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

Percentage Accurate: 97.7% → 98.9%

Time: 15.4s

Alternatives: 14

Speedup: 1.0×

• 33.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. associate--l+ 98.8%

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

   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%

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

   4. fma-neg 99.2%

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

   5. neg-mul-1 99.2%

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

   6. *-commutative 99.2%

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

   7. associate-*l/ 99.2%

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

   8. associate-/l* 99.2%

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

   9. *-commutative 99.2%

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

   10. associate-*r/ 99.2%

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

   11. metadata-eval 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 2: 98.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. associate-+l- 98.8%

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

   2. *-commutative 98.8%

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

   3. associate-+l- 98.8%

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

   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%

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

   7. associate-/l* 99.1%

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

3. Simplified 99.1%

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

5. Final simplification 99.1%

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

Alternative 3: 44.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -3 \cdot 10^{+26}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1.05 \cdot 10^{-307}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-317}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4.5 \cdot 10^{-205}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))))
   (if (<= (* x y) -3e+26)
     (* x y)
     (if (<= (* x y) -4e-183)
       t_1
       (if (<= (* x y) -1.05e-307)
         c
         (if (<= (* x y) 2e-317)
           t_1
           (if (<= (* x y) 4.5e-205)
             c
             (if (<= (* x y) 2.5e+68) t_1 (* x y)))))))))

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) <= -3e+26) {
		tmp = x * y;
	} else if ((x * y) <= -4e-183) {
		tmp = t_1;
	} else if ((x * y) <= -1.05e-307) {
		tmp = c;
	} else if ((x * y) <= 2e-317) {
		tmp = t_1;
	} else if ((x * y) <= 4.5e-205) {
		tmp = c;
	} else if ((x * y) <= 2.5e+68) {
		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 = a * (b * (-0.25d0))
    if ((x * y) <= (-3d+26)) then
        tmp = x * y
    else if ((x * y) <= (-4d-183)) then
        tmp = t_1
    else if ((x * y) <= (-1.05d-307)) then
        tmp = c
    else if ((x * y) <= 2d-317) then
        tmp = t_1
    else if ((x * y) <= 4.5d-205) then
        tmp = c
    else if ((x * y) <= 2.5d+68) 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 = a * (b * -0.25);
	double tmp;
	if ((x * y) <= -3e+26) {
		tmp = x * y;
	} else if ((x * y) <= -4e-183) {
		tmp = t_1;
	} else if ((x * y) <= -1.05e-307) {
		tmp = c;
	} else if ((x * y) <= 2e-317) {
		tmp = t_1;
	} else if ((x * y) <= 4.5e-205) {
		tmp = c;
	} else if ((x * y) <= 2.5e+68) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	tmp = 0
	if (x * y) <= -3e+26:
		tmp = x * y
	elif (x * y) <= -4e-183:
		tmp = t_1
	elif (x * y) <= -1.05e-307:
		tmp = c
	elif (x * y) <= 2e-317:
		tmp = t_1
	elif (x * y) <= 4.5e-205:
		tmp = c
	elif (x * y) <= 2.5e+68:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (Float64(x * y) <= -3e+26)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -4e-183)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.05e-307)
		tmp = c;
	elseif (Float64(x * y) <= 2e-317)
		tmp = t_1;
	elseif (Float64(x * y) <= 4.5e-205)
		tmp = c;
	elseif (Float64(x * y) <= 2.5e+68)
		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 = a * (b * -0.25);
	tmp = 0.0;
	if ((x * y) <= -3e+26)
		tmp = x * y;
	elseif ((x * y) <= -4e-183)
		tmp = t_1;
	elseif ((x * y) <= -1.05e-307)
		tmp = c;
	elseif ((x * y) <= 2e-317)
		tmp = t_1;
	elseif ((x * y) <= 4.5e-205)
		tmp = c;
	elseif ((x * y) <= 2.5e+68)
		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[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3e+26], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e-183], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.05e-307], c, If[LessEqual[N[(x * y), $MachinePrecision], 2e-317], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4.5e-205], c, If[LessEqual[N[(x * y), $MachinePrecision], 2.5e+68], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.99999999999999997e26 or 2.5000000000000002e68 < (*.f64 x y)

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0 85.5%

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

      1. fma-neg 85.5%

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

      2. distribute-lft-neg-in 85.5%

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

      3. metadata-eval 85.5%

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

      4. *-commutative 85.5%

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

      5. associate-*l* 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in x around inf 62.1%

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

   if -2.99999999999999997e26 < (*.f64 x y) < -4.00000000000000002e-183 or -1.0500000000000001e-307 < (*.f64 x y) < 1.99999997e-317 or 4.49999999999999956e-205 < (*.f64 x y) < 2.5000000000000002e68

   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 0 67.9%

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

      1. fma-neg 67.9%

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

      2. distribute-lft-neg-in 67.9%

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

      3. metadata-eval 67.9%

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

      4. *-commutative 67.9%

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

      5. associate-*l* 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in a around inf 43.5%

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

      1. *-commutative 43.5%

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

      2. associate-*r* 43.5%

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

      3. *-commutative 43.5%

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

   8. Simplified 43.5%

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

   if -4.00000000000000002e-183 < (*.f64 x y) < -1.0500000000000001e-307 or 1.99999997e-317 < (*.f64 x y) < 4.49999999999999956e-205

   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 58.4%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3 \cdot 10^{+26}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-183}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -1.05 \cdot 10^{-307}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-317}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 4.5 \cdot 10^{-205}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 45.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{if}\;x \cdot y \leq -1.3 \cdot 10^{+77}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.9 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-317}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 8.6 \cdot 10^{-172}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.6 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (* t 0.0625))))
   (if (<= (* x y) -1.3e+77)
     (* x y)
     (if (<= (* x y) -3.9e-290)
       t_1
       (if (<= (* x y) 2e-317)
         (* a (* b -0.25))
         (if (<= (* x y) 8.6e-172)
           c
           (if (<= (* x y) 1.6e+69) 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) <= -1.3e+77) {
		tmp = x * y;
	} else if ((x * y) <= -3.9e-290) {
		tmp = t_1;
	} else if ((x * y) <= 2e-317) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 8.6e-172) {
		tmp = c;
	} else if ((x * y) <= 1.6e+69) {
		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) <= (-1.3d+77)) then
        tmp = x * y
    else if ((x * y) <= (-3.9d-290)) then
        tmp = t_1
    else if ((x * y) <= 2d-317) then
        tmp = a * (b * (-0.25d0))
    else if ((x * y) <= 8.6d-172) then
        tmp = c
    else if ((x * y) <= 1.6d+69) 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) <= -1.3e+77) {
		tmp = x * y;
	} else if ((x * y) <= -3.9e-290) {
		tmp = t_1;
	} else if ((x * y) <= 2e-317) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 8.6e-172) {
		tmp = c;
	} else if ((x * y) <= 1.6e+69) {
		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) <= -1.3e+77:
		tmp = x * y
	elif (x * y) <= -3.9e-290:
		tmp = t_1
	elif (x * y) <= 2e-317:
		tmp = a * (b * -0.25)
	elif (x * y) <= 8.6e-172:
		tmp = c
	elif (x * y) <= 1.6e+69:
		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) <= -1.3e+77)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -3.9e-290)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-317)
		tmp = Float64(a * Float64(b * -0.25));
	elseif (Float64(x * y) <= 8.6e-172)
		tmp = c;
	elseif (Float64(x * y) <= 1.6e+69)
		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) <= -1.3e+77)
		tmp = x * y;
	elseif ((x * y) <= -3.9e-290)
		tmp = t_1;
	elseif ((x * y) <= 2e-317)
		tmp = a * (b * -0.25);
	elseif ((x * y) <= 8.6e-172)
		tmp = c;
	elseif ((x * y) <= 1.6e+69)
		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], -1.3e+77], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.9e-290], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-317], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 8.6e-172], c, If[LessEqual[N[(x * y), $MachinePrecision], 1.6e+69], t$95$1, N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.3000000000000001e77 or 1.59999999999999992e69 < (*.f64 x y)

   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 89.8%

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

      1. fma-neg 89.8%

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

      2. distribute-lft-neg-in 89.8%

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

      3. metadata-eval 89.8%

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

      4. *-commutative 89.8%

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

      5. associate-*l* 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in x around inf 65.8%

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

   if -1.3000000000000001e77 < (*.f64 x y) < -3.89999999999999973e-290 or 8.5999999999999995e-172 < (*.f64 x y) < 1.59999999999999992e69

   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. Step-by-step derivation

      1. +-commutative 99.0%

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

      2. associate-/l* 98.9%

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

      3. associate-/r/ 99.0%

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

      4. fma-define 99.0%

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

      5. div-inv 99.0%

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

      6. metadata-eval 99.0%

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

   4. Applied egg-rr 99.0%

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

   5. Taylor expanded in z around inf 64.0%

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

      1. *-commutative 64.0%

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

      2. associate-*r* 64.0%

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

      3. *-commutative 64.0%

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

      4. associate-*l* 64.0%

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

   7. Simplified 64.0%

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

   8. Taylor expanded in z around inf 39.9%

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

      1. associate-*r* 39.9%

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

   10. Simplified 39.9%

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

   if -3.89999999999999973e-290 < (*.f64 x y) < 1.99999997e-317

   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 0 78.8%

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

      1. fma-neg 78.8%

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

      2. distribute-lft-neg-in 78.8%

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

      3. metadata-eval 78.8%

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

      4. *-commutative 78.8%

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

      5. associate-*l* 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in a around inf 59.2%

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

      1. *-commutative 59.2%

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

      2. associate-*r* 59.2%

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

      3. *-commutative 59.2%

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

   8. Simplified 59.2%

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

   if 1.99999997e-317 < (*.f64 x y) < 8.5999999999999995e-172

   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 53.1%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.3 \cdot 10^{+77}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.9 \cdot 10^{-290}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-317}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 8.6 \cdot 10^{-172}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.6 \cdot 10^{+69}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_2 := x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -6.5 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{-92}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.25 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625)))) (t_2 (- (* x y) (* (* b a) 0.25))))
   (if (<= (* x y) -1.8e+74)
     t_2
     (if (<= (* x y) -6.5e-291)
       t_1
       (if (<= (* x y) 3e-92)
         (+ c (* a (* b -0.25)))
         (if (<= (* x y) 1.25e+70) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (t * (z * 0.0625));
	double t_2 = (x * y) - ((b * a) * 0.25);
	double tmp;
	if ((x * y) <= -1.8e+74) {
		tmp = t_2;
	} else if ((x * y) <= -6.5e-291) {
		tmp = t_1;
	} else if ((x * y) <= 3e-92) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 1.25e+70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (t * (z * 0.0625d0))
    t_2 = (x * y) - ((b * a) * 0.25d0)
    if ((x * y) <= (-1.8d+74)) then
        tmp = t_2
    else if ((x * y) <= (-6.5d-291)) then
        tmp = t_1
    else if ((x * y) <= 3d-92) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((x * y) <= 1.25d+70) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (t * (z * 0.0625));
	double t_2 = (x * y) - ((b * a) * 0.25);
	double tmp;
	if ((x * y) <= -1.8e+74) {
		tmp = t_2;
	} else if ((x * y) <= -6.5e-291) {
		tmp = t_1;
	} else if ((x * y) <= 3e-92) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 1.25e+70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (t * (z * 0.0625))
	t_2 = (x * y) - ((b * a) * 0.25)
	tmp = 0
	if (x * y) <= -1.8e+74:
		tmp = t_2
	elif (x * y) <= -6.5e-291:
		tmp = t_1
	elif (x * y) <= 3e-92:
		tmp = c + (a * (b * -0.25))
	elif (x * y) <= 1.25e+70:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(t * Float64(z * 0.0625)))
	t_2 = Float64(Float64(x * y) - Float64(Float64(b * a) * 0.25))
	tmp = 0.0
	if (Float64(x * y) <= -1.8e+74)
		tmp = t_2;
	elseif (Float64(x * y) <= -6.5e-291)
		tmp = t_1;
	elseif (Float64(x * y) <= 3e-92)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 1.25e+70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (t * (z * 0.0625));
	t_2 = (x * y) - ((b * a) * 0.25);
	tmp = 0.0;
	if ((x * y) <= -1.8e+74)
		tmp = t_2;
	elseif ((x * y) <= -6.5e-291)
		tmp = t_1;
	elseif ((x * y) <= 3e-92)
		tmp = c + (a * (b * -0.25));
	elseif ((x * y) <= 1.25e+70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.8e+74], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -6.5e-291], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3e-92], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.25e+70], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.79999999999999994e74 or 1.2500000000000001e70 < (*.f64 x y)

   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 89.7%

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

   4. Taylor expanded in c around 0 81.9%

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

   if -1.79999999999999994e74 < (*.f64 x y) < -6.50000000000000002e-291 or 3.00000000000000013e-92 < (*.f64 x y) < 1.2500000000000001e70

   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 z around inf 67.1%

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

      1. associate-*r* 67.1%

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

      2. *-commutative 67.1%

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

      3. associate-*r* 67.1%

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

   5. Simplified 67.1%

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

   if -6.50000000000000002e-291 < (*.f64 x y) < 3.00000000000000013e-92

   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 inf 74.1%

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

      1. *-commutative 74.1%

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

      2. associate-*l* 74.1%

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

   5. Simplified 74.1%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+74}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq -6.5 \cdot 10^{-291}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{-92}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.25 \cdot 10^{+70}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -3.9 \cdot 10^{+149}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -1.5 \cdot 10^{-289}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-93}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.15 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625)))) (t_2 (+ c (* x y))))
   (if (<= (* x y) -3.9e+149)
     t_2
     (if (<= (* x y) -1.5e-289)
       t_1
       (if (<= (* x y) 3.2e-93)
         (+ c (* a (* b -0.25)))
         (if (<= (* x y) 2.15e+69) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (t * (z * 0.0625));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -3.9e+149) {
		tmp = t_2;
	} else if ((x * y) <= -1.5e-289) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e-93) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 2.15e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (t * (z * 0.0625d0))
    t_2 = c + (x * y)
    if ((x * y) <= (-3.9d+149)) then
        tmp = t_2
    else if ((x * y) <= (-1.5d-289)) then
        tmp = t_1
    else if ((x * y) <= 3.2d-93) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((x * y) <= 2.15d+69) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (t * (z * 0.0625));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -3.9e+149) {
		tmp = t_2;
	} else if ((x * y) <= -1.5e-289) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e-93) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 2.15e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (t * (z * 0.0625))
	t_2 = c + (x * y)
	tmp = 0
	if (x * y) <= -3.9e+149:
		tmp = t_2
	elif (x * y) <= -1.5e-289:
		tmp = t_1
	elif (x * y) <= 3.2e-93:
		tmp = c + (a * (b * -0.25))
	elif (x * y) <= 2.15e+69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(t * Float64(z * 0.0625)))
	t_2 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -3.9e+149)
		tmp = t_2;
	elseif (Float64(x * y) <= -1.5e-289)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.2e-93)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 2.15e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (t * (z * 0.0625));
	t_2 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -3.9e+149)
		tmp = t_2;
	elseif ((x * y) <= -1.5e-289)
		tmp = t_1;
	elseif ((x * y) <= 3.2e-93)
		tmp = c + (a * (b * -0.25));
	elseif ((x * y) <= 2.15e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.9e+149], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -1.5e-289], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.2e-93], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.15e+69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.8999999999999999e149 or 2.14999999999999996e69 < (*.f64 x y)

   1. Initial program 97.6%

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

   3. Taylor expanded in x around inf 78.0%

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

   if -3.8999999999999999e149 < (*.f64 x y) < -1.4999999999999999e-289 or 3.1999999999999999e-93 < (*.f64 x y) < 2.14999999999999996e69

   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 z around inf 65.0%

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

      1. associate-*r* 65.0%

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

      2. *-commutative 65.0%

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

      3. associate-*r* 65.0%

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

   5. Simplified 65.0%

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

   if -1.4999999999999999e-289 < (*.f64 x y) < 3.1999999999999999e-93

   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 inf 74.1%

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

      1. *-commutative 74.1%

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

      2. associate-*l* 74.1%

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

   5. Simplified 74.1%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.9 \cdot 10^{+149}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.5 \cdot 10^{-289}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-93}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.15 \cdot 10^{+69}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := \left(b \cdot a\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+26}:\\ \;\;\;\;c + \left(x \cdot y + t\_1\right)\\ \mathbf{elif}\;x \cdot y \leq 7.2 \cdot 10^{+68}:\\ \;\;\;\;\left(c + t\_1\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (* (* b a) 0.25)))
   (if (<= (* x y) -2.8e+26)
     (+ c (+ (* x y) t_1))
     (if (<= (* x y) 7.2e+68) (- (+ c t_1) t_2) (- (+ 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 = (b * a) * 0.25;
	double tmp;
	if ((x * y) <= -2.8e+26) {
		tmp = c + ((x * y) + t_1);
	} else if ((x * y) <= 7.2e+68) {
		tmp = (c + t_1) - t_2;
	} 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 = (b * a) * 0.25d0
    if ((x * y) <= (-2.8d+26)) then
        tmp = c + ((x * y) + t_1)
    else if ((x * y) <= 7.2d+68) then
        tmp = (c + t_1) - t_2
    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 = (b * a) * 0.25;
	double tmp;
	if ((x * y) <= -2.8e+26) {
		tmp = c + ((x * y) + t_1);
	} else if ((x * y) <= 7.2e+68) {
		tmp = (c + t_1) - t_2;
	} 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 = (b * a) * 0.25
	tmp = 0
	if (x * y) <= -2.8e+26:
		tmp = c + ((x * y) + t_1)
	elif (x * y) <= 7.2e+68:
		tmp = (c + t_1) - t_2
	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(b * a) * 0.25)
	tmp = 0.0
	if (Float64(x * y) <= -2.8e+26)
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	elseif (Float64(x * y) <= 7.2e+68)
		tmp = Float64(Float64(c + t_1) - t_2);
	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 = (b * a) * 0.25;
	tmp = 0.0;
	if ((x * y) <= -2.8e+26)
		tmp = c + ((x * y) + t_1);
	elseif ((x * y) <= 7.2e+68)
		tmp = (c + t_1) - t_2;
	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[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.8e+26], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7.2e+68], N[(N[(c + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.8e26

   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 a around 0 90.2%

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

   if -2.8e26 < (*.f64 x y) < 7.1999999999999998e68

   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 x around 0 95.6%

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

   if 7.1999999999999998e68 < (*.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 z around 0 90.1%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+26}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 7.2 \cdot 10^{+68}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+93} \lor \neg \left(b \cdot a \leq 10^{+149}\right):\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -5e+93) (not (<= (* b a) 1e+149)))
   (- (* x y) (* (* 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 (((b * a) <= -5e+93) || !((b * a) <= 1e+149)) {
		tmp = (x * y) - ((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 (((b * a) <= (-5d+93)) .or. (.not. ((b * a) <= 1d+149))) then
        tmp = (x * y) - ((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 (((b * a) <= -5e+93) || !((b * a) <= 1e+149)) {
		tmp = (x * y) - ((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 ((b * a) <= -5e+93) or not ((b * a) <= 1e+149):
		tmp = (x * y) - ((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(b * a) <= -5e+93) || !(Float64(b * a) <= 1e+149))
		tmp = Float64(Float64(x * y) - Float64(Float64(b * 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 (((b * a) <= -5e+93) || ~(((b * a) <= 1e+149)))
		tmp = (x * y) - ((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[(b * a), $MachinePrecision], -5e+93], N[Not[LessEqual[N[(b * a), $MachinePrecision], 1e+149]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - N[(N[(b * a), $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) < -5.0000000000000001e93 or 1.00000000000000005e149 < (*.f64 a b)

   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 89.4%

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

   4. Taylor expanded in c around 0 84.5%

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

   if -5.0000000000000001e93 < (*.f64 a b) < 1.00000000000000005e149

   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 91.0%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+93} \lor \neg \left(b \cdot a \leq 10^{+149}\right):\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+93} \lor \neg \left(b \cdot a \leq 10^{-44}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -5e+93) (not (<= (* b a) 1e-44)))
   (- (+ c (* x y)) (* (* 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 (((b * a) <= -5e+93) || !((b * a) <= 1e-44)) {
		tmp = (c + (x * y)) - ((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 (((b * a) <= (-5d+93)) .or. (.not. ((b * a) <= 1d-44))) then
        tmp = (c + (x * y)) - ((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 (((b * a) <= -5e+93) || !((b * a) <= 1e-44)) {
		tmp = (c + (x * y)) - ((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 ((b * a) <= -5e+93) or not ((b * a) <= 1e-44):
		tmp = (c + (x * y)) - ((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(b * a) <= -5e+93) || !(Float64(b * a) <= 1e-44))
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(b * 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 (((b * a) <= -5e+93) || ~(((b * a) <= 1e-44)))
		tmp = (c + (x * y)) - ((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[(b * a), $MachinePrecision], -5e+93], N[Not[LessEqual[N[(b * a), $MachinePrecision], 1e-44]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $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) < -5.0000000000000001e93 or 9.99999999999999953e-45 < (*.f64 a b)

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0 87.8%

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

   if -5.0000000000000001e93 < (*.f64 a b) < 9.99999999999999953e-45

   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 96.1%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+93} \lor \neg \left(b \cdot a \leq 10^{-44}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.6 \cdot 10^{+26} \lor \neg \left(x \cdot y \leq 1.25 \cdot 10^{+68}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -6.6e+26) (not (<= (* x y) 1.25e+68)))
   (+ c (* x y))
   (+ c (* a (* b -0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -6.6e+26) || !((x * y) <= 1.25e+68)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-6.6d+26)) .or. (.not. ((x * y) <= 1.25d+68))) then
        tmp = c + (x * y)
    else
        tmp = c + (a * (b * (-0.25d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -6.6e+26) || !((x * y) <= 1.25e+68)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -6.6e+26) or not ((x * y) <= 1.25e+68):
		tmp = c + (x * y)
	else:
		tmp = c + (a * (b * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -6.6e+26) || !(Float64(x * y) <= 1.25e+68))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -6.6e+26) || ~(((x * y) <= 1.25e+68)))
		tmp = c + (x * y);
	else
		tmp = c + (a * (b * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -6.6e+26], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.25e+68]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -6.59999999999999987e26 or 1.2500000000000001e68 < (*.f64 x y)

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf 71.6%

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

   if -6.59999999999999987e26 < (*.f64 x y) < 1.2500000000000001e68

   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 inf 63.6%

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

      1. *-commutative 63.6%

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

      2. associate-*l* 63.6%

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

   5. Simplified 63.6%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.6 \cdot 10^{+26} \lor \neg \left(x \cdot y \leq 1.25 \cdot 10^{+68}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7000000000 \lor \neg \left(x \cdot y \leq 2.05 \cdot 10^{+71}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -7000000000.0) (not (<= (* x y) 2.05e+71))) (* 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) <= -7000000000.0) || !((x * y) <= 2.05e+71)) {
		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) <= (-7000000000.0d0)) .or. (.not. ((x * y) <= 2.05d+71))) 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) <= -7000000000.0) || !((x * y) <= 2.05e+71)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -7000000000.0) or not ((x * y) <= 2.05e+71):
		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) <= -7000000000.0) || !(Float64(x * y) <= 2.05e+71))
		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) <= -7000000000.0) || ~(((x * y) <= 2.05e+71)))
		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], -7000000000.0], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.05e+71]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -7e9 or 2.0500000000000001e71 < (*.f64 x y)

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0 86.2%

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

      1. fma-neg 86.3%

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

      2. distribute-lft-neg-in 86.3%

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

      3. metadata-eval 86.3%

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

      4. *-commutative 86.3%

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

      5. associate-*l* 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in x around inf 62.6%

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

   if -7e9 < (*.f64 x y) < 2.0500000000000001e71

   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 28.7%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7000000000 \lor \neg \left(x \cdot y \leq 2.05 \cdot 10^{+71}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

Python

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

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = c + (((x * y) + ((z * t) / 16.0)) - ((b * a) / 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[(b * a), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.8%

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

3. Final simplification 98.8%

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

Alternative 13: 55.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+164} \lor \neg \left(a \leq 2 \cdot 10^{+33}\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -4.5e+164) (not (<= a 2e+33))) (* a (* b -0.25)) (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -4.5e+164) || !(a <= 2e+33)) {
		tmp = a * (b * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a <= (-4.5d+164)) .or. (.not. (a <= 2d+33))) then
        tmp = a * (b * (-0.25d0))
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -4.5e+164) || !(a <= 2e+33)) {
		tmp = a * (b * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -4.5e+164) or not (a <= 2e+33):
		tmp = a * (b * -0.25)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -4.5e+164) || !(a <= 2e+33))
		tmp = Float64(a * Float64(b * -0.25));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -4.5e+164) || ~((a <= 2e+33)))
		tmp = a * (b * -0.25);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -4.5e+164], N[Not[LessEqual[a, 2e+33]], $MachinePrecision]], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.49999999999999975e164 or 1.9999999999999999e33 < a

   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. Taylor expanded in z around 0 78.7%

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

      1. fma-neg 78.7%

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

      2. distribute-lft-neg-in 78.7%

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

      3. metadata-eval 78.7%

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

      4. *-commutative 78.7%

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

      5. associate-*l* 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in a around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. associate-*r* 50.1%

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

      3. *-commutative 50.1%

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

   8. Simplified 50.1%

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

   if -4.49999999999999975e164 < a < 1.9999999999999999e33

   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 x around inf 57.1%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+164} \lor \neg \left(a \leq 2 \cdot 10^{+33}\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 22.6% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Taylor expanded in c around inf 21.1%

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

4. Final simplification 21.1%

   \[\leadsto c \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024034 
(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))