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

      2. fma-def 99.1%

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

      3. associate-*l/ 99.1%

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

      4. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in c around inf 39.0%

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

   if 7.7000000000000001e-28 < y < 8.6000000000000003e148

   1. Initial program 97.8%

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

      1. associate-+l- 97.8%

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

      2. fma-def 97.8%

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

      3. associate-*l/ 97.8%

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

      4. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 71.4%

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

   5. Taylor expanded in t around inf 43.7%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-115}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 7.7 \cdot 10^{-28}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+148}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 14: 37.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.8 \cdot 10^{+86}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 56000000:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -2.8e+86) c (if (<= c 56000000.0) (* x y) c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -2.8e+86) {
		tmp = c;
	} else if (c <= 56000000.0) {
		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 <= (-2.8d+86)) then
        tmp = c
    else if (c <= 56000000.0d0) 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 <= -2.8e+86) {
		tmp = c;
	} else if (c <= 56000000.0) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -2.8e+86:
		tmp = c
	elif c <= 56000000.0:
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -2.8e+86)
		tmp = c;
	elseif (c <= 56000000.0)
		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 <= -2.8e+86)
		tmp = c;
	elseif (c <= 56000000.0)
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -2.8e+86], c, If[LessEqual[c, 56000000.0], N[(x * y), $MachinePrecision], c]]

Derivation

1. Split input into 2 regimes

2. if c < -2.80000000000000004e86 or 5.6e7 < c

   1. Initial program 96.8%

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

      1. associate-+l- 96.8%

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

      2. fma-def 97.7%

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

      3. associate-*l/ 97.7%

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

      4. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in c around inf 48.1%

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

   if -2.80000000000000004e86 < c < 5.6e7

   1. Initial program 96.5%

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

      1. associate-+l- 96.5%

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

      2. fma-def 96.5%

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

      3. associate-*l/ 96.5%

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

      4. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in z around 0 70.2%

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

   5. Taylor expanded in y around inf 34.5%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.8 \cdot 10^{+86}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 56000000:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 15: 22.2% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.6%

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

   1. associate-+l- 96.6%

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

   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. associate-*l/ 97.0%

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

   4. associate-*l/ 97.6%

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

3. Simplified 97.6%

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

4. Taylor expanded in c around inf 26.1%

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

5. Final simplification 26.1%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023224 
(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))