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

Percentage Accurate: 97.6% → 98.5%

Time: 9.7s

Alternatives: 14

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: 97.6% 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: 98.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around 0 33.3%

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

   4. Taylor expanded in c around 0 33.3%

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

   5. Taylor expanded in t around inf 83.5%

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

      1. associate-*r* 83.5%

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

      2. *-commutative 83.5%

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

      3. associate-*l* 83.5%

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

   7. Simplified 83.5%

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

4. Final simplification 99.6%

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

Alternative 2: 99.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. associate-+l- 97.7%

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

   2. associate--l+ 97.7%

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

   3. fma-def 99.2%

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

   4. associate-*l/ 99.2%

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

   5. fma-neg 99.2%

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

   6. sub-neg 99.2%

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

   7. distribute-neg-in 99.2%

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

   8. remove-double-neg 99.2%

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

   9. associate-/l* 99.1%

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

   10. distribute-frac-neg 99.1%

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

   11. associate-/r/ 99.2%

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

   12. fma-def 99.2%

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

   13. neg-mul-1 99.2%

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

   14. *-commutative 99.2%

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

   15. associate-/l* 99.2%

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

   16. metadata-eval 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 3: 98.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. sub-neg 97.7%

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

   2. associate-+l+ 97.7%

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

   3. fma-def 98.8%

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

   4. associate-*l/ 98.8%

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

   5. distribute-frac-neg 98.8%

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

   6. distribute-rgt-neg-out 98.8%

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

   7. associate-/l* 98.7%

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

   8. neg-mul-1 98.7%

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

   9. associate-/r* 98.7%

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

   10. metadata-eval 98.7%

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

3. Simplified 98.7%

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

5. Final simplification 98.7%

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

Alternative 4: 66.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -8.8 \cdot 10^{+80}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.45 \cdot 10^{-83}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.28 \cdot 10^{+76}:\\ \;\;\;\;c + t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= (* x y) -8.8e+80)
     (+ c (* x y))
     (if (<= (* x y) 1.45e-83)
       (+ c (* a (* b -0.25)))
       (if (<= (* x y) 1.28e+76) (+ c t_1) (+ (* x y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if ((x * y) <= -8.8e+80) {
		tmp = c + (x * y);
	} else if ((x * y) <= 1.45e-83) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 1.28e+76) {
		tmp = c + t_1;
	} else {
		tmp = (x * y) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if ((x * y) <= (-8.8d+80)) then
        tmp = c + (x * y)
    else if ((x * y) <= 1.45d-83) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((x * y) <= 1.28d+76) then
        tmp = c + t_1
    else
        tmp = (x * y) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if ((x * y) <= -8.8e+80) {
		tmp = c + (x * y);
	} else if ((x * y) <= 1.45e-83) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 1.28e+76) {
		tmp = c + t_1;
	} else {
		tmp = (x * y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if (x * y) <= -8.8e+80:
		tmp = c + (x * y)
	elif (x * y) <= 1.45e-83:
		tmp = c + (a * (b * -0.25))
	elif (x * y) <= 1.28e+76:
		tmp = c + t_1
	else:
		tmp = (x * y) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -8.8e+80)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(x * y) <= 1.45e-83)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 1.28e+76)
		tmp = Float64(c + t_1);
	else
		tmp = Float64(Float64(x * y) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((x * y) <= -8.8e+80)
		tmp = c + (x * y);
	elseif ((x * y) <= 1.45e-83)
		tmp = c + (a * (b * -0.25));
	elseif ((x * y) <= 1.28e+76)
		tmp = c + t_1;
	else
		tmp = (x * y) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -8.8e+80], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.45e-83], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.28e+76], N[(c + t$95$1), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -8.80000000000000011e80

   1. Initial program 93.6%

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

   3. Taylor expanded in x around inf 80.5%

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

   if -8.80000000000000011e80 < (*.f64 x y) < 1.45e-83

   1. Initial program 98.5%

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

   3. Taylor expanded in a around inf 70.5%

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

      1. *-commutative 70.5%

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

      2. associate-*r* 70.5%

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

   5. Simplified 70.5%

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

   if 1.45e-83 < (*.f64 x y) < 1.27999999999999994e76

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 83.0%

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

   if 1.27999999999999994e76 < (*.f64 x y)

   1. Initial program 98.0%

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

   3. Taylor expanded in a around 0 79.1%

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

   4. Taylor expanded in c around 0 75.3%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.8 \cdot 10^{+80}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.45 \cdot 10^{-83}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.28 \cdot 10^{+76}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{-81}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.75 \cdot 10^{+70}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))))
   (if (<= (* x y) -2.7e+74)
     t_1
     (if (<= (* x y) 3e-81)
       (+ c (* a (* b -0.25)))
       (if (<= (* x y) 2.75e+70) (+ c (* 0.0625 (* z t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if ((x * y) <= -2.7e+74) {
		tmp = t_1;
	} else if ((x * y) <= 3e-81) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 2.75e+70) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c + (x * y)
    if ((x * y) <= (-2.7d+74)) then
        tmp = t_1
    else if ((x * y) <= 3d-81) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((x * y) <= 2.75d+70) then
        tmp = c + (0.0625d0 * (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if ((x * y) <= -2.7e+74) {
		tmp = t_1;
	} else if ((x * y) <= 3e-81) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 2.75e+70) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	tmp = 0
	if (x * y) <= -2.7e+74:
		tmp = t_1
	elif (x * y) <= 3e-81:
		tmp = c + (a * (b * -0.25))
	elif (x * y) <= 2.75e+70:
		tmp = c + (0.0625 * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -2.7e+74)
		tmp = t_1;
	elseif (Float64(x * y) <= 3e-81)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 2.75e+70)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -2.7e+74)
		tmp = t_1;
	elseif ((x * y) <= 3e-81)
		tmp = c + (a * (b * -0.25));
	elseif ((x * y) <= 2.75e+70)
		tmp = c + (0.0625 * (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.7e+74], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3e-81], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.75e+70], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.6999999999999998e74 or 2.74999999999999993e70 < (*.f64 x y)

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 74.8%

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

   if -2.6999999999999998e74 < (*.f64 x y) < 2.9999999999999999e-81

   1. Initial program 98.5%

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

   3. Taylor expanded in a around inf 70.5%

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

      1. *-commutative 70.5%

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

      2. associate-*r* 70.5%

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

   5. Simplified 70.5%

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

   if 2.9999999999999999e-81 < (*.f64 x y) < 2.74999999999999993e70

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 83.0%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+74}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{-81}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.75 \cdot 10^{+70}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+22} \lor \neg \left(x \cdot y \leq 3.15 \cdot 10^{+69}\right):\\ \;\;\;\;c + \left(x \cdot y - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(z \cdot t\right) - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)))
   (if (or (<= (* x y) -1.8e+22) (not (<= (* x y) 3.15e+69)))
     (+ c (- (* x y) t_1))
     (+ c (- (* 0.0625 (* z t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double tmp;
	if (((x * y) <= -1.8e+22) || !((x * y) <= 3.15e+69)) {
		tmp = c + ((x * y) - t_1);
	} else {
		tmp = c + ((0.0625 * (z * t)) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    if (((x * y) <= (-1.8d+22)) .or. (.not. ((x * y) <= 3.15d+69))) then
        tmp = c + ((x * y) - t_1)
    else
        tmp = c + ((0.0625d0 * (z * t)) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double tmp;
	if (((x * y) <= -1.8e+22) || !((x * y) <= 3.15e+69)) {
		tmp = c + ((x * y) - t_1);
	} else {
		tmp = c + ((0.0625 * (z * t)) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	tmp = 0
	if ((x * y) <= -1.8e+22) or not ((x * y) <= 3.15e+69):
		tmp = c + ((x * y) - t_1)
	else:
		tmp = c + ((0.0625 * (z * t)) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if ((Float64(x * y) <= -1.8e+22) || !(Float64(x * y) <= 3.15e+69))
		tmp = Float64(c + Float64(Float64(x * y) - t_1));
	else
		tmp = Float64(c + Float64(Float64(0.0625 * Float64(z * t)) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	tmp = 0.0;
	if (((x * y) <= -1.8e+22) || ~(((x * y) <= 3.15e+69)))
		tmp = c + ((x * y) - t_1);
	else
		tmp = c + ((0.0625 * (z * t)) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.8e+22], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.15e+69]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.8e22 or 3.15000000000000004e69 < (*.f64 x y)

   1. Initial program 96.2%

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

   3. Taylor expanded in z around 0 90.2%

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

   if -1.8e22 < (*.f64 x y) < 3.15000000000000004e69

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0 97.4%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+22} \lor \neg \left(x \cdot y \leq 3.15 \cdot 10^{+69}\right):\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 45.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.2 \cdot 10^{+71}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.1 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -8.2e+71)
   (* x y)
   (if (<= (* x y) 1.1e-85)
     (* b (* a -0.25))
     (if (<= (* x y) 1.55e+74) (* t (* z 0.0625)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -8.2e+71) {
		tmp = x * y;
	} else if ((x * y) <= 1.1e-85) {
		tmp = b * (a * -0.25);
	} else if ((x * y) <= 1.55e+74) {
		tmp = t * (z * 0.0625);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x * y) <= (-8.2d+71)) then
        tmp = x * y
    else if ((x * y) <= 1.1d-85) then
        tmp = b * (a * (-0.25d0))
    else if ((x * y) <= 1.55d+74) then
        tmp = t * (z * 0.0625d0)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -8.2e+71) {
		tmp = x * y;
	} else if ((x * y) <= 1.1e-85) {
		tmp = b * (a * -0.25);
	} else if ((x * y) <= 1.55e+74) {
		tmp = t * (z * 0.0625);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -8.2e+71:
		tmp = x * y
	elif (x * y) <= 1.1e-85:
		tmp = b * (a * -0.25)
	elif (x * y) <= 1.55e+74:
		tmp = t * (z * 0.0625)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -8.2e+71)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 1.1e-85)
		tmp = Float64(b * Float64(a * -0.25));
	elseif (Float64(x * y) <= 1.55e+74)
		tmp = Float64(t * Float64(z * 0.0625));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -8.2e+71)
		tmp = x * y;
	elseif ((x * y) <= 1.1e-85)
		tmp = b * (a * -0.25);
	elseif ((x * y) <= 1.55e+74)
		tmp = t * (z * 0.0625);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -8.2e+71], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.1e-85], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.55e+74], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.2000000000000004e71 or 1.55000000000000011e74 < (*.f64 x y)

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 74.8%

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

   4. Taylor expanded in x around inf 68.9%

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

   if -8.2000000000000004e71 < (*.f64 x y) < 1.1e-85

   1. Initial program 98.5%

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

   3. Taylor expanded in x around 0 95.7%

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

   4. Taylor expanded in c around 0 67.8%

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

   5. Taylor expanded in t around 0 42.3%

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

      1. associate-*r* 42.3%

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

      2. *-commutative 42.3%

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

   7. Simplified 42.3%

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

   if 1.1e-85 < (*.f64 x y) < 1.55000000000000011e74

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 87.2%

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

   4. Taylor expanded in c around 0 52.8%

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

   5. Taylor expanded in t around inf 48.4%

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

      1. associate-*r* 48.4%

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

      2. *-commutative 48.4%

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

      3. associate-*l* 48.4%

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

   7. Simplified 48.4%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.2 \cdot 10^{+71}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.1 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+21} \lor \neg \left(b \leq 2.3 \cdot 10^{+121} \lor \neg \left(b \leq 2.9 \cdot 10^{+135}\right) \land b \leq 2.05 \cdot 10^{+156}\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -1.8e+21)
         (not
          (or (<= b 2.3e+121) (and (not (<= b 2.9e+135)) (<= b 2.05e+156)))))
   (* b (* a -0.25))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.8e+21) || !((b <= 2.3e+121) || (!(b <= 2.9e+135) && (b <= 2.05e+156)))) {
		tmp = b * (a * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-1.8d+21)) .or. (.not. (b <= 2.3d+121) .or. (.not. (b <= 2.9d+135)) .and. (b <= 2.05d+156))) then
        tmp = b * (a * (-0.25d0))
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.8e+21) || !((b <= 2.3e+121) || (!(b <= 2.9e+135) && (b <= 2.05e+156)))) {
		tmp = b * (a * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -1.8e+21) or not ((b <= 2.3e+121) or (not (b <= 2.9e+135) and (b <= 2.05e+156))):
		tmp = b * (a * -0.25)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -1.8e+21) || !((b <= 2.3e+121) || (!(b <= 2.9e+135) && (b <= 2.05e+156))))
		tmp = Float64(b * Float64(a * -0.25));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -1.8e+21) || ~(((b <= 2.3e+121) || (~((b <= 2.9e+135)) && (b <= 2.05e+156)))))
		tmp = b * (a * -0.25);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -1.8e+21], N[Not[Or[LessEqual[b, 2.3e+121], And[N[Not[LessEqual[b, 2.9e+135]], $MachinePrecision], LessEqual[b, 2.05e+156]]]], $MachinePrecision]], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.8e21 or 2.2999999999999999e121 < b < 2.8999999999999999e135 or 2.0500000000000001e156 < b

   1. Initial program 94.6%

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

   3. Taylor expanded in x around 0 87.7%

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

   4. Taylor expanded in c around 0 77.2%

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

   5. Taylor expanded in t around 0 65.8%

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

      1. associate-*r* 65.8%

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

      2. *-commutative 65.8%

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

   7. Simplified 65.8%

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

   if -1.8e21 < b < 2.2999999999999999e121 or 2.8999999999999999e135 < b < 2.0500000000000001e156

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf 65.5%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+21} \lor \neg \left(b \leq 2.3 \cdot 10^{+121} \lor \neg \left(b \leq 2.9 \cdot 10^{+135}\right) \land b \leq 2.05 \cdot 10^{+156}\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+133} \lor \neg \left(a \cdot b \leq 10^{+113}\right):\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e+133) (not (<= (* a b) 1e+113)))
   (+ c (- (* x y) (* (* a b) 0.25)))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+133) || !((a * b) <= 1e+113)) {
		tmp = c + ((x * y) - ((a * b) * 0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((a * b) <= (-5d+133)) .or. (.not. ((a * b) <= 1d+113))) then
        tmp = c + ((x * y) - ((a * b) * 0.25d0))
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+133) || !((a * b) <= 1e+113)) {
		tmp = c + ((x * y) - ((a * b) * 0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -5e+133) or not ((a * b) <= 1e+113):
		tmp = c + ((x * y) - ((a * b) * 0.25))
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -5e+133) || !(Float64(a * b) <= 1e+113))
		tmp = Float64(c + Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25)));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -5e+133) || ~(((a * b) <= 1e+113)))
		tmp = c + ((x * y) - ((a * b) * 0.25));
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e+133], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1e+113]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.99999999999999961e133 or 1e113 < (*.f64 a 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. Add Preprocessing

   3. Taylor expanded in z around 0 91.8%

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

   if -4.99999999999999961e133 < (*.f64 a b) < 1e113

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 93.2%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+133} \lor \neg \left(a \cdot b \leq 10^{+113}\right):\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.8 \cdot 10^{+81}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 8 \cdot 10^{-279}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 3.9 \cdot 10^{+69}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -4.8e+81)
   (* x y)
   (if (<= (* x y) 8e-279)
     (* b (* a -0.25))
     (if (<= (* x y) 3.9e+69) c (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -4.8e+81) {
		tmp = x * y;
	} else if ((x * y) <= 8e-279) {
		tmp = b * (a * -0.25);
	} else if ((x * y) <= 3.9e+69) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x * y) <= (-4.8d+81)) then
        tmp = x * y
    else if ((x * y) <= 8d-279) then
        tmp = b * (a * (-0.25d0))
    else if ((x * y) <= 3.9d+69) then
        tmp = c
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -4.8e+81) {
		tmp = x * y;
	} else if ((x * y) <= 8e-279) {
		tmp = b * (a * -0.25);
	} else if ((x * y) <= 3.9e+69) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -4.8e+81:
		tmp = x * y
	elif (x * y) <= 8e-279:
		tmp = b * (a * -0.25)
	elif (x * y) <= 3.9e+69:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -4.8e+81)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 8e-279)
		tmp = Float64(b * Float64(a * -0.25));
	elseif (Float64(x * y) <= 3.9e+69)
		tmp = c;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -4.8e+81)
		tmp = x * y;
	elseif ((x * y) <= 8e-279)
		tmp = b * (a * -0.25);
	elseif ((x * y) <= 3.9e+69)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -4.8e+81], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 8e-279], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.9e+69], c, N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.79999999999999979e81 or 3.8999999999999999e69 < (*.f64 x y)

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 74.8%

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

   4. Taylor expanded in x around inf 68.9%

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

   if -4.79999999999999979e81 < (*.f64 x y) < 8.00000000000000044e-279

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 95.4%

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

   4. Taylor expanded in c around 0 71.2%

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

   5. Taylor expanded in t around 0 43.0%

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

      1. associate-*r* 43.0%

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

      2. *-commutative 43.0%

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

   7. Simplified 43.0%

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

   if 8.00000000000000044e-279 < (*.f64 x y) < 3.8999999999999999e69

   1. Initial program 98.1%

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

      1. sub-neg 98.1%

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

      2. associate-+l+ 98.1%

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

      3. fma-def 98.1%

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

      4. associate-*l/ 98.1%

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

      5. distribute-frac-neg 98.1%

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

      6. distribute-rgt-neg-out 98.1%

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

      7. associate-/l* 98.1%

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

      8. neg-mul-1 98.1%

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

      9. associate-/r* 98.1%

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

      10. metadata-eval 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in c around inf 40.6%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.8 \cdot 10^{+81}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 8 \cdot 10^{-279}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 3.9 \cdot 10^{+69}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+23} \lor \neg \left(x \cdot y \leq 3.7 \cdot 10^{+78}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1e+23) (not (<= (* x y) 3.7e+78)))
   (+ c (* x y))
   (+ c (* 0.0625 (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1e+23) || !((x * y) <= 3.7e+78)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-1d+23)) .or. (.not. ((x * y) <= 3.7d+78))) then
        tmp = c + (x * y)
    else
        tmp = c + (0.0625d0 * (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1e+23) || !((x * y) <= 3.7e+78)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1e+23) or not ((x * y) <= 3.7e+78):
		tmp = c + (x * y)
	else:
		tmp = c + (0.0625 * (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1e+23) || !(Float64(x * y) <= 3.7e+78))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1e+23) || ~(((x * y) <= 3.7e+78)))
		tmp = c + (x * y);
	else
		tmp = c + (0.0625 * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1e+23], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.7e+78]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.9999999999999992e22 or 3.69999999999999985e78 < (*.f64 x y)

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 73.2%

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

   if -9.9999999999999992e22 < (*.f64 x y) < 3.69999999999999985e78

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf 64.1%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+23} \lor \neg \left(x \cdot y \leq 3.7 \cdot 10^{+78}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 77.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+24} \lor \neg \left(b \leq 10^{+156}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -3.5e+24) (not (<= b 1e+156)))
   (+ c (* a (* b -0.25)))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -3.5e+24) || !(b <= 1e+156)) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-3.5d+24)) .or. (.not. (b <= 1d+156))) then
        tmp = c + (a * (b * (-0.25d0)))
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -3.5e+24) || !(b <= 1e+156)) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -3.5e+24) or not (b <= 1e+156):
		tmp = c + (a * (b * -0.25))
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -3.5e+24) || !(b <= 1e+156))
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -3.5e+24) || ~((b <= 1e+156)))
		tmp = c + (a * (b * -0.25));
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -3.5e+24], N[Not[LessEqual[b, 1e+156]], $MachinePrecision]], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.5000000000000002e24 or 9.9999999999999998e155 < b

   1. Initial program 94.3%

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

   3. Taylor expanded in a around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-*r* 75.0%

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

   5. Simplified 75.0%

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

   if -3.5000000000000002e24 < b < 9.9999999999999998e155

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 87.9%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+24} \lor \neg \left(b \leq 10^{+156}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.05 \cdot 10^{+21} \lor \neg \left(x \cdot y \leq 4.2 \cdot 10^{+70}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.05e+21) (not (<= (* x y) 4.2e+70))) (* x y) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.05e+21) || !((x * y) <= 4.2e+70)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-1.05d+21)) .or. (.not. ((x * y) <= 4.2d+70))) then
        tmp = x * y
    else
        tmp = c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.05e+21) || !((x * y) <= 4.2e+70)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.05e+21) or not ((x * y) <= 4.2e+70):
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.05e+21) || !(Float64(x * y) <= 4.2e+70))
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1.05e+21) || ~(((x * y) <= 4.2e+70)))
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.05e+21], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.2e+70]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.05e21 or 4.20000000000000015e70 < (*.f64 x y)

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 73.2%

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

   4. Taylor expanded in x around inf 66.8%

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

   if -1.05e21 < (*.f64 x y) < 4.20000000000000015e70

   1. Initial program 98.7%

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

      1. sub-neg 98.7%

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

      2. associate-+l+ 98.7%

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

      3. fma-def 98.7%

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

      4. associate-*l/ 98.7%

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

      5. distribute-frac-neg 98.7%

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

      6. distribute-rgt-neg-out 98.7%

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

      7. associate-/l* 98.6%

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

      8. neg-mul-1 98.6%

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

      9. associate-/r* 98.6%

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

      10. metadata-eval 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in c around inf 32.2%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.05 \cdot 10^{+21} \lor \neg \left(x \cdot y \leq 4.2 \cdot 10^{+70}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 22.0% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. sub-neg 97.7%

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

   2. associate-+l+ 97.7%

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

   3. fma-def 98.8%

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

   4. associate-*l/ 98.8%

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

   5. distribute-frac-neg 98.8%

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

   6. distribute-rgt-neg-out 98.8%

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

   7. associate-/l* 98.7%

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

   8. neg-mul-1 98.7%

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

   9. associate-/r* 98.7%

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

   10. metadata-eval 98.7%

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

3. Simplified 98.7%

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

5. Taylor expanded in c around inf 22.6%

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

6. Final simplification 22.6%

   \[\leadsto c \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024026 
(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))