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

Percentage Accurate: 97.6% → 98.9%

Time: 12.2s

Alternatives: 12

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.6% 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: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. associate--l+ 98.4%

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

   2. fma-define 99.2%

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

   3. associate-/l* 99.2%

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

   4. fma-neg 99.6%

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

   5. distribute-neg-frac2 99.6%

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

   6. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 98.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. associate-+l- 98.4%

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

   2. *-commutative 98.4%

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

   3. associate-+l- 98.4%

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

   4. fma-define 99.2%

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

   5. *-commutative 99.2%

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

   6. associate-/l* 99.2%

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

   7. associate-/l* 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 3: 65.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := c + b \cdot \left(a \cdot -0.25\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+95}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -3 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{-166}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+131}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* 0.0625 (* z t))))
        (t_2 (+ c (* b (* a -0.25))))
        (t_3 (+ c (* x y))))
   (if (<= (* a b) -5e+95)
     t_2
     (if (<= (* a b) -3e-123)
       t_1
       (if (<= (* a b) -4e-166)
         t_3
         (if (<= (* a b) 5e-83) t_1 (if (<= (* a b) 5e+131) 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 * (z * t));
	double t_2 = c + (b * (a * -0.25));
	double t_3 = c + (x * y);
	double tmp;
	if ((a * b) <= -5e+95) {
		tmp = t_2;
	} else if ((a * b) <= -3e-123) {
		tmp = t_1;
	} else if ((a * b) <= -4e-166) {
		tmp = t_3;
	} else if ((a * b) <= 5e-83) {
		tmp = t_1;
	} else if ((a * b) <= 5e+131) {
		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 * (z * t))
    t_2 = c + (b * (a * (-0.25d0)))
    t_3 = c + (x * y)
    if ((a * b) <= (-5d+95)) then
        tmp = t_2
    else if ((a * b) <= (-3d-123)) then
        tmp = t_1
    else if ((a * b) <= (-4d-166)) then
        tmp = t_3
    else if ((a * b) <= 5d-83) then
        tmp = t_1
    else if ((a * b) <= 5d+131) 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 * (z * t));
	double t_2 = c + (b * (a * -0.25));
	double t_3 = c + (x * y);
	double tmp;
	if ((a * b) <= -5e+95) {
		tmp = t_2;
	} else if ((a * b) <= -3e-123) {
		tmp = t_1;
	} else if ((a * b) <= -4e-166) {
		tmp = t_3;
	} else if ((a * b) <= 5e-83) {
		tmp = t_1;
	} else if ((a * b) <= 5e+131) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (0.0625 * (z * t))
	t_2 = c + (b * (a * -0.25))
	t_3 = c + (x * y)
	tmp = 0
	if (a * b) <= -5e+95:
		tmp = t_2
	elif (a * b) <= -3e-123:
		tmp = t_1
	elif (a * b) <= -4e-166:
		tmp = t_3
	elif (a * b) <= 5e-83:
		tmp = t_1
	elif (a * b) <= 5e+131:
		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(z * t)))
	t_2 = Float64(c + Float64(b * Float64(a * -0.25)))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(a * b) <= -5e+95)
		tmp = t_2;
	elseif (Float64(a * b) <= -3e-123)
		tmp = t_1;
	elseif (Float64(a * b) <= -4e-166)
		tmp = t_3;
	elseif (Float64(a * b) <= 5e-83)
		tmp = t_1;
	elseif (Float64(a * b) <= 5e+131)
		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 * (z * t));
	t_2 = c + (b * (a * -0.25));
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((a * b) <= -5e+95)
		tmp = t_2;
	elseif ((a * b) <= -3e-123)
		tmp = t_1;
	elseif ((a * b) <= -4e-166)
		tmp = t_3;
	elseif ((a * b) <= 5e-83)
		tmp = t_1;
	elseif ((a * b) <= 5e+131)
		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[(z * t), $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[(a * b), $MachinePrecision], -5e+95], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -3e-123], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -4e-166], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 5e-83], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 5e+131], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.00000000000000025e95 or 4.99999999999999995e131 < (*.f64 a b)

   1. Initial program 97.9%

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

   3. Taylor expanded in a around inf 73.6%

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

      1. associate-*r* 73.6%

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

   5. Simplified 73.6%

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

   if -5.00000000000000025e95 < (*.f64 a b) < -2.99999999999999984e-123 or -4.00000000000000016e-166 < (*.f64 a b) < 5e-83

   1. Initial program 99.1%

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

   3. Taylor expanded in a around 0 95.6%

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

   4. Taylor expanded in x around 0 69.7%

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

   if -2.99999999999999984e-123 < (*.f64 a b) < -4.00000000000000016e-166 or 5e-83 < (*.f64 a b) < 4.99999999999999995e131

   1. Initial program 98.1%

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

   3. Taylor expanded in a around 0 93.7%

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

   4. Taylor expanded in t around 0 73.5%

      \[\leadsto \color{blue}{c + x \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 73.5%

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

   6. Simplified 73.5%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+95}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq -3 \cdot 10^{-123}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{-166}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-83}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+131}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+188} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+131} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+190}\right) \land a \cdot b \leq 10^{+220}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -4e+188)
         (not
          (or (<= (* a b) 5e+131)
              (and (not (<= (* a b) 2e+190)) (<= (* a b) 1e+220)))))
   (+ c (* b (* a -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) <= -4e+188) || !(((a * b) <= 5e+131) || (!((a * b) <= 2e+190) && ((a * b) <= 1e+220)))) {
		tmp = c + (b * (a * -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) <= (-4d+188)) .or. (.not. ((a * b) <= 5d+131) .or. (.not. ((a * b) <= 2d+190)) .and. ((a * b) <= 1d+220))) then
        tmp = c + (b * (a * (-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) <= -4e+188) || !(((a * b) <= 5e+131) || (!((a * b) <= 2e+190) && ((a * b) <= 1e+220)))) {
		tmp = c + (b * (a * -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) <= -4e+188) or not (((a * b) <= 5e+131) or (not ((a * b) <= 2e+190) and ((a * b) <= 1e+220))):
		tmp = c + (b * (a * -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) <= -4e+188) || !((Float64(a * b) <= 5e+131) || (!(Float64(a * b) <= 2e+190) && (Float64(a * b) <= 1e+220))))
		tmp = Float64(c + Float64(b * Float64(a * -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) <= -4e+188) || ~((((a * b) <= 5e+131) || (~(((a * b) <= 2e+190)) && ((a * b) <= 1e+220)))))
		tmp = c + (b * (a * -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], -4e+188], N[Not[Or[LessEqual[N[(a * b), $MachinePrecision], 5e+131], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e+190]], $MachinePrecision], LessEqual[N[(a * b), $MachinePrecision], 1e+220]]]], $MachinePrecision]], N[(c + N[(b * N[(a * -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) < -4.0000000000000001e188 or 4.99999999999999995e131 < (*.f64 a b) < 2.0000000000000001e190 or 1e220 < (*.f64 a b)

   1. Initial program 97.0%

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

   3. Taylor expanded in a around inf 88.4%

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

      1. associate-*r* 88.4%

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

   5. Simplified 88.4%

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

   if -4.0000000000000001e188 < (*.f64 a b) < 4.99999999999999995e131 or 2.0000000000000001e190 < (*.f64 a b) < 1e220

   1. Initial program 98.9%

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

   3. Taylor expanded in a around 0 90.5%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+188} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+131} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+190}\right) \land a \cdot b \leq 10^{+220}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 43.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{if}\;x \cdot y \leq -7.6 \cdot 10^{+146}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{+127}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (* t 0.0625))))
   (if (<= (* x y) -7.6e+146)
     (* x y)
     (if (<= (* x y) 1.55e-54)
       t_1
       (if (<= (* x y) 4.1e+127) c (if (<= (* x y) 4.1e+157) t_1 (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * (t * 0.0625);
	double tmp;
	if ((x * y) <= -7.6e+146) {
		tmp = x * y;
	} else if ((x * y) <= 1.55e-54) {
		tmp = t_1;
	} else if ((x * y) <= 4.1e+127) {
		tmp = c;
	} else if ((x * y) <= 4.1e+157) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (t * 0.0625d0)
    if ((x * y) <= (-7.6d+146)) then
        tmp = x * y
    else if ((x * y) <= 1.55d-54) then
        tmp = t_1
    else if ((x * y) <= 4.1d+127) then
        tmp = c
    else if ((x * y) <= 4.1d+157) then
        tmp = t_1
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * (t * 0.0625);
	double tmp;
	if ((x * y) <= -7.6e+146) {
		tmp = x * y;
	} else if ((x * y) <= 1.55e-54) {
		tmp = t_1;
	} else if ((x * y) <= 4.1e+127) {
		tmp = c;
	} else if ((x * y) <= 4.1e+157) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = z * (t * 0.0625)
	tmp = 0
	if (x * y) <= -7.6e+146:
		tmp = x * y
	elif (x * y) <= 1.55e-54:
		tmp = t_1
	elif (x * y) <= 4.1e+127:
		tmp = c
	elif (x * y) <= 4.1e+157:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * Float64(t * 0.0625))
	tmp = 0.0
	if (Float64(x * y) <= -7.6e+146)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 1.55e-54)
		tmp = t_1;
	elseif (Float64(x * y) <= 4.1e+127)
		tmp = c;
	elseif (Float64(x * y) <= 4.1e+157)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = z * (t * 0.0625);
	tmp = 0.0;
	if ((x * y) <= -7.6e+146)
		tmp = x * y;
	elseif ((x * y) <= 1.55e-54)
		tmp = t_1;
	elseif ((x * y) <= 4.1e+127)
		tmp = c;
	elseif ((x * y) <= 4.1e+157)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -7.6e+146], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.55e-54], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4.1e+127], c, If[LessEqual[N[(x * y), $MachinePrecision], 4.1e+157], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -7.59999999999999958e146 or 4.10000000000000016e157 < (*.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 a around 0 86.1%

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

   4. Taylor expanded in t around 0 72.5%

      \[\leadsto \color{blue}{c + x \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 72.5%

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

   6. Simplified 72.5%

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

   7. Taylor expanded in x around inf 69.4%

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

   if -7.59999999999999958e146 < (*.f64 x y) < 1.55000000000000002e-54 or 4.09999999999999983e127 < (*.f64 x y) < 4.10000000000000016e157

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. associate-*r/ 99.3%

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

      3. *-commutative 99.3%

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

      4. fma-define 99.3%

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

      5. div-inv 99.3%

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

      6. metadata-eval 99.3%

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

   4. Applied egg-rr 99.3%

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

   5. Taylor expanded in a around 0 62.9%

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

      1. +-commutative 62.9%

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

      2. +-commutative 62.9%

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

      3. fma-define 62.9%

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

      4. associate-*r* 62.9%

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

   7. Simplified 62.9%

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

   8. Taylor expanded in x around 0 57.8%

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

      1. +-commutative 57.8%

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

      2. associate-*r* 57.8%

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

   10. Simplified 57.8%

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

   11. Taylor expanded in t around inf 36.8%

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

       1. associate-*r* 36.8%

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

   13. Simplified 36.8%

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

   if 1.55000000000000002e-54 < (*.f64 x y) < 4.09999999999999983e127

   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 c around inf 40.7%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.6 \cdot 10^{+146}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{-54}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{+127}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{+157}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+105} \lor \neg \left(a \cdot b \leq 10^{+123}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e+105) (not (<= (* a b) 1e+123)))
   (- (+ 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+105) || !((a * b) <= 1e+123)) {
		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+105)) .or. (.not. ((a * b) <= 1d+123))) 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+105) || !((a * b) <= 1e+123)) {
		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+105) or not ((a * b) <= 1e+123):
		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+105) || !(Float64(a * b) <= 1e+123))
		tmp = Float64(Float64(c + 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+105) || ~(((a * b) <= 1e+123)))
		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+105], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1e+123]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.00000000000000046e105 or 9.99999999999999978e122 < (*.f64 a b)

   1. Initial program 97.9%

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

   3. Taylor expanded in z around 0 85.7%

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

   if -5.00000000000000046e105 < (*.f64 a b) < 9.99999999999999978e122

   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 a around 0 95.0%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+105} \lor \neg \left(a \cdot b \leq 10^{+123}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+105}:\\ \;\;\;\;\left(c + t\_1\right) - t\_2\\ \mathbf{elif}\;a \cdot b \leq 10^{+123}:\\ \;\;\;\;c + \left(x \cdot y + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (* (* a b) 0.25)))
   (if (<= (* a b) -5e+105)
     (- (+ c t_1) t_2)
     (if (<= (* a b) 1e+123) (+ c (+ (* x y) t_1)) (- (+ c (* 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 * (z * t);
	double t_2 = (a * b) * 0.25;
	double tmp;
	if ((a * b) <= -5e+105) {
		tmp = (c + t_1) - t_2;
	} else if ((a * b) <= 1e+123) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + (x * y)) - 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 * (z * t)
    t_2 = (a * b) * 0.25d0
    if ((a * b) <= (-5d+105)) then
        tmp = (c + t_1) - t_2
    else if ((a * b) <= 1d+123) then
        tmp = c + ((x * y) + t_1)
    else
        tmp = (c + (x * y)) - 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 * (z * t);
	double t_2 = (a * b) * 0.25;
	double tmp;
	if ((a * b) <= -5e+105) {
		tmp = (c + t_1) - t_2;
	} else if ((a * b) <= 1e+123) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + (x * y)) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = (a * b) * 0.25
	tmp = 0
	if (a * b) <= -5e+105:
		tmp = (c + t_1) - t_2
	elif (a * b) <= 1e+123:
		tmp = c + ((x * y) + t_1)
	else:
		tmp = (c + (x * y)) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if (Float64(a * b) <= -5e+105)
		tmp = Float64(Float64(c + t_1) - t_2);
	elseif (Float64(a * b) <= 1e+123)
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	else
		tmp = Float64(Float64(c + Float64(x * y)) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	t_2 = (a * b) * 0.25;
	tmp = 0.0;
	if ((a * b) <= -5e+105)
		tmp = (c + t_1) - t_2;
	elseif ((a * b) <= 1e+123)
		tmp = c + ((x * y) + t_1);
	else
		tmp = (c + (x * y)) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+105], N[(N[(c + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+123], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.00000000000000046e105

   1. Initial program 97.1%

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

   3. Taylor expanded in x around 0 91.9%

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

   if -5.00000000000000046e105 < (*.f64 a b) < 9.99999999999999978e122

   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 a around 0 95.0%

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

   if 9.99999999999999978e122 < (*.f64 a b)

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 88.6%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+105}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 10^{+123}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+103} \lor \neg \left(x \cdot y \leq 1.5 \cdot 10^{+157}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2.7e+103) (not (<= (* x y) 1.5e+157)))
   (+ 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) <= -2.7e+103) || !((x * y) <= 1.5e+157)) {
		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) <= (-2.7d+103)) .or. (.not. ((x * y) <= 1.5d+157))) 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) <= -2.7e+103) || !((x * y) <= 1.5e+157)) {
		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) <= -2.7e+103) or not ((x * y) <= 1.5e+157):
		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) <= -2.7e+103) || !(Float64(x * y) <= 1.5e+157))
		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) <= -2.7e+103) || ~(((x * y) <= 1.5e+157)))
		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], -2.7e+103], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.5e+157]], $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) < -2.69999999999999993e103 or 1.50000000000000005e157 < (*.f64 x y)

   1. Initial program 96.3%

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

   3. Taylor expanded in a around 0 85.4%

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

   4. Taylor expanded in t around 0 71.2%

      \[\leadsto \color{blue}{c + x \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 71.2%

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

   6. Simplified 71.2%

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

   if -2.69999999999999993e103 < (*.f64 x y) < 1.50000000000000005e157

   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 66.6%

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

   4. Taylor expanded in x around 0 59.3%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+103} \lor \neg \left(x \cdot y \leq 1.5 \cdot 10^{+157}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+26} \lor \neg \left(x \cdot y \leq 1.7 \cdot 10^{+125}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2.7e+26) (not (<= (* x y) 1.7e+125))) (* x y) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -2.7e+26) || !((x * y) <= 1.7e+125)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-2.7d+26)) .or. (.not. ((x * y) <= 1.7d+125))) then
        tmp = x * y
    else
        tmp = c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -2.7e+26) || !((x * y) <= 1.7e+125)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -2.7e+26) or not ((x * y) <= 1.7e+125):
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -2.7e+26) || !(Float64(x * y) <= 1.7e+125))
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -2.7e+26) || ~(((x * y) <= 1.7e+125)))
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2.7e+26], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.7e+125]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.7e26 or 1.6999999999999999e125 < (*.f64 x y)

   1. Initial program 96.8%

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

   3. Taylor expanded in a around 0 82.0%

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

   4. Taylor expanded in t around 0 65.5%

      \[\leadsto \color{blue}{c + x \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 65.5%

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

   6. Simplified 65.5%

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

   7. Taylor expanded in x around inf 61.9%

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

   if -2.7e26 < (*.f64 x y) < 1.6999999999999999e125

   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 c around inf 28.7%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+26} \lor \neg \left(x \cdot y \leq 1.7 \cdot 10^{+125}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

3. Final simplification 98.4%

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

Alternative 11: 53.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-10} \lor \neg \left(t \leq 6.2 \cdot 10^{+89}\right):\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -3.6e-10) (not (<= t 6.2e+89)))
   (* z (* t 0.0625))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -3.6e-10) || !(t <= 6.2e+89)) {
		tmp = z * (t * 0.0625);
	} 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 ((t <= (-3.6d-10)) .or. (.not. (t <= 6.2d+89))) then
        tmp = z * (t * 0.0625d0)
    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 ((t <= -3.6e-10) || !(t <= 6.2e+89)) {
		tmp = z * (t * 0.0625);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -3.6e-10) or not (t <= 6.2e+89):
		tmp = z * (t * 0.0625)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -3.6e-10) || !(t <= 6.2e+89))
		tmp = Float64(z * Float64(t * 0.0625));
	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 ((t <= -3.6e-10) || ~((t <= 6.2e+89)))
		tmp = z * (t * 0.0625);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -3.6e-10], N[Not[LessEqual[t, 6.2e+89]], $MachinePrecision]], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.6e-10 or 6.2e89 < t

   1. Initial program 96.4%

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

      1. +-commutative 96.4%

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

      2. associate-*r/ 96.4%

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

      3. *-commutative 96.4%

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

      4. fma-define 97.3%

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

      5. div-inv 97.3%

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

      6. metadata-eval 97.3%

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

   4. Applied egg-rr 97.3%

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

   5. Taylor expanded in a around 0 82.3%

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

      1. +-commutative 82.3%

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

      2. +-commutative 82.3%

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

      3. fma-define 84.0%

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

      4. associate-*r* 84.0%

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

   7. Simplified 84.0%

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

   8. Taylor expanded in x around 0 65.8%

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

      1. +-commutative 65.8%

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

      2. associate-*r* 65.8%

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

   10. Simplified 65.8%

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

   11. Taylor expanded in t around inf 55.1%

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

       1. associate-*r* 55.1%

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

   13. Simplified 55.1%

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

   if -3.6e-10 < t < 6.2e89

   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 65.1%

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

   4. Taylor expanded in t around 0 56.7%

      \[\leadsto \color{blue}{c + x \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 56.7%

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

   6. Simplified 56.7%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-10} \lor \neg \left(t \leq 6.2 \cdot 10^{+89}\right):\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 22.9% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

3. Taylor expanded in c around inf 20.2%

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

4. Final simplification 20.2%

   \[\leadsto c \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024044 
(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))